MULTI - OBJECTIVE EVOLUTIONARY OPTIMIZATION IN GREENHOUSE CONTROL FOR IMPROVED CROP YIELD AND ENERGY TRADEOFFS By José R. Llera Ortiz A DISSERTATION Submitted to Michigan State University i n partial fulfillment of the requirements f or the degree of Electric al Engineering Doctor of Philosophy 2020 ABSTRACT MULTI - OBJECTIVE EVOLUTIONARY OPTIMIZATION IN GREENHOUSE CONTROL FOR IMPROVED CROP YIELD AND ENERGY TRADEOFFS By José R. Llera Ortiz T he worldwide increase in demand for fresh fruits and vegetables has led t o a search for strategies to manage greenhouses in ways that not only meet this demand, but that are also economically viable and environmentally sus tainable. A well - established approach for managing greenhouse microclimate is through the automatic control of its mechan ical systems such as heaters, ventilators, and shade screens. Such a system is a form of closed - loop control, but only with respect to the greenhouse microclimate, rather than the crop being grown. In practice, conventional greenhouse control is criticized for this focus on climate control instead of crop production, as well as the complexity of managing these systems due to an excessive number of user settings [1] . A more comprehensive form of c losed - loop optimal control in greenhouses has been proposed to p rovide a better degree of control by adjus ting the greenhouse climate in response to the growth of the crop being cultivate d, but it is still dependent on the external climate around the greenhouse and can lack accepta ble alternatives due to the non linear nature of the interactions between environ mental conditions and plant growth. Unfortunately, monitorin g of the real - time response of the crop is not viable for this type of closed - loop control what can be used instead is a rather sophisticated state model of crop production so that the microclim ate conditions can be controlled in order to optimize their effects on the predicted seasonal crop production. Further, this model and the greenhouse microclimate model into which it is integrated must be executable in a short enough timeframe to allow run ning it thousands of times to optimize the performance of th e controller for a given greenhouse structure and location. Having developed such a model, w e propose using a form of evoluti onary multi - objective optimiza tion to discover a suite of user - selectab le c ontrol strategies that balance crop productivity with th e financial costs of greenhouse climate control. Each of the Pareto - optimal controllers discovered by this approach defines a range of conditions to be maintained via specified control actions, de pending upon the crop state and externa l environmental conditions. Due to the large number of candidates present as the output, the decision - making process will be aided by considering common user preferences as well as algorithmically examining the robust ness of solutions in the final Pareto - o ptimal frontier. iii ACKNOWLEDGMENTS I would like to thank Prof. Percy Pierre for his financial support and guidance through the Sloan Engineering Program , as well as his heartfelt efforts to see my degree to its compl e tion even after ret irement. The international collaboration between Prof. Lihong Xu , his graduate students, and the BEACON Center at MSU was invaluable for the completion of this dissertation. Dr. Chenwen Zhu and Dr. Prakarn Unachak he lped build the found a tions for th e simul ation software used in this dissertation , and this research would not have been as fruitful without their efforts . Prof. Erik S. extensive knowledge on growing plants in controlled environments was invaluable in steering our re s earch in the right direction tool for producing useful and innovative design principles inspired the methodology for interpreting the results in this dissertation. Prof. Nelson Sepúlve d r t, gu idance , and contagious optimism was invaluable during the last stages of my Ph.D. program . mentorship, financial support , and above all confidence in my abilities throughout these years was indispe n sable, especially i n times where I would doubt my own abilities . I will always be grateful for being provided a unique opportunity to take on this complex, multidisciplinary engineering problem by using some of the fascinating techniques developed in the f ield of evolutionary computation. iv T ABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ ........................ vii LIST OF FIGURES ................................ ................................ ................................ ....................... ix 1 Introduction ................................ ................................ ................................ ............................. 1 1.1 Objectives and Scope ................................ ................................ ................................ ....... 1 1.2 Introduction ................................ ................................ ................................ ...................... 1 1.3 Control Strategy Optimization Methodology ................................ ................................ ... 5 2 Literature Review ................................ ................................ ................................ .................... 7 3 Modification of a Classical Greenhouse Control Mo del for Evolutionary Optimization ..... 15 3.1 Individual Control Strategies ................................ ................................ ......................... 17 3.2 Objective Functions ................................ ................................ ................................ ........ 19 3.3 Gr eenhouse Model ................................ ................................ ................................ ......... 21 3.4 Meteorological Data Acquisition and Configuration ................................ ..................... 22 3.5 Description of Early Evolved Results ................................ ................................ ............ 23 3.6 Result Comparison ................................ ................................ ................................ ......... 24 3.7 Control Strategy Selection ................................ ................................ ............................. 25 3.8 Discussion ................................ ................................ ................................ ...................... 26 4 Evolution of a Classical Controller Using Improved Model ................................ ................. 29 4.1 Combined Model Overview ................................ ................................ ........................... 29 4.1.1 Microclimate - Crop Yield Model ................................ ................................ ................ 29 4.1.2 Economic Model ................................ ................................ ................................ ......... 30 4.1.3 Greenhouse Design and Control ................................ ................................ ................. 31 4.2 Model Validation Results ................................ ................................ ............................... 32 4.3 Greenhouse Simulation and Evolution Setup ................................ ................................ . 34 4.3.1 Greenh ouse Design ................................ ................................ ................................ ..... 34 4.3.2 Outdoor Climate Data ................................ ................................ ................................ . 34 4.3.3 Control Strategy Implementation ................................ ................................ ............... 35 4.3.4 NSGA - II Initialization ................................ ................................ ................................ 35 4.3.5 Chromosome Representat ion ................................ ................................ ...................... 36 4.3.6 Fitness Function ................................ ................................ ................................ .......... 3 7 4.3.7 Post - Pareto Front Processing ................................ ................................ ...................... 37 4.4 Pareto Front, Validation Step and Sorting ................................ ................................ ..... 37 4.4.1 Pareto Front ................................ ................................ ................................ ................ 37 4.4.2 Validation Step ................................ ................................ ................................ ........... 38 4.4.3 Sorting Results ................................ ................................ ................................ ............ 39 4.4.4 Decision Making ................................ ................................ ................................ ......... 40 4.5 Discussion ................................ ................................ ................................ ...................... 42 5 Using Multi - objective Optimization to Ev olve More Sophisticated Controllers .................. 44 v 5.1 Problem Formulation ................................ ................................ ................................ ...... 44 5.2 Methodology and Results ................................ ................................ ............................... 47 5 .3 Decision Making ................................ ................................ ................................ ............ 51 5.4 Performance of the Time - Partitioning Feature ................................ ............................... 55 5.5 Discussion ................................ ................................ ................................ ...................... 57 6 Analyzing Genotypes of Evolved Controllers ................................ ................................ ....... 59 6.1 Introdu ction ................................ ................................ ................................ .................... 59 6.2 Evolved Classical Controller (No Time Partitioning) ................................ .................... 62 6.2.1 Introduction ................................ ................................ ................................ ................ 62 6.2.2 T AirVentOn ................................ ................................ ................................ ...................... 65 6.2.3 T AirVentOff ................................ ................................ ................................ ..................... 66 6.2.4 RH AirVentOn ................................ ................................ ................................ ................... 67 6.2.5 CO 2AirVentOn ................................ ................................ ................................ ................. 68 6.2.6 T AirBoilOn ................................ ................................ ................................ ...................... 69 6.2.7 T OutThScrOn ................................ ................................ ................................ .................... 70 6.2.8 CO 2AirExtMax ................................ ................................ ................................ ................. 71 6.2.9 CO 2AirExtMin ................................ ................................ ................................ .................. 72 6.2.10 I GlobMax ................................ ................................ ................................ ......................... 73 6.2.11 Discussion ................................ ................................ ................................ ................... 73 6.3 Evolved Classical Controller (Added Time Partitioning) ................................ .............. 75 6.3.1 Introduction ................................ ................................ ................................ ................ 75 6.3.2 T AirVentOn ................................ ................................ ................................ ...................... 79 6.3.3 T AirVentOff ................................ ................................ ................................ ..................... 80 6.3.4 RH AirVentOn ................................ ................................ ................................ ................... 81 6.3.5 CO 2AirVentOn ................................ ................................ ................................ ................. 83 6.3.6 T AirBoilOn ................................ ................................ ................................ ...................... 84 6.3.7 T OutThScrOn ................................ ................................ ................................ .................... 85 6.3.8 CO 2AirExtMax ................................ ................................ ................................ ................. 86 6.3.9 CO 2AirExtMin ................................ ................................ ................................ .................. 87 6.3 .10 I GlobMax ................................ ................................ ................................ ......................... 88 6.3.11 Discussion ................................ ................................ ................................ ................... 89 6.4 Evolved Controller (Additional Featu res) ................................ ................................ ...... 90 6.4.1 Introduction ................................ ................................ ................................ ................ 90 6.4.2 T AirVentOn ................................ ................................ ................................ ...................... 95 6.4.3 T AirVentOff ................................ ................................ ................................ ..................... 97 6.4.4 RH AirVentOn ................................ ................................ ................................ ................... 98 6.4.5 CO 2Air VentOn ................................ ................................ ................................ ................. 99 6.4.6 T AirBoilOn ................................ ................................ ................................ .................... 100 6.4.7 T OutThScrOn ................................ ................................ ................................ .................. 102 6.4.8 CO 2AirExtMax ................................ ................................ ................................ ............... 103 6.4.9 CO 2AirExtMin ................................ ................................ ................................ ................ 104 6.4.10 I GlobMax ................................ ................................ ................................ ....................... 105 6.4.1 1 Sunrise and Sunset Offsets (sr_offset, ss_offset) ................................ ..................... 107 6.4.12 Discussion ................................ ................................ ................................ ................. 108 6.5 Improved Controller without Penalty for Inadequate Relative Humidity .................... 109 6.5.1 Introduction ................................ ................................ ................................ .............. 109 vi 6.5.2 T AirVentOn ................................ ................................ ................................ .................... 113 6.5.3 T AirVentOff ................................ ................................ ................................ ................... 115 6.5.4 T AirBoilOn ................................ ................................ ................................ .................... 116 6.5.5 T OutTh ScrOn ................................ ................................ ................................ .................. 117 6.5.6 PID Boiler ................................ ................................ ................................ ..................... 118 6.5.7 PID Fog ................................ ................................ ................................ ........................ 119 6.5.8 PID Vent ................................ ................................ ................................ ....................... 121 6.5.9 Sunrise and Sunset Offsets (sr_offset, ss_offset) ................................ ..................... 122 6 .5.10 CO 2AirExtMax ................................ ................................ ................................ ............... 123 6.5.11 CO 2AirExtMin ................................ ................................ ................................ ................ 124 6.5.12 I GlobMax ................................ ................................ ................................ ....................... 125 6.5.13 Discussion ................................ ................................ ................................ ................. 126 6.6 Same Improved Controller with Penalty for Inadequate Relative Humidity ............... 127 6.6.1 Introduction ................................ ................................ ................................ .............. 127 6.6.2 T AirVentOn and T AirVentOff ................................ ................................ ............................. 128 6.6.3 T AirBoilOn ................................ ................................ ................................ .................... 135 6.6.4 T OutThScrOn ................................ ................................ ................................ .................. 136 6.6.5 PID Boiler ................................ ................................ ................................ ..................... 137 6.6.6 PID Fog ................................ ................................ ................................ ........................ 139 6.6.7 PID Vent ................................ ................................ ................................ ....................... 140 6.6.8 Sunrise and Sunset Offsets (sr_offset, ss_offset) ................................ ..................... 142 6.6.9 CO 2AirExtMax ................................ ................................ ................................ ............... 143 6.6.10 CO 2AirExtMin ................................ ................................ ................................ ................ 144 6.6.11 I GlobMax ................................ ................................ ................................ ....................... 145 6.6.12 Discussion ................................ ................................ ................................ ................. 145 6.7 Conclusions ................................ ................................ ................................ .................. 146 7 Metrics fo r Decision Making ................................ ................................ ............................... 150 7.1 Introduction ................................ ................................ ................................ .................. 150 7.2 Net Financial Result (NFR) ................................ ................................ .......................... 151 7.3 Normalized Hypervolume Between Controller Types ................................ ................. 153 7.4 Robustness Against Unknown Weather Data ................................ .............................. 155 7.5 Robustness Against Genotype Perturbations ................................ ............................... 156 8 Summary and Conclusions ................................ ................................ ................................ .. 160 LITERATURE CITED ................................ ................................ ................................ ............... 164 vii LIST OF TABLES Table 3.1. Capacities and coefficients for the major greenhouse desig n elements as so ciated with active climate management. Transmission and reflection coefficients for near infrared (NIR), far infrared (FIR), and photosynthetically active rad iation (PAR) of the inter nal shading screen, external shading screen, and thermal s creen are inc lu ded. ................................ ........................... 21 Table 4.1. Capacities for the major greenhouse desig n elements associated with active cl imate management. ................................ ................................ ................................ ................................ . 31 Table 4.2. Av er age outdoor climate values provided by a) Vanthoor [4], compa red with b) the estimated weather for the same site used in this thesis. ................................ ................................ 32 Table 4.3. Simulation com parison results b etween a) Van th oor [25], compared with b) our simulated results for the 2006 - 2007 season. ................................ ................................ ............... 33 Table 4.4. NSGA - II p arameters used for this study. ................................ ................................ ..... 35 Table 4.5. Chromosome representation. Values in this range are stored as integers after multiplica tion with an appropriate factor. ................................ ................................ ..................... 36 Table 4.6. Greenhouse simulation parameters used for evo lv ing setpoints in Almería, Spain case s (F) and a CO 2 enrichment sy stem (C). ................................ ................................ .......................... 37 Table 4. 7. Economic m od - 2 ×year - 1 - - results (NFR) for all four years are added up. ................................ ................................ .............. 39 Table 4.8. Worst - - 2 ×year - 1 ) of the nine best evolved solutions (in terms of NFR) in optimization runs with different p opulation sizes. ................................ ........... 39 Ta - h - ................................ ................................ ............................ 40 Table 5.1. Chromosome representation. Values in this range a re stored as integers after multiplying by an appr opriate factor. ................................ ................................ ............................ 46 - 2 ×year - 1 ), comparing the original setpoints financial results (NFR) for all four years are added up. ................................ ............................... 51 Table 5.3. Worst - - 2 ×year - 1 ) of the top eight evolved solutions (sorted by decreasing NFR), of a) the evolved controller and b) the evolved controller with time partitioning. ................................ ................................ ................................ ................................ ... 51 viii Table 5.4. Original setpoints compared with setpoints of two evolved solutions: a low - cost solution and a high - yield solution. ................................ ................................ ................................ 52 Table 5.5 . Mann - Whitney U test results comparing groups of hypervolumes, where a) is the non - time - partitioned controller, while b) uses time - partitioning. ................................ ........................ 57 Table 6.1. General controller implementation and ODE solver details. These values are shared among all controllers described in this chapter unless otherwise specified. ................................ . 60 Table 6.2. Chromosome containing the setpoints used in the evolved classical controller. The genotype consists of 9 integer values. ................................ ................................ ........................... 64 Table 6.3. Chromosome containi ng the setpoints used in the evolved classical controller with setpoint partitioning based on ti me of day. The genotype consists of 27 integer values. ............. 77 Table 6.4. Different times of day as defined in the greenhouse controller logic in this section. If the greenhouse controller detects ni ghttime due to lack of global radiation (i.e., I Glob = 0), either morning or evening setpoints wil l be used (depending on the current time). ............................... 78 Table 6.5. Chromosome containing the setpoints use d in the evolved classical controlle r, with additional features. The total size of the genotype consists of 58 integer values. ........................ 94 Table 6.6. Chromosome containing the s etpoints used in this cont roller, with additional features. The total size of the genotype consists of 54 integer values. ................................ ...................... 112 Table 7.1. Economic model output for the four main greenhouse controller types described in th is thesis. ................................ ................................ ................................ ................................ .... 151 Table 7.2. Example of ec onomic model output (euros × m - 2 × year - 1 ), comparing the classical Vanthoor strategy with the same strategy with evolved setpoints. Weather data for the 2009 2010 season was only used to evaluate control strategies after the optimization step was completed. The fogging system is assumed to have no restrictions in this example to illustrate how some weather seasons can be economically unviable (due to negative NFR), but still have an overall positive result if multiple weather seasons are considered. ................................ ....... 155 Table 7.3. Partial list of evolved solutions sorted by increasing convex hull area. .................... 158 ix LIST OF FIGURES Figure 1.1. Detailed illustration of the proposed method for optimizing greenhouse control strategies: NSGA - II, a multi - objective problem solver (a), components of the fitness function (b), and a resulting Pareto set of control strategies (c). ................................ ................................ ......... 4 horizontal axes o n the left and right represent instantaneous c anopy temperature and 24 - hour mean temperature, respectively. The solid lines represent a non - differentiable implementation of the functions, while the dotted lines represent a differentiable version of the fun ctions. The values h Tcan and h TCan24 are used as scaling factors that limit the flow of carbohydrates into the tomato crop. ................................ ................................ ................................ ................................ .... 4 l - based greenhou se design method [4], the optimization step, which was previously aimed towards greenhouse design optimization with a single objective (net financial result), is replaced with a multi - objective optimization step that considers crop yield va lue and variable costs. Inputs such as the canopy temperature (T Can ), greenhouse air CO 2 concentration (CO 2Air ), photosynthetically active radiation flux density (R PAR ), greenhouse air temperature (T Air ), and the vapor pressure of the greenhouse air (VP Air ) are used in th e tomato yield model to obtain the final yield. ................................ ........................ 12 Figure 3.1. Potential design elements used to manage the greenhous e climate. The colored arrows represent the various mass and energy fluxes wh ... 17 Figure 3.2. Example of an implementation of the proposed interval controller, for some arbitrary time of day. Instead of strictly following temperature s etpoints, it allows for a range of temperatures in which some control actions (or none) may be taken as long as the temperature stays within a certain range. ................................ ................................ ................................ .......... 19 Figure 3.3. Summary of the monthl y mean values for the outside air temperature (T Out ), global radiation (I Glob ), and outside vapor pressure (VP Out ) for the 2007 2012 years in the Shanghai region. An ambient CO 2 concentration of 340 ppm was assumed. ................................ .............. 23 Figure 3.4. Yearly resource cost and crop yield for three independent Pareto - optimal sets on validation weather data (hollow points). Objective values for a classical setpoint controller on the same weather data (solid p oints). A ccumulated boiler and shade screen usage for an evolved strategy compared to the setpoint controller (a). ................................ ................................ ........... 25 Figure 3.5. Th e image on the left portrays the effect of changing x in a single - objec tive problem. The image on the right shows the effect of changing x1, x2 and x3 in a two - objective problem. [35] ................................ ................................ ................................ ................................ ................ 27 Figure 4.1. Vanthoor predicted tomato yield vs our predicted yield as a functi on of greenhouse technology level. ................................ ................................ ................................ ........................... 34 x Figure 4.2. Pareto front consisting of the evolved control setpoints compared against the original control setpoints. The worst - case net financial result of the original setpoint and t wo evolved setpoints is shown. ................................ ................................ ................................ ........................ 38 Figure 4.3. High - yield solution control signals over a 24 - hour period. ................................ ........ 40 Figure 4.4. High - yield solution microclimate over a 24 - hour period. T_Out denotes the outside air temperature, T_Air denotes the greenhouse air temperature, CO 2 _Air denotes the CO 2 concentration of the greenhouse air and C_Ref denotes the current value of the dynamic CO 2 setpoint. ................................ ................................ ................................ ................................ ......... 41 Figu re 4.5. Low - cost solution control signals over a 24 - hour period. ................................ .......... 41 Figure 4.6. Low - cost soluti on microclimate over a 24 - hour period. T_Out denotes the outside air temperature, T_Air denotes the greenhouse air temperature, CO 2 _Air denotes the CO 2 concentration of the greenhouse air and C_Ref denotes the current value of the dynamic C O 2 setpoint. ................................ ................................ ................................ ................................ ......... 42 Figure 5.1. Introducing time partitioning to a greenhouse control strategy. ................................ . 47 Figure 5.2. Overlapped Pareto fronts consisting of th e evolved control setpoints (NTP, red) and the evolved control setpoints with time partitioning (TP, green) compared against classical control setpoints (blue). ................................ ................................ ................................ ................ 49 Figure 5.3. Example of control setpoints with time partitioning (TP, green) benefiting from seeding with evolved setpoints without time partitioning (NTP, red). The green lower right ................................ 50 Figure 5.4. High - yield - solution control signals in a 24 - hour period. ................................ ........... 52 Figure 5.5. High - yield - solution microclimate over an example 24 - hour period. T_Out i s outside air temperature, T_Air is greenhouse air temperature, CO 2 _Air is CO 2 concentration of gree nhouse air and C_Ref is current value of the dynamic CO 2 setpoint. ................................ .... 53 Figure 5.6. Low - cost - sol ution control signals in a 24 - hour per iod. ................................ .............. 53 Figure 5.7. Low - cost - solution microclimate over an example 24 - hour period. T_Out is outside air temperature, T_Air is greenh ouse air temperature, CO 2 _Air is CO 2 concentration of greenhouse air and C_Ref is current value of the dynamic CO 2 setpoint. ................................ .... 54 Figu re 5.8. Normalized hypervolume for the evolved, non - time - partitioned controller (red), and the evolved, time - partitioned controller (green). ................................ ................................ .......... 54 Figure 6.1. Pareto - optimal fronts for the evolved control strategies in this chapter, with a classical strategy using def ault setpoints for reference. Red circles represent the classical strategy with evolved setpoints (NTP). Green circles represent the classical strategy with setpoint partitioning based on time (TP). Blue circles represent a similar strategy that adds setpo int partitionin g based on both time and plant development stage, but also uses sunrise and sunset xi calculations to transition between nighttime and daytime strategies (TP+). Purple setpoints represent a control strategy with all the previous features, addit ional control l ogic, additional nighttime setpoints, and PID control for fogging, heating, and ventilation systems (TP++). ...... 61 Figure 6.2. Pareto - optimal front for the control strategy discussed in this section . Solutions from this Pareto front which also dominate the classical Vanthoor strategy are marked in green. ....... 62 Figure 6.3. Classical control strategy example. Based on the current greenhouse air temperature, the controller will take different actions to maintain an optimal temperature range for the crop, as in fluenced also by CO 2 concentration and relative humidity in the greenhouse. [4] ................... 63 Figure 6.4. This setpoint determines the temperatu re above which the greenhouse controller will keep the ventilation open. ................................ ................................ ................................ ............. 65 Figure 6.5. This setpoint d etermines the temperature below whi ch the ventilation will always remain closed. ................................ ................................ ................................ ............................... 66 Figure 6.6. This setpoint determines the relativ e humidity above which ventilation is conditionally turned on. ................................ ................................ ................................ ................ 67 Figure 6.7. This setpoint determines the greenhouse air CO 2 concen tration below which ventilation is conditionally turned on. ................................ ................................ .......................... 68 Figure 6.8. This setpoint determin es the temperature below which the g reenhouse controller will turn on the boiler heating. ................................ ................................ ................................ ............. 69 Figure 6.9. This setpoint determines the outside temperature below which the greenhouse controller wi ll deploy the thermal screen. ................................ ................................ ..................... 70 Figure 6.10. This variable determines the upper bound for the dynamic CO 2 setpoint used during CO 2 injection. ................................ ................................ ................................ ................................ 71 Figure 6.11. This variable determines the lower bound for th e dynamic CO 2 setpoint used during CO 2 injection. ................................ ................................ ................................ ................................ 72 Figure 6.12. This variable determines how quickly is maximized, and subsequently contributes to how quickly the dynamic CO 2 setpoint (CO 2AirExtOn ) is maximized. ..................... 73 Figure 6.13. Pareto - optimal front fo r the control strategy discusse d in this section. Solutions from this Pareto front which also dominate the classical Vanthoor strategy are marked in green. ....... 75 Figure 6.14. This setpoint determines the temperature above which the greenhouse controller will keep the ventilation open. ................................ ................................ ................................ ............. 78 Figure 6.15. This setpoint determines the temperature below which the ventilation will always remain closed. ................................ ................................ ................................ ............................... 80 xii Figure 6.16. This setpoint determines the relative humidity above which ventilation is conditionally turned on. ................................ ................................ ................................ ................ 81 Figure 6.17. This setpoint det ermines the greenhouse air CO 2 concentration below which ventilation is conditionally turned on. ................................ ................................ .......................... 82 Figure 6.18. This setpoint deter mines the temperature below which the greenhouse controller will turn on the boiler heating. ................................ ................................ ................................ ...... 83 Figure 6.19 . This setpoint determines the outside temperature below which the greenhouse controller will deploy the thermal screen. ................................ ................................ ..................... 85 Figure 6 .20. This variable determines the upper bound for the dynamic CO 2 setpoint used during CO 2 injection. ................................ ................................ ................................ ................................ 86 Figure 6.21. This variable d etermines the lower boun d for the dynamic CO 2 setpoint used during CO 2 injection. ................................ ................................ ................................ ................................ 87 Figure 6.22. This variable determines how quickl y is maximized, and subsequently contributes to how quickly the dynamic CO 2 setpoint is maximized. ................................ .......... 88 Figure 6.23. Pareto - optimal front for the control strategy discussed in this section. Solutions from this Pareto front which also dominate the classical Vanthoor st rategy are marked in green. ....... 91 Figure 6.24. The greenhouse controller differentiates between daytime and nighttime to determine whether the thermal screen should be deployed, which is only used during nighttime. Both sr_offset and ss_off set are evolved values which will modify the overall length of both nighttime and daytime control strategies. These offsets remain fixed for each control strategy, while sunrise and sunset times (shaded region) ch ange over the course of the year. ................... 92 Figure 6.25. Sunrise/sunset times and average outside air temperatures calculated for the Almería, Spain location in 2006. ................................ ................................ ................................ .. 92 Figure 6.26. Flowchart describing the process for determining whether daytime or nighttime strategies are used. ................................ ................................ ................................ ........................ 93 Figure 6.27. This setpoint determines the temper ature above which the greenhouse controller will keep the ventilation open. ................................ ................................ ................................ ............. 95 Figure 6.28 . This setpoint determines the temperature below which the ventilation will always remain closed. ................................ ................................ ................................ ............................... 96 Figure 6.29. This setpoint deter mines the relative humidity above which ventilation is conditionally turned on. ................................ ................................ ................................ ................ 98 Figure 6.30. This s e tpoint determines the greenhou se air CO 2 concentration below which ventilation is conditionally turned on. ................................ ................................ .......................... 99 xiii Figure 6.31. This setpoint determines the temperatur e below which the greenhouse c on troller will turn on the boiler heating. ................................ ................................ ................................ .... 100 Figure 6.32 . This setpoint determines the outside temperature below which the greenhouse controller will deploy the thermal screen. ................................ ................................ ................... 101 Figure 6 .33. This variable determines the upper bound for the dynamic CO 2 setpoint used during CO 2 injection. ................................ ................................ ................................ .............................. 103 Figure 6.34. This variable d e te rmines the lower bound for the dynamic CO 2 setpoint used during CO 2 injection. ................................ ................................ ................................ .............................. 104 Figure 6.35. This variable determines how quickl y is maximized, and subsequently contributes to ho w quickly the dynamic CO 2 setpoint is maximized. ................................ ........ 105 Figure 6.36. The c opies of sr_offset and ss_offset are used to subtract from the current calculated time for sunrise and sunset, respective ly . ................................ ................................ ................... 106 Figure 6.37. Pareto - optimal front for the control strategy discussed in this section. Solutions from this Pareto front which also dominate the classical Vanthoor strategy are marked in g re en. ..... 110 Figure 6.38. Simple flowchart describing the handling of the special case of T AirVentOff > T AirVentOn . ................................ ................................ ................................ ................................ ..... 111 Figure 6.39. Th is setpoint determines the temperature above which the greenhouse controller will keep the ventilation open. ................................ ................................ ................................ ........... 113 Figure 6.40. This setpoint determines the temperature below which the ventilation w ill always remain closed. ................................ ................................ ................................ ............................. 114 Figure 6.41. This setpoint determines the temperature below which the greenhouse controller will turn on the boiler heating. ................................ ................................ ................................ .... 116 Figure 6.42. This setpoint determines the outside temperature below which the greenhouse controller will deploy the thermal screen. ................................ ................................ ................... 117 Figure 6.43. PID gain paramet er s for boiler heating control. ................................ ..................... 118 Figure 6.44. PID gain parameters for fogging system control. ................................ ................... 119 Figure 6.45 . PID gain parameter s for greenhouse ventilation control. ................................ ....... 121 Figure 6.46 . The copies of sr_offset and ss_offset are used to subtract from the current calculated time for sunrise and sunset, respectively. ................................ ................................ ................... 122 Figure 6.47. This variable determines the upper bound for the dynamic CO 2 setpoint used during CO 2 injection. ................................ ................................ ................................ .............................. 123 xiv Figure 6.48. This varia bl e determines the lower bound for the dynamic CO 2 setpoint used during CO 2 injection. ................................ ................................ ................................ .............................. 124 Figure 6.49. This variable determines how quickly is maximized, and subsequently contributes to how quickly the dynamic CO 2 setpoint is maximized. ................................ ........ 125 Figure 6.50. Pareto - optimal front for the control strategy discussed in this sec tion. Solutions from this Pareto front which also dominate the classical Vanthoor strategy are marked in green. ..... 128 Figure 6.51. Evolved nighttime setpoints for T AirVentOn and T AirVentOff . The e ffects of adding a crop value penalty on the resulting evolved setpoints are examined (right) and compared with the same s etpoints without the crop value penalty (left). Red values are cases when T AirVentOn is greater than T AirVentOff . ................................ ................................ ................................ ................. 129 Figure 6.52. Evo lved morning setpoints for T AirVentOn and T AirVentOff . The effects of adding a crop value penalty on the resulting evolved setpoints are examined (right) and compared with the same setpoints wit hout the crop value penalty (left). Red values are cases when T AirVentOn is greater than T AirVentOff . ................................ ................................ ................................ ................. 130 Figure 6.53. Evolved midday setpoints for T AirVentOn and T AirVentOff . The effects of add in g a crop value penalty on the resulting evolved setpoints are examined (right) and compared with the same setpoints without the crop value penalty (left). Red values are cases when T AirVentOn is greater than T AirVentOff . ................................ ................................ ................................ ................. 132 Figure 6.54. Evolved evening setpoints for T AirVentOn and T AirVentOff . The effects of adding a crop value penalty on the resulting evolved setpoints are examined (r ight) and compared with the same setpoints without the crop value penalty (left). Red values are cases when T AirVentOn is greater than T AirVentOff . ................................ ................................ ................................ ................. 133 Figure 6.55. This setpoint determines the temperature below which the greenhouse controller will turn on the boiler heating. ................................ ................................ ................................ .... 135 Figure 6.56. This setpoint determines the outside temperature below which the greenhouse controller will deploy the thermal screen. ................................ ................................ ................... 136 Figure 6.57. PID gain parameters for boiler heating control. ................................ ..................... 137 Figure 6.58. PID gain parameters for fogging system control. ................................ ................... 139 Figure 6.59 . PID gain parameters for greenhouse ventilation control. ................................ ....... 140 Figure 6.60. The copies of sr_offset and ss_offset are used to subtract from the current ca lculated time for sunrise and sunset, respectively. ................................ ................................ ................... 142 Figure 6.61. This variable determines the upper bound for the dynamic CO 2 setpoint used during CO 2 injection. ................................ ................................ ................................ .............................. 143 xv Figure 6.62. This variable determines the lower bound for the dynamic CO 2 setp oint used during CO 2 injection. ................................ ................................ ................................ .............................. 144 Figure 6.63. This variable determines how quickly is maximized, and subsequently cont ributes to how quickly the dynamic CO 2 setpoint is maximized. ................................ ........ 145 Figure 7.1 . Example Pareto fronts of all the control strategies describe d in this thesis, compared with the classical Vanthoor strategy. All control strategies were evolved for 100 generations. 151 Figure 7.2. Example of normalized hypervolumes for each evolved cont roller described in this thesis, calculated every generation. ................................ ................................ ............................ 153 Figure 7.3. Example output of the proposed metric. A solution from the original Pareto front (black) is sampled 100 times with r andom perturbations, and their fitness function is calculated for each new sample (red). The outer points of these new solutions are used to obtain the convex hull (red shaded region). ................................ ................................ ................................ ............. 157 Figur e 7.4. Exampl e Pareto front showing the effects of adding perturbations to each solution. The grey region shows the union of all the polygons generated by the perturbed samples of the Pareto front. The least sensitive solutions tend to be low - variable - cost solutions (b lue region), while high - crop - value solutions can be extremely sensitive (green region). .............................. 158 xvi KEY TO SYMBOLS AND ABBREVIATIONS State variables CO 2 Carbon dioxide concentration (mg/m 3 ) T Temperature (°C) VP Vapo r P ressure ( Pa) Subscripts 24 24 - hour mean 48 48 - hour mean _fr Subscript denoting a post - fruit - set variable or setpoint Air Greenhouse air compartment Blow Indirect air heating system Boil Boiler heating system Boiler Alternate subscript denoting th e boiler hea ting system D Denotes that variable applies to midday period Dst Destination E Denotes that variable applies to evening period Electricity Denoting the use of electricity as a resource ExtCO2 External CO 2 source Fog Fogging system Glob Glo bal radiatio n (W/m 2 ) xvii M Denotes that variable app lies to morning period N Denotes that variable applies to nighttime period Off Threshold for a greenhouse actuator to be turned off On Threshold for a greenhouse actuator to be turned on Out Outside air temperature Pad Pad and fan cooling system Roof Greenhouse roof ventilation opening Shading_i Greenhouse internal shading screen Shading_e Greenhouse external shading screen Side Greenhouse side ventilation opening Src Source ThScr Thermal screen Therma l Alternate subscript for thermal screen Vent Gre enhouse roof and side ventilation openings Water Denoting the use of water as a resource Other abbreviations Cap Capacity of the associated state variable and/or greenhouse design element CNY Chinese Yuan CRS Contro lled R andom S earch cv Cultivar Eq Equation xviii Eqs Equations FIR Far Infrared Radiation MIMO Multi - I nput - M ulti - O utput MOCC Multi - O bjective C ompatible C ontrol MOEA Multi - O bjective E volutionary A lgorithm MPC Model P redictive C ontrol NFR Net F inancial R e sult NIR Near Infrared Radiation NSGA - II Non - D ominated S orting G enetic A lgorithm II p Cost associated with consumption of a limited resource (CNY) ppm Parts Per Million P Cost associated with operation of a greenhouse element (CNY) PAR Pho tosynthetica lly Active Radiation PE Polyethylene PID Proportional - Integral - Derivative controller R Flux density (W/m 2 ) RH Relative H umidity u Climate control variable U Alternate abbreviation for a climate control variable VPD Vapor Pressure Deficit xix Other varia bles CO 2Air ExtMax Upper bound for the dynamic CO 2 setpoint (ppm) CO 2AirExtMin Lower bound for the dynamic CO 2 setpoint (ppm) CO 2AirExtOn Current value of the dynamic CO 2 setpoint (ppm) h Tcan24 Growth inhibition function based on 24 - hour mean c anopy temper ature h Tcan Growth inhibition function based on instantaneous canopy temperature I Glob Outside global radiation (W/m 2 ) I GlobMax Threshold for the outside global radiation above which the CO 2 setpoint will be at its maximum (W/m 2 ) MC Fruit Ra t e of c arbohy drate flow into fruit (mg/m 2 × s) n_Dev Total number of fruit development stages , of which the last stage may be harvested sr_offset Offset used to subtract from calculated sunrise time (minutes) ss_offset Offset used to subtract from calculate d sunse t time (minutes) t 0 Greenhouse simulation starting time t f Greenhouse simulation ending time v wind Outdoor wind speed (m/s) Symbols Capacity of the associated system Euro currency sign Reflection coefficient Transmission coefficient 1 1 I n troduction 1.1 O bjectives and S cope The objective of this thesis is to build upon existing greenhouse models that allow the simulation of greenhouse and tomato plant growth dynamics, and to use evolutionary algorithms with this model in order to find and anal y ze practical control strategies that can improve upon existing strategies. Validation of these strategies will consist of reproducing the original results utilizing a classical control strategy and then comparing them to the se opt imized control strategies . Optimized c ontrol strategies th at are found will be examined for economic viability as well as robustness against varyi ng weather conditions and sensitivity to variations in control parameters. Resulting control strategies are de signed and expected to be viable for v alidation in real greenhouses but doing so is b eyond the scope of this thesis , as it would involve considerable time and expense . Since greenhouse parameters as well as user requirements have a staggering am ount of var iation, we are limited to only paramet ers currently available to us. However, the methodology propose d here can be applied by others by introducing their own greenhouse parameters, costs, and other design constraints. 1.2 Introduction Worldwide, the greenhouse industry is the fastest g rowing secto r of agricultural production, with global demand for fruits and vegetables having doubled in the last ten years [2] . A key factor in meeting this demand is employing automatic greenhouse control that adjust s the microclimate of a greenhouse base d on sensor feedback . This demand is particularly acute in China, which has funded a team at Tongji University, under the leadership of Prof. Lihong Xu, to study ways in which greenhouse productivity can be optimized. Through a long - established research relationship with Prof. Erik Goodman of MSU, they have assembled a team i n cluding Prof . Erik Runkle of the Department of Horticulture, MSU ; Prakarn Unachak, a former Ph.D. student at MSU ; Chenwen Zhu, a former Ph.D. student at Tongji University and visiting scholar at MSU ; and Dr. Yuanping Su, p rogram and v isiting scholar at MSU. The author and Prof. Goodman have made several visits to Tongji University and the 2 experimental greenhouses they have constructed, helping their understanding of the real - world facets o f greenhouse control. The activiti e s of this te am laid the groundwork under which this work was begun by the author. Collaboration continues with Prof. Xu, Dr. Su, and Prof. Runkle; the others have graduated and moved on to other activities. Due to the re liance on open - loop control or on c losed - loop c ontrol aimed only at maintaining preselected setpoints for various greenhouse microclimate variables , most commercially available conventional greenhouse controllers have problems providing optimal control due to the lack of an on - line feedbac k mechanism t hat allows the controller to make adjustments based on the current growth dynamics of the entire crop production system [1] . A related method, closed - loop greenhouse control, promises higher crop yield at lower cost by adjusting the indoor climate in accordance with the response of the crop being cu l tivated. Eve n so, an obstacle to acceptance of these controllers is the lack of decision freedom of the user, which is necessary for adapting to unexpected environmental condition s [1] . An approach that is more energy efficien t than conventional control and provides users w ith the freed om to adjust controller be h avior is nee ded to help meet the increasing demand for fruits and vegetables considering yield, quality, and production inputs . Our proposed approach incorporates a tomato crop yield model as part of the clos ed - loop control by using the model - predicted se a sonal crop y ield as a n overall measure of fitness for a control strategy. Thus, this control approach requires a detailed crop growth model allowing prediction of the effect of microclimatic conditions at any time on the ultimate seasonal yield, by tracki n g their effe cts on a state model of the crop growth. This approach will yield multiple solutions that show the tradeoff s between crop yield and energy costs using evolutionary algorithms. Usin g multi - objectiv e evolutionary algorithms, or MOEAs, we can obt a in a set of greenhouse contro l strategies that can balance multiple conflicting objectives. For our purposes , energy consumption and crop production are considered as the objectives to optimize. One particula r property we are interested in while using MOE A s is that of elitism during search, which involves preserving the fittest Pareto non - dominated individuals from a previous generation and keeping them unchanged into the next generation. 3 This guarantees that the overall quality of solutions does not decre a se from one generation to the next. In and the offspring are combined and then sorted according to the concept of non - domination. Since all the paren t members are included, this ensures elitism is employed in the algorithm. The next generation is then created by adding members from the current sorted, combined population starting from the lowest ranked members. If all solutions from a particu lar rank c a n no t be adde d to the nex t parent population, the crowding operator is used to rank in order of descending crowding distance, and then the necessary number of members is chosen to fill the population. One example of such an algorithm is described i n Figure 1 . 1 . Energy savings are lity to tolerate environmental fluctuations. This is known due to the effects of sub - opt imal and supra - optimal instantaneous and mean temperatures being studied extensively for tomatoes, which has led to the development of temperature - based growth inhibition functions for the tomato crop model [3] . This behavior allows us to relax controller setpoints to allow a wider range of temperatures than would normally be deemed acceptable in practi c e , as long a s the control strategy itself does not trigger the negative effects of these growth inhibition factors. For example, it may be unnecessary to mai ntain a high nighttime tem pera ture if there was little photosynthetic activity during the day and t he outdoor t emperature is low. User decision freedom is achieved by enabling users to choose among a set of evolved control strategies, with different control parameters for the lower and upper limits to allow variation, depending on the crop state and ty p ical externa l weather conditions of th is illustrated in Figure 1 . 2 . These define an optimal range of temperatures for both instantaneous and 24 - hour mean temperatur e s in order t o grow the crop, and subsequently play a major role in maximizing crop yield. Of c ourse, these curves are only one of the components in the instantaneous photosynthesis model, which also depends heavily on leaf area index, level of photosynthe t ically activ e radiation (PAR) , and of CO 2 concentration in the greenhouse canopy. 4 Figure 1 . 1 . Detailed illustration of the proposed method for optimizing greenhouse control strategies: NSGA - II, a multi - obj e ctive proble m solver (a), components of the fitness function (b), and a resulting Pareto set o f control strategies (c). Figure 1 . 2 [4] . The horizontal ax e s on the left and right rep resent instantaneous canopy temperature and 24 - hour mean temperature, respectively. The solid lines represent a non - differentiable implementation of the functions, wh i le the dotte d lines represent a differentiable version of the function s. The values h Tcan and h TCan24 are used as scaling factors that limit the flow of carbohydrates into the tomato crop. 5 1.3 Control Strategy Optimization M ethodology o ach for the greenhouse design optimization step utilizes CRS (population - based controlled random search [5] ), which is appropriate for the scope of the optimization problem framed originally: limited search space and single objective. Due to th e introductio n of crop yield as an objective and dramatically expanding the search space , we changed the approach by using a type of heuristic multi - - dominated Sorting Genetic Algorithm - II (NSGA - [6] . Anoth er major difference is that the end - goal of our optimization step is the acqu isition of novel control strategies by optimizing over a wide range of possible control parameters while using a fixed set of greenhouse elements; Vanthoor utilize d a fixed contro l strategy. Environmental effects on attributes of the tomato crop that are a ssociated with its quality (e.g., flavor, nutrition, etc.) are not considered in the economic model (described in Section 4.1.2 ) , and it w a s assumed th at the greenhouse environmental conditions produced by the evolved control strategies discussed in this thesis do not affect tomato quality. Instead, the output of the t omato crop yield model while using evolved control strategies will only di f fer from a c lassical strategy (described in Section 6.2 ) with regards to the amount that w as harvested. The use of NSGA - II allows us to find multiple solutions consisting of the Pareto - optimal set of control strategies. We trea t greenhouse climate control as a multi - objective problem comprising two conflicting objectives: resource cost (water, electricity, etc.) and crop yield. Evolutionary algorithms maintain a population of candidate solutions in which individuals compete with one another based on a fitness function. In this case, candidate solutions are greenhouse control strategies, and the fitness function is based on a simulation of an integrated cultivation system including a greenhouse climate state model combined with a t omato growth state model. As in biological evolution, new candidate solutions are generated via recombination and muta tion of highly incorporated into the population, and, if highly fit themselves, compete f or space in the next generation [7] . 6 Figure 1 . 1 is a detailed illustration of our approach. In Figure 1 . 1 a , NSGA - II is used to obtain sets of Pareto - optimal green h ouse control lers. Each individual in the NSGA - II population is a control strategy that is evaluated by a fitness function to determine its survivability, as depicted in Figure 1 . 1 b . This fitness function comprises three components : the objecti ve functions being optimized, the greenhouse/crop yield model that is used to evaluate the control strategy, and the meteorological data used as input to the greenhouse model. A sample Pareto - o ptimal set of control strategies is shown in Figure 1 . 1 c . Details regarding the individual control strategies and each component of the fitness function are described i n more detail below. 7 2 Literature Review M odeling of greenhouse production of crops has been a longstanding researc h topic, beca use of the importance of optimizing the behavior of the greenhouse control system to maximize crop production while minimizing ope rating costs. These sometimes - conflicting objectives give the decision maker a great deal of freedom to choose, b u t also the r esponsibility of choosing wisely. Historically, even the earliest efforts [8] at automated greenhouse control recognized the importance of making the control system responsive to c h anges in ext ernal environmental conditions (including temperature, relative humidity, wind speed and direction, etc.) . The majority of greenho use optimization studies focus on control performance and climate control with regards to maximizing net financia l gain [1] , that is, combining the value of the crop produ c ed and the c ost of producing it. Due to the scope of these studies, components such as a crop yield model are typically not considered , with t he focus instead being on maintaining the greenhouse microclimate in a state thought to be optimal for plant prod u ctivity . Par t of this is due to there being a limited number of plants that are well enough understood to form a complete state model, as well as the lack of well - studied and economically viable methods to obtain real - time feedback on plant biomass increa s e. The later approaches, such as that implemented by Vanthoor [4] , introduce simplified models of plant growth, increasing the robustness of the approach by calculating the effects on the ultimate objective, crop y ield, rather than on an arbitrarily determined physical parameter(s) of the greenhouse. However, introduction of crop modeling dramatically increases the complexity of the simulation requ ired to determine the benefits of a particular control algorithm, so progress on this front has partially relied on the advance in computational speeds before researchers have used such models. In order to determine the economic and crop yield effects of a specific greenhouse controller, it is necessary to combine several models toget her: a greenhouse climate (or microclimate) model, a crop yield model and an economic model. Of these three, finding an adequate crop yield model proves to be particularly cha llenging; even with the use of parallel computing and a relatively s m all number o f 8 greenhouse designs to evaluate, the computational time required for applying optimization algorithms can be prohibitive [4] . That said, tomato currently makes for an ideal crop, as knowl edge on model l ing tomato y ield is widely available [9] . Most of the early publications approached the topic of opt i mal greenhou se control from the point of view of classical control methods, which define greenhouse environmental control as an optimal control problem. For example, N. Sigrimis and N. Rerras applied a linear model for greenhouse control whi ch views the g reenhouse en vironment as a m ulti - i nput - m ulti - o utput (MIMO) system [10] . It uses as inputs such variables as external temperature, relative humidity, wind velocity and direc tion, and ins o lation . It a lso uses internally measured evapotranspiration rate s, and state variables such as internal air temperature, internal air relative humidity and soil temperature to determine how various control actions should be modulated (heaters , window open i ngs, exhaust fans , etc.). H. J. Tantau discussed the benefits of optimal control of temperature, humidity, and supplemental lighting, resulting in reduced overall costs, reduced growing periods and increased crop yields [11] . However, he also note d the importance of plant growth models, as they can provide valuable feedback to online control systems, and knowledge in this ar ea was still l acking at th e time. E. J. v an Henten and J. Bontsema defined greenhouse cultivation of a lettuce crop as an optimal control problem to determine the ideal temperature and CO 2 strategies for its cultivation, using the mean values of historical weather data as a method of forecasting [12] . This resulted in lower energy costs and CO 2 consumption compared to using control strategi e s that do no t take the weat her into account. While it ha d its benefits, they also note d that this method needs improvement to better cope with differences between predicted and actual weather. K. G. Arvanitis , P. N. Paraskevopoulos and A. A. Vernardos pro p osed an adap tive control st rategy for greenhouse air temperature [13] . Multiple samples of the greenhouse air temperature were taken over the course of a predefined sampling period, which were then used to compute a constant - gain controller that modulates the h eating syste m. 9 I. Seginer a nd R. W. McClendon compared various dynamic optimization techniques and talked about their drawbacks in the context of greenhouse cultivation : depending on the technique used, a grower may have difficulty making multiple sequent i al decisions during a growi ng season, or it may be unacceptably inefficient when solving problems with many state variables [14] . T o address thi s problem, they proposed reducing the number of state variables in one of their approaches to reduce the computational complexity of the problem. Depending on which state variables were removed, the results ranged from sub - optimal but acceptab l e to more in ferior results. They also used historical data from previous optimal control solutions to train a neural network that could produce control decisions that are appropriate for current environmental conditions , with good results . A related effor t , aimed at r educing the num ber of state variables in the greenhouse model, was undertaken by the team at Tongji University, as reported in [15] . It proposed a simplified model with significantly reduced state variables while still describing a combined greenhouse climate and crop yield model. In addition, s ome of the state variables we r e simplified through curve fitting techniques. The results show that the reduced model was effective at producing similar results to its counterpart. Moreover, this research shows one method for validating these results by using already available data fro m a previousl y validated gre enhouse microclimate - crop yield model [4] . Several researchers have approached the multi - objective optimization problem using the techniques of stochastic optimization, including particl e swarm op tim ization and evolutionary methods. A. Hasni et al. test the use of genetic algorithms versus particle swarm optimization to obtain the optimal set of parameters for the greenhouse itself by simulating a reduced greenhouse model iteratively with the param ete rs optimized through said methods [16] . They found that their particle swarm implementation outperformed their genetic algorithm approach. Q. Zou et a l. propos ed a control strategy developed using model predictive control (MPC), combined with particle swarm optimization [17] . The proposed control strategy was able to reduce energy consumption 10 due to heating and ventilation while maintaining the same temperature ranges as their conventional controller. A. Ramírez - Arias et al. address ed the existence of multiple conflicting objectives when it comes to optimal greenhouse control [18] . They define three main objectives: m aximizing profit, fruit quality and water - use efficiency. In order to find setpoints that balance these three objec t ives, they p roposed a hierarchical control architecture that takes advantage of the different time scales in which greenhouse - related proces ses operate. This way, optimal setpoints may be calculated for slower processes (such as crop growth), and then sen t to the next greenhouse air temperature). The use of multiple timescales for both state and environmental variables is found in [19] . H. Hu et al. used evolut i onary algori thms to address the issue of determining p roportional i ntegral and d erivative (PID) control parameters for greenhouse climate co ntrol [20] . By defining multiple performance measures as objectives and using NSGA - II, an evolutionary algo rithm, they were able to develop a tuning method for PID controllers used in greenhouses that can account for multi p le conflicti ng objectives. In this sense, it is an important precursor of the work reported in this dissertation, which uses a genetic algor ithm to optimize PID parameters of various controllers. M. Mahdavian , S. Sudeng, and N. Wattanapongsakorn similarly used NSGA - II , with the focus lying on optimizing PID controller performance with regards to temperature and light supplementation [21] . In this case, a crop yiel d model was not considered. Y. Su , L. Xu, and E. D. Goodman proposed an approach based on adaptive dynamic programming [22] , which uses neural networks to estimate the value function and resu lting control strategy for the greenhouse. o l inputs for the greenhouse actuators that were not always attainable in a real setting, resulting in cases where a 11 A notable example utilizing multi - objective optimization methods o n greenhouse problems is the use of multi - objective compatible control, or MOCC [23] . The method behind MOCC relies on dividing the optimization process into two layers: the compatible o ptimization level and the compatible control level. The former works by obtaining Pareto - optimal fronts for control variables while also o btaining additional sub - optimal solutions. The process of obtaining sub - optimal solutions involves relaxing the contro l variables associated with a point in the Pareto - optimal front, which makes for a useful backbone for creating practical sol u tions by pro viding a set of alternatives. The multi - objective work above, and the work reported in this dissertation all make use of evolutionary computation techniques. These approaches, including especially the genetic algorithm metaheuristic used here, date from th [24] , who first put forth the genetic algorithm, a lthough it w as not yet called that. Another milestone was the book of David Goldberg [25] , and there have been thousands of paper s published since using the genetic algorithm and other derivative forms of evolution a ry computati on. In the context of multi - objective evolutionary optimization, the article by K . Deb et al. [6] in which NSGA - II was first presented has been cited more than 35 ,000 times. An excellent overview of the field was presented in [26] . The most important prior work, provi d ing much of the modeling framework for the algorithms developed here, is that of Vanthoor [4] . It provides a complete mechanistic model by incorporating a tomato crop yield model and also addresses potential issue s and design considerations when attempting to optimize various aspects of a greenhouse system; he also points out that multi - factorial optimization for greenhou se design is promising due to prior research on complex problems in other application domains. Part of the - based greenhouse design method involves determining the economic analysis and viability of a greenhouse design, a long with an optimization step to improve the net financial gain of operating the greenhouse. A s mentioned i n Section 1.3 , h is proposed approach utilizes population - based controlled random search, or CRS [5] . Due to the scope of the optimization problem being limited to a small set of greenhouse design element s (to form dif ferent combinations with) 12 and a single objec tive, this was a satisfactory approach to determining an optimal solution. However, it was imperative that this approach be modified in order to account for our approach being a multi - objective optim i zation probl em with many more parameters to be determine d, requiring evaluation of thousands of seasons of simulated greenhouse operation under a variety of climatic conditions in order to allow evolution of optimal and robust controller behaviors. Such s i mulation wou ld have been impractical enhouse model, as that model used numerical integration methods that often reduced timesteps to millisecond levels to achieve numerical convergence, because of the stiffness of the equations used in h is state mod el. An overview of a model - based greenhouse design method can be seen in Figure 2 . 1 , along with the modification of the optimization process. Figure 2 . 1 . In our i mpleme n tation of Va - based greenhouse design method [4] , the optimization step, which was previously aimed towards greenhouse design optimization with a single objective (net financial result ), is replaced w i th a multi - o bjective optimization step that considers crop yield value and variable costs. Inputs such as the canopy temperature (T Can ), greenhouse air CO 2 concentration (CO 2Air ), photosynthetically active radiation flux density (R PAR ), greenhouse air tem p er ature (T Ai r ), and the vapor pressure of the greenhouse air (VP Air ) are used in the tomato yield model to obtain the final yield. Hi storically, one of the challenges with crop yield modeling is the complexity of their description. Mechanistic models, suc h a s TOMGRO [27] , define the processes that drive the tomato crop growth as a set of state variables whose behavior is describe d b y differen tial equations. Even in its earliest, simplest form, TOMGRO defined 69 state variables, expanding to 574 state variables for the latest version at the 13 time [9] . This can be daunting not only from the perspective of reproducibility of results when implementing such a model, but also because it makes using these crop yield models to optimize gre e nh ouse contr ol impractical, if not outright impossible. These challenges have led to multiple efforts to simplify the models while maintaining acceptable levels of accuracy [18, 28 - 30] . goal in his work was to describe a methodology for obtaining a greenhouse design suitable for a given climate and locale [4] , one of the advantages of his combined model description is that the total number of sta t e variables is relatively small despite including the three model s pictured in Figure 2 . 1 ( i.e., g reenhouse climate model, tomato yield model, and economic model) . To achieve this, some assumptions and simplificati o ns were made by Vanthoor among the three models, but subsequent validation studies confirmed their efficacy. In addition, having an economic model provided the framework for evaluating the viability of a greenhouse design by incorporating the fixed and va r iab le costs of operating a greenhouse (as well as the resulting profit of the tomato crop), allowing for well - (such as leaf area index, or LAI) which may b e o btuse for non - growers. greenhouse design elements included in the greenhouse climate model description contained the necessary information for reliable r e pro ducibilit y of its intended behavior. Second, the inclusion of certain greenhouse design elements caused an excessive increase in the stiffness of the differential equations describing the greenhouse model, resulting in computational times that made it i mpr actical t o use evolutionary algorithms like NSGA - II. Finally, since detailed descriptions on greenhouse controllers and their behavior are not available, it presents difficulties in determining whether an improved greenhouse control strategy would help imp rove the economic viability of a design. Since the objective of this thesis is to find more optimal greenhouse control strategies by using evolutionary algorithms, these challenges were addressed by doing the following: 1) greenhouse design elements wi t h i nsufficie nt information for reliable reproducibility of their behavior are omitted, 2) 14 greenhouse design elements that were found to contribute excessive stiffness to the differential equations describing the greenhouse model are omitted, and 3) a s a b a sel ine, a gr eenhouse controller based on the assumptions necessary for the controller to be functional. Due to the modularity of the greenhouse cl i mat e model d escribed by Vanthoor, the omissions made of certain climate control elements (like pad and fan cooling, for example) do not adversely affect the efficacy of the model . M oreover, this approach coincide s with the greenhouse design and climate mo d el used in o ne of his studies. More details on these changes are available in Chapter 4 . 15 3 Modification of a Classical Greenhouse Control Model for Evolu tionary Optimization T he contents of this chapter are parti a lly based on our prior published work, and can be found in [31] . The validation step performed by Vanthoor [4] used ordinary differential equation ( ODE ) solvers with variable time steps in order to solve all model equations. D ue to the stiffness of the differential equations in these models and the high number of greenhouse season eval u ations that are needed when doing evolutionary multi - objective optimization on a more flexible control architectu re, the optimization process and model used by Vanthoor are impractical due to their excessive computational time . In order to address this, t h e model has been refined such that a fixe d integration time step of 60 seconds can be used, and a fourth - order Run ge - Kutta solver is used instea d of a variable - step - size solver, which dramatically reduces t he runtime of the optimization process . s climate mod el is defined by a set of energy and mass fluxes in the form of temperature, CO 2 co ncentration and vapor pressure. An example of these fluxes and how they relate to state variables can be seen in Figure 3 . 1 . Th is model assumes that the air inside each compartment in the greenhouse is completely mixed . However, even with this assumption these fluxes (or transfers) of mass and energy between well - mixed compartments often resu lt in high levels of stiffness of the different i al equations , and therefore unacceptably high computational costs that make it impractical to use s uch a model for optimization purposes. Most notably, the fluctuations in temperature induced by using these e quations with a fixed and longer timestep are n o t what physi cal laws would predict, and the large gradient induced would actually result in mixing between compartments that would dramatically exceed the limits of the climate model . In order to ensure prope r mixing, after each step of the ODE solver , we implemented a mixing equation , T Mix_SrcDst , for more even distribution of heat fluxes from a source state variable T Src and a destination state variable T Dst : 16 w here cap Src (J × K - 1 × m - 2 ) is the heat capacity of the source air compartment of the flux, T Src ( °C ) is the current temperature from the source air compartment of the flux. These mixing equations con serve heat between t h e compartmen ts they are mixing and have a strong stabilizing effect on the behavior of the greenhouse climate model. The terms cap Dst and T Dst are similarly defined, but for a destination air compartment Dst . Once T Mix_SrcDst is calculated, the new heat f l ux, H Mix_Src Dst is defined as: w here cap Src (J × K - 1 × m - 2 ) is the heat capacity of the source air compartment of the flux, T Src ( °C ) is the current temperature from the source air comp artment of the flux, and T Mix_SrcDst is the mixed temperature between the s ource and destination air compartments. Lastly, the state variables are updated with the heat flux contributed by H Mix_SrcDst : 17 Figure 3 . 1 . Potential design elements used to manage the greenhouse climate. The colored ar rows represent the various mass [4] . 3.1 Individual Control Strategies One of the major factors in tomato crop culti vation is , under varying environmental conditions , to properly balance temperatur e with the available light, so as not to waste energy maintaining optimal temperatures while the photosynthetic light is in short supply, unless artificial lighting is available to boost photosynthes is. This will help maximi ze accumulation of carbohydrates in the plant as well as carbohydrate outflow to its various organs , which ultimately results in maximizing harvestable fruit . Higher temperatures under lower light conditions simply raise the loss o f carbohydrates to respir ation, which is higher at higher temperatures, so to expend energy to raise canopy temperature under low light conditions is counterproductive . Based on concepts from compatible control [23] , we developed an interval controller that is designed to maintain the internal greenhouse temper ature within crop - favorab le ranges , depending on environmental conditions, which can dramatically affect the energy cost/crop production tradeoff. This controller includes switc hing rules for decisions about heating, 18 dehumidification, ventilation, shading, and carbon dioxide injec tion and is supplemented with conflict - resolving rules and provides for limited user intervention. Figure 3 . 2 con tains an example of such an interval controller. We have divided the overall control strategy into two main segments : daytime and nighttime control strategies. This allows the greenhouse to have differing temperature ranges during these times when the presence of sunlight affects the usefulness of maintaining a specific range of temperatures. This is further divided durin g daytime into morning, midday, and evening temperature intervals. In a ddition, switching times between daytime and nighttime strategies are defined in order to allow the controller to pre - emptively change strategies before sunrise or sunset so that it may accommodate the anticipated changes in temperature and light levels an d in desirable temperature and light levels . G reenhouse heat ing and cooling is accomplished using PID controllers; this includes boilers, cooling pads and ventilation. Each of these has its respective gain parameters which will also be optimized, making pa rt of the optimization process a parameter tuning problem. CO 2 injection is also assumed to be available and used by the control strategy, and a range of CO 2 values is main tained by the controller. Finally , a threshold for global radiation is defined which the controller uses to determine whether deployment of a shading screen is necessary. To evolve these interval controllers, individuals (i.e., sets of the optimizable parameters of the controller) within the evolutionary algorithm comprise a set of discre tized floating point numbers : daytime and nighttime temperature intervals , PID gain parameters (for controlling boiler, cooling pad and ventilation greenhouse elements), carbon dioxide intervals, daytime and nighttime strategy switching times, and maximum global radiation values. During fitness evaluation, these parameters define the behavior of the controller and how it responds to the meteorological data used as input to the greenhouse model. 19 Figure 3 . 2 . Example of an implementation of the proposed interval controller , for some arbitrary time of day . Instead of strictly following temperature setpoints, it allows for a range of temperatur es in which some control actions (or none ) may be taken as long as the temperature stays within a certain range. 3.2 Objective Functions The two objectives being optimized are crop production ( f Yield ) and resource cost ( f Cost ). These objectives are calculated following the simulation of the greenhouse/crop yield model with an individual control strategy over a predefined time horizon ([ t 0 , t f ]). Specifically, crop production is the finite integration of the carbohydrates flowing into fruit ( MC Fruit ) during the final development stage ( n_Dev ) . The integral that defines f Yield is described in Eq. (3.5). 20 The r esource cost s consist of the sum of costs related to resource consumption, including water ( p Water ) , electricity ( p Electricity ), and supplemental C O 2 ( p CO2 ) in Chinese Yuan (CNY , based on locale of the weather data that w ere available for this study ). T he cost for each unit of these resources was constant and supplemental lighting was not considered. The capacities associated with each actuator are b ased on data provided by Vanth oor [4] , and a summary of the most important values for actuators associated with climate management can be seen in Ta ble 3 . 1 . Resource costs are driven by the operation of the following actuators : b oiler ( u Boiler , P Boiler ), pad and fan ( u Pad , Cap Pad , P Pad ), roof vents ( u Roof , P Roof ), side vents ( u Side , P Side ), thermal screen ( u Thermal , P Thermal ), external shading screen ( u Shading _e , P Shading _e ), internal shadi ng screen ( u Shading_i , P Shading_i ), and CO 2 enrichment ( u CO2 , Cap CO2 ) . The integral that defines f Cost is defined in Eq. (3.6). Assuming both objectives are modeled as minimization problems, one would determine the lower bound for each objective, or ideal point, and try to reach it. However, the tradeoff between these two objectives determines how closely the evolved Pareto set can approach the ideal point. 21 Ta ble 3 . 1 . Capacities and coefficients for t he major greenhouse design elements associated with active climate management. Transmission and reflection coefficients for near infrared (NIR), far infrared (FIR), an d photosynthetically active radiation (PAR) of the internal shading screen, external shad ing screen, and thermal screen are included. Parameter Description Parameter Name/Symbol Unit Value Capacity of the CO 2 enrichment system Cap CO2 mg/s 4.3 ×10 5 Capacity of the air flux through the pad and fan cooling system Cap Pad m 3 /s 50 Capacity of the boiler heating system Cap Boil Megawatts (MW) 1 NIR reflection coefficient of the internal shading screen Shading_i NIR - 0.3 PAR reflection coefficient of the internal shading screen Shading_i PAR - 0.3 FIR reflection coefficient of the internal shading screen Shading_i FIR - 0 NIR transmission coefficient of the internal shading screen Shading_iNIR - 0.6 PAR transmission coefficient of the internal shading screen Shading_iPAR - 0.6 FIR transmission coefficient of the internal shading screen Shading_iFIR - 0.1 NIR reflection coefficient of the external shading screen Shading_eNIR - 0.2 PAR reflectio n coefficient of the external shading screen Shading_ePAR - 0.2 FIR reflection coefficient of the external shading screen Shading_eFIR - 0 NIR transmission coefficient of the external shading screen Shading_eNIR - 0.7 PAR transmission co efficient of the external shading screen Shading_ePAR - 0.7 FIR transmission coefficient of the external shading screen Shading_eFIR - 0.1 NIR reflection coefficient of the thermal screen ThermalNIR - 0.7 PAR reflection coefficient of the thermal screen ThermalP AR - 0.7 FIR reflection coefficient of the thermal screen ThermalFIR - 0.45 NIR transmission coefficient of the thermal screen ThermalNIR - 0.25 PAR transmission coefficient of the thermal screen ThermalPAR - 0.25 FIR transmission coefficient of the thermal screen ThermalFIR - 0.11 3.3 Greenhouse Model To estimate fruit production and resource cost for an individual control strategy, we have imple mented and adapted a comprehensive greenhouse and tomato crop mode l [4] . The greenhouse climate is based on an energy and mass balance model, while the tomato growth ( based on Lycopersicon esculentum L. cv. Pitenza [32] ) i s described by a buffer of carbohydrates that accumulates with photosynthesis, and must 22 balance the distribution of these car bohydrates among all plant organs: the stems, leaves, and fruit (if fruit set has occurred) . T he tomato cultivar was chosen based on the coefficients that were available to convert from dry matter to fresh weight [32 ] . Although flexible enough to fit a var iety of realistic greenhouses , the model implementation is very detailed and computation ally expensive, especially consid ering that a new simulation is required for every unique individual encountered during evoluti onary search. We therefore performed several model simplifications, including the reduction of time resolution by forcing a fixed time step of 60 seconds , merging of state variables (e.g., reducing overall depth considered for the soil temperature from 5 l ayers to 1 ) , and model revisions on flux calculations such as those described in Eqs. ( 3.1 3.4 ) . Based upon sensitivity analyses in the simulation domain, these modifications appear to have negligible impact on the overall behavior of the model and decre ase computation time dramatically. 3.4 Meteorological Data Acquisition and Configuration We used a meteorological database consisting of hourly weather d ata collected over six years in the Shanghai area [33] as weather input to the greenhouse/crop yield model. A summary of the mean values for the weather data used in this chapter is shown in Figure 3 . 3 . The data required by the model includes external temperature, humidit y, wind speed, carbon dioxide concentration, and solar radiation. These were extracted and linearly interpolated to a finer resolution as needed. Considering the typical time scales of greenhouse systems, we selected 5 minutes as the constant control inter val. This provides a small enough interval for finer gr eenhouse control while allowing a fixed time step of the same size. Unless otherwise specified, simulations were p erformed over a 300 - day produc tion period for each individual in the population . For re producibility of results , other simulation lengths may be used . In addition, multiple runs with different weather inputs were used to ensure the robustness of the final Pareto - optimal set. To avoid over - fitting of resulting control strategies , leave - one - ou t cross - validation [34] was used to structure the data for training and independent validation. 23 Figure 3 . 3 . Summary of the monthly mean values for the outside air temperature (T Out ), global radiation (I Glob ), and outside vapor pressure (VP Out ) for the 2007 2012 years in the Shanghai region. An ambient CO 2 concentration of 340 ppm w as assumed. 3.5 Description of Early E volved Results Figure 3 . 4 plots the Pareto - optimal sets from three indep endent simulations of our evolu tionary algorithm (hollow marks, lower left). Shown here are the values of the two different o bjectives, resource c ost and crop production. To improve interpretation, we report the negative harvestable fresh fruit ( i.e., - 1 × kg/m 2 ) such that the goal for both objectives is to minimize their respective values as much as possible. Each of 24 the three re plicates was trained on different weather data; Figure 3 . 4 show s the objective values for weather data that were but used for this simulated season . As shown here, productivity r anged from 5.5 to 10.5 kg/m 2 per year , while resource cost ranged from 62,100 to 113,000 CNY per year . Examining the parameters of the resultin g individual control strategies show ed that a relatively high nighttime temperature was always preferred if high produc tivity was desi red, around 18 degrees Celsius . This would guarantee the tomato crop would remain inside an optimal range of temperatures that would prevent crop growth inhibition. On the other hand, low - yield points in the Pareto set had lower resource cos t s due to having lower nighttime temperature s overall , around 12 14 degrees Celsius . Intuitively, lower nighttime temperatures are pref erred for the crop since it reduces plant respiration and maintaining higher nighttime temperatures will result in incr eased heating costs without immediate benefit to crop growth. However, the increased crop production resulting from these higher nighttim e temperatures suggest s that it is beneficial to maintain these temperatures in anticipation of daytime, allowing for t he greenhouse to reach an optimal temperature for crop growth once sunlight is available. 3.6 Result Comparison To compare the effectiveness of the optimization process , we evaluated a classic al set point - based controller [4] on the same greenhouse/crop yield model and weather data. The i solated solid points in Figure 3 . 4 are the objective values corre sponding to this controller on the three sets of weather data. Compared t o the set point controll er, the average evolved strategy reduced resource cost by 10.2% an d increased yield by 12.9%. Moreover, we found a 19.9% increase in yield given the same resource cost, and a 32.5% decrease in resource cost given the same yield. Some understanding of the d ifferences between the evolved control strategies and the set - poin t controller can be gained by examining the accumulated actuator usage for the boiler and the external shad ing screen. As shown in Figure 3 . 4 a , a randomly selected e vol ved controller (dotted line) used both the boiler and 25 shading screen less frequently than the set - point controller (solid line), which lowered the resource co st and increased photosynthetic activity, respectively. Figure 3 . 4 . Yearly r esource cost and crop yield for three independent Pareto - optimal sets on validation weather data (hollow points). Objective values for a classical setpoint controller on the same weather data (solid points). Accumulated boile r a nd shade screen usage for an evolv ed strategy compared to the set point controller (a). 3.7 Control Strategy Selection The t h ree Pareto sets in Figure 3 . 4 all share the same trend. Picking th as an example, a ll the s olutions in this set are relatively evenly distributed throughout objective space. This leads to an interesting qu estion: How should a user select a strategy to control a greenhouse? While expert knowledge plays a n important role in this decision - making pr ocess , there are several approaches that can be identified: (1) maximum fruit yield, (2) maximum affordable resour ce cost, (3) maximum average fruit yield per unit of resource, (4) minimum resou rce input per unit fruit yield, and (5) expected economic retu rn. While approaches (1) and (2) do not explicitly take both objectives into account, approaches (3) and (4), whic h specifically acknowledge both objectives, are likely to select a control strategy near the 26 middle of the Pareto set. Approach (5) would requ ire a more sophisticated economic analysis that goes beyond determining energy costs of the greenhouse during a cr op cycle. 3.8 Discussion Although these results are encouraging, additional refinement of the microclimate and plant models is necessary. Once co mpared with results reported by Vanthoor, it i s clear that there are some drawbacks with the model implementation in these early results: the crop yield is inadequate for the weather and the greenhouse configuration used (which included roof and side venti lation, cooling pads and boiler heating ). Since this type of greenhouse configuration provides excellent climate c ontrol that ensures the tomato crop can grow in near - optimal conditions, very high crop yields were expected, but not attained in this case. A dditionally, such a greenhouse configuration would be very costly to implement and would require a proportionally large return on investment to be worthwhile. In contrast, results, - type greenhouse , which only inclu des manual ventilation and whitewash, could tion depicted in Figure 3 . 4 [4] . To address this, the greenhouse crop yield model was revisited, and improvements in the model resulted in increased crop yield thanks to increased canopy PAR absorption which allowed us to better validate the results. In addition, various performance measures were proposed and used in this thesis to narrow down solutions from a large pool of candidates, as the process of control strategy selection de scribed earlier is still relatively vague. First, while it is possible to find a very good solution that contains desirable trade - offs between operatio nal costs and yield, it is important to consider the effect of any perturbations in the decision space of the solution. For example, it is possible that during the deployment of a candidate control strategy , the greenhouse system is unable to strictly enfo rce each of the parameters inside the chromosome. This can lead to a variety of undesirable effects; thes e range from a considerable reduction in fitness to a solution becoming financially unviable (by having a negative net financial result, or NFR, covere d in Section 7.2 ) . One of the earlier propos als to measure robustness in evolutionary algorithms can be seen in [35] , which 27 involves obtaining the effective fitness of an i ndividual by calculating the mean with resp ect to its neighboring individuals. Figure 3 . 5 shows the effect of determining mean fitness around the neighborhood of a Pareto - optimal set of solutions. Figure 3 . 5 . The image on the left portrays the effect of changing x in a single - objective problem. The image on the right shows the effect of changing x1, x2 and x3 in a two - objective problem. [35] The robustness of the evolutionary process is examined next. Multiple independent NSGA - II runs were performed and the trends of the Pareto - optimal set over time were exami ned for consistency. If th ese runs converge on a similar Pareto - optimal set over many generations, it will help confirm that NSGA - II is appropriately exhausting the search space and approaching a global optimum set of solutions. To this end, we used the no rmalized hypervolume of th e Pareto - optimal set as a performance measure for multiple independent runs. This performanc e metric can also be used as part of a procedure to compare different types of evolved controllers to assess their feasibility (with respe ct to each other). These r esults are reported in Section 7.3 . Finally, robustness against variations in weather conditions as well as control setpoints was examined. For the former, i n order for a solution to be of practical use to a decision maker , it m ust be able to perform reasonably well with a variety of weather patterns. To achieve this, each individual in the population is examined against multiple sets of weat her data. The choice of which weather data sets are used depends largely on the location and user preference. Results of th is study are reported in Section 7.4 . For t he latter, 28 we introduce perturbations on the evolved control setpoints and measure its negative impact on each objective. We then summarize this impact by calculating the area of the enclosing polygon created from the perturbations, which provides a straig htforward method for sorting solutions based on their robustness to these perturbations. Details on this approach, as well as the results are reported in Section 7.5 . 29 4 Evolution of a Classical Controller Using Improved Model T he contents of this chapter are partially based on our prior published work, and can be found in [36] . In the previous section, we detailed some of the major changes and their rationale in a modified version we produced of the microclimate - crop yield model described in [4] . Despite the considerable performa nce improvements, the difference between the results obtained and validated by Vanthoor and the simulated crop yields from the modified model was unacceptably high, even though the dynamics of the two models appeared quite similar. Thus, we proposed implem enting the microclimate - crop - yield model largely as Vanthoor presented it but making major modifications to the control strategies themselves after combined model, we we re able to leave out extraneous elements that need not be included in the configurations of a greenhouse we chose to simulate. While this approach is still significantly more computationally expensive than our model reporte d in Chapter 3 , these configurations are much more amenable to optimization through evolutionary computation, as the stiffness of their underlying differential equations does not have a large effect on the runtime of the ODE sol ver. In this section we show first our attempt at replicating the behavior of a classical controller designed for tomato crops to validate the agreement of our revised model with earlier published work. Second, we use N SGA - II to evolve microclimate contro l setpoints based on an earlier model - based greenhouse design method, which includes an economic model driven by the microclimate - crop yield model. 4.1 Combined Model Overview All the parameters required to describe the characteristics of the greenhouse design and climate control, including the economic parameters associated with them , study in Almería, Spain [4] . 4.1.1 Microclimate - C rop Yield Model The microclimate - crop yield m odel consists of a mechanistic model that describes mass and energy flows among the crop, greenhouse compartments, surrounding greenhouse construction elements and the 30 outside weather, inducing changes over time in temperature, CO 2 concentration, plant wei ght and vapor pressure. These flows are defined as a set of differential equations, which allows the use of ordinary differential equation solvers. The combined model state variables and their respective differential equations were implemented as describe d by Vanthoor, with minor model simplifications. The state variables of the tomato crop yield model represent the accumulation of carbohydrates in the plant from photosynthesis and how they are distributed to fruits, leaves, stems, and roots. Other essent ial plant proc esses, such as maintenance and growth respiration, plant transpiration and fruit set, are modeled as well. Irrigation and fertigation are assumed to be non - limiting and their cost is included in the economic model. The final tomato crop yield is obtained b y accumulating the amount of dry matter that is harvested in real time after fruit set begins, and then converting it to fresh weight. 4.1.2 Economic Model defines the n et financial result as: where Q CropYield - 2 ×year - 1 ) is the value of the tomato crop, Q Var - 2 ×year - 1 ) consists of t he variable costs (costs associated with the crop, resources used and labor), and Q Fixed - 2 ×year - 1 ) represents the cost of all tangible assets that do not depend on crop growth . For consistency and ease of comparison, be u sed as the curr ency for this (and subsequent) chapters. Sin ce Q Var and Q CropYield both depend on state variables that change over time, they are also treated as state variables themselves in the combined model. Market price fluctuations and tomato crop qua lity were not c onsidered, and a mean tomato price is assign ed to each greenhouse design instead based on the climate control techniques available and market prices observed by Vanthoor during the entire growing season. 31 4.1.3 Greenhouse Design and Control Ten gr eenhouse design s were evaluated in the economic model study by Vanthoor in [4] . A classical control strategy was used, which supports a combination of static temperature and relative humidity setpoints and a dynamic CO 2 setpoint. The CO 2 setpoint increases linearly with ou tside global radiation and decreases linearly with respect to the current roof and side ventilation opening. The available climate management techniques include d roof and side ventilation, a retractable thermal s cree n, whitewash, indirect air heating, boil er heating, a fogging system, and a CO 2 enrichment system. Based on the layout of the greenhouse designs described by Vanthoor , the thermal screen is assumed to be positioned between the greenhouse air compartmen t an d top compartment. The setpoint is disab led if its associated greenhouse construction element is not included in the design. For example, the dynamic CO 2 setpoint requires a CO 2 enrichment system , otherwise it will remain unused . All the greenhouse des igns that were simulated in this chapter ass ume that the greenhouse structure is covered in a single polyethylene (PE) layer which provides a global transmission of 57% (54% with a thermal screen deployed), with a rectangular shape of 200 x 50 meters, resu ltin g in a floor area of 10000 m 2 . Whitewash applications vary depending on the time of year and can be either result in a 25% or 50% decrease of the global transmission (these values were decreased further by 50% if a fogging system was present). A summar y of the important values associated with th e greenhouse design elements is in Table 4 . 1 , and further details can be found in [4] . Table 4 . 1 . Capacities for the major greenhouse design e lements associated with active climate management. Parameter Description Parameter Name/Symbol Unit Value Capacity of the CO 2 enrichment system ExtCO2 mg/s 1.39 × 10 4 Capacity of the fogging system Fog kg/s 1.39 Capacity of the indirect air heating system Cap Blow Megawatts (MW) 0.50 Capacity of the boiler heating system Cap Boil Megawatts (MW) 1.16 32 4.2 Model Validation Results Vanthoor conducted a study in which ten different types of greenhouse designs were simulated , with the goal of finding the design with the best net financial result. These results were provided for one growing season (2006 - 2007) and show a variety of useful outputs, such as t he crop yield, crop economic return, fixed costs, and variable cost s . To help validate our model implementation , t hese results w ere used to compare against ours. Due to the limited availability of the weather data used by Vanthoor in his studies, we used s oftware to estimate weather data based on a given location and time of yea r (with additional details available on Section 4.3.2 ). The average outdoor climate values in Table 4 . 2 show that there are some discrepancies between the original and estimated climatic input values . Most notably, the estimated temperature mean is significantly lower, while having greater extre mes. However, the average global radiation, relative humi dity and wind velocity values are more similar, of which global radiation is particularly important because it strongly affects both microclimate and photosynthetic rate. Table 4 . 2 . Average outdoor climate va lues provided by a) Vanthoor [4] , compared with b) the estimated weather for the same site used in this thesis . Period T out (°C) T out <5% (°C) T out >95% (°C) Global radiation (MJ×m - 2 ×day - 1 ) RH (%) v wind (m/s) a) 2006 - 2007 17.7 9.1 27.4 16.9 69.7 2.9 2007 - 2008 17.8 10.2 27.7 17.1 67.7 3.3 2008 - 2009 17.2 8.3 28.1 17.2 67.9 3.3 b) 2006 - 2007 14.4 3. 7 29.4 16.4 58.4 2.6 2007 - 2008 15. 5 5. 3 29.4 16.9 58.9 2.7 2008 - 2009 15. 8 4. 9 31.5 17.7 56.7 2.8 Table 4 . 3 contains a summary of our economic model output compared with the original simulated output. The outputs consist of tomato crop yield (kg×m - 2 - 2 ×year - 1 ), variable costs (VC, - 2 ×year - 1 - 2 ×year - 1 ) of te n greenhouse designs. Parral (P) is a type - The greenhouse construction elements used 33 for the different designs are as follows : a whitewash application ( W ), a CO 2 enrichment system (C) , a fogging system (F) , an indirect air heating system ( H_ ), and a boiler heating system (H). Fixed costs are not shown, as they are identical for both c ases. The main sources of discrepancy in the variable costs come from CO 2 utilization being overestimated and wate r costs being underestimated. The CO 2 enrichment system was treated as an on off controller, which , combined with the controller update interv al of five minutes , resulted in excessive CO 2 utilization. This can be remedied by using a smaller update interval for controlling the CO 2 enrichment system. Insufficient plant transpiration is the cause of low water costs, as this plant process determines the amount of water that is used for irrigation. We used a mean tomato price for the entire growing season while Vanthoor used a mean wee kly tomato price, thus conversions from crop yield to crop value will differ. Despite these discrepancies and the diff erences in the estimated weather, Figure 4 . 1 shows t he Ideally, matching historical weather data should be used for more accurate comparison, but such data were not availab le . Table 4 . 3 . Simulation com parison results between a) Vanthoor [25], compared with b) our simulated results for the 2006 - 2007 season. a) P W WC WF WFC WH_ WH WHC WHF WHFC Yield 21.88 23.99 25.78 26.45 28. 15 27.71 28.35 31.89 31.34 35.03 Value 9.77 11.01 11.86 12.33 13.15 13.65 14.89 17.22 16.42 18.47 VC 6.59 6.82 7.82 7.17 8.25 9.31 8.88 10.18 9.28 10.65 NFR - 0.25 - 0.31 - 0.84 0.15 - 0.49 - 0.92 - 0.94 - 0.29 - 0.32 - 0.03 b) Yield 22.42 24.24 25.2 5 25.23 26.44 29.86 33.57 36.09 35.27 37.79 Value 9.28 10.82 11.75 11.03 12.06 15.03 17.85 18.85 17.76 19.03 VC 6.38 6.62 7.89 6.76 8.9 10.46 9.32 10.68 9.52 10.98 NFR - 0.53 - 0.29 - 1.02 - 0.74 - 2.24 - 0.69 1.58 0.84 0.78 0.19 34 Figure 4 . 1 . Vanthoor predicted tomato yield vs our predicted yield as a function of greenhouse technology level. 4.3 Greenhouse Simulation and Evolution Setup 4.3.1 Greenhouse Design Out of the ten available designs, we chose the greenhouse d esign with the most climate management and therefore maximizes the search space for optimizing the originally published control strategy. The micro climate - crop model is implemented in C+ +, combined with the Open BEAGLE framework for evolutionary computation [37] that supports NSGA - II, modified to allow parallelization using the OpenMP API [38] . To solve the differential equations that govern the microclimate - cro p model, we used a library that support s an adaptive step - size, fourth - order Runge - Kutta method [39] . 4.3.2 Outdoor Climate Data Because Van thoor did not make available the weathe r data used in his research , we used a meteorological service [40] that uses weather prediction models to approximate the climate data for a specified date and locale namely, Almería, Spain, the location Vanthoor used in his thesis to evaluate his economic model. The latitude and longitude coordi nates and height above sea level wer e used as inputs to obtain hourly climate data for the same time periods in 2006 2009 . Outdoor CO 2 levels were obtained by interpolating 35 monthly global CO 2 measurements provided by the National Oceanic & Atmospheric Ad ministration [41] . T he average values of the output provided by the estimated weather is summarized in Table 4 . 2 . 4.3.3 Control Strategy Implementation Some assumptions were necessary for the controller implementation. Unless otherwise specified, all actuators operate on an on - off basis, including roof and side ventilation. First, the controller has an update in terval of five minutes. Sec ond, the boiler valve output is determined by a PID controller, with gain parameters (not shown) evolved ahead of time using NSGA - II, to match the fuel consumption costs reported by Vanthoor. Third, the thermal screen is retracta ble in two stages. Fourth, the fogging system operates for a maximum of 120 seconds in any five - minute interval. This is based on practice [42] to avoid wetting the leaves and potentially damaging the plants due to the salt content in the fogging 1 . 4.3.4 NSGA - II Initialization Evolution parameters can be seen in Table 4 . 4 . The parameters w ere pragmatically chosen based on the computing resources available and the size of the chromosome. Each simulation was run on a computer with two 2.4Ghz 14 - core Intel Xeon E5 - 2680v4 processors, for a maximum of 28 cores. Since the simulation is paralleliz ed by assigning one individual to each core, the population size is set to multiples of 28 to minimize do wntime from unused cores. The number of generations was determined based on the approximate amount that can be completed in 96 hours. Table 4 . 4 . NSGA - II parameters used for this study . Parameter Value Population size 28 - 84 Generations 360 - 1000 Two - point crossover probability 0.3 Uniform mutation probability 0.04 1 In some cases, we may show examples of evolv ed control strategies that assume that the fogging system can operate without any limitations (i.e., up to 5 minutes at a time). Such cases are only used for easier interpreta tion of results and will be labeled accordingly. 36 4.3.5 Chromosome Representation The chromo some consists of values stored in an integer vector that are converted to floating point values when used in the model. Before using a value from the chromosome, the integer value is converted to a floating - point number using the specified range and step s ize. This makes the search process more efficient by eliminating differences that are not significant in practice. Since the goal is to optimize greenhouse control setpoints, the chromosome simply consists of a combination of static setpoint valu es and the thresholds on climatic variables used to calculate the dynamic CO 2 setpoint. T AirVentOn defines the greenhouse air temperature above which roof and side ventilation is always open. Similarly, T AirVentOff defines the greenhouse air temperature be low which roof and side ventilation is always closed. RH AirVentOn is the greenhouse air relative humidity threshold above which ventilation is turned on. CO 2Air V ent On is the greenhouse air CO 2 concentration below which ventilation is turned on (to replenis h the gree nhouse air CO 2 concentration back to ambient levels) . T AirBoilOn is the greenhouse air temperature below which the boiler heating system is turned on. T Out ThScr O n is the outside air temperature below which the thermal screen is deployed. The dynamic CO 2 se tpoint is a function of: CO 2 AirExtMax , which determines the upper bound for the CO 2 setpoint, CO 2 AirExtMin , which determines the lower bound of the CO 2 setpoint an d I GlobMax , which determines the global radiation threshold above which the CO 2 setpoint reac hes its upper bound. Below that , the setpoint decreases linearly towards its lower bound with global radiation. The chromosome with its range of values and desired resolution can be seen in Table 4 . 5 . Table 4 . 5 . Chromosome representation. Values in this range are stored as integers after multiplication with an appropriate factor. Parameter Range Step Size T AirVentOn (°C) [10, 30] 0.1 T AirVentOff (°C) [10, 30] 0.1 RH AirVentOn [0.1, 1 ] 0.01 CO 2 AirV ent On (ppm) [100, 500] 0.1 T AirB oil O n (°C) [10, 30] 0.1 T OutThScrOn (°C) [10, 30] 0.1 CO 2 AirExtMax (ppm) [500, 1000] 0.1 CO 2 AirExtMin (ppm) [100, 500] 0.1 I GlobMax (W×m - 2 ) [200, 1000] 0.1 37 4.3.6 Fitness Function The fitness function consist Eq. ( 5. 1), divided into two objectives: the economic value of the crop yield and the variable costs. We use the negative of the crop value so that both objectives are treated as minimization problems. We use three consecutive growing seasons based on the estimate d weather data in the growing periods summarized in Table 4 . 6 , with a pair of objective values generated for each season. To determine the final values for each objecti ve, we choose the worst - case objective pair of all three (i.e., the year that yields the worst net financial result). Table 4 . 6 . Greenhouse simulation parameters used for evolving setpoints in Almería, Spain c ase stu of whitewash (W), a boiler heating system (H), a fogging system (F) and a CO 2 enrichment system (C) . Parameter Value Growing periods August 1 st , 2006 July 1 st , 2007 August 1 st , 2007 July 1 st , 2008 August 1 st , 2008 July 1 st , 2009 Simulation Length 334 days Coordinates Height above sea level 151 meters Greenhouse design WHFC 4.3.7 Post - Pareto Front Processing Once a satisfactory Pareto front is obtained, the fitness of each individual in the population is rec alculated weather ( sometimes called a validation step). The population is also sorted based on the net financial result, which allows us to easily prun e solutions that either perform worse than the original setpoints or otherwise fall below an acceptable threshold for net financial result . 4.4 Pareto Front, Validation Step and Sorting 4.4.1 Pareto Front The Pareto front is shown in Figure 4 . 2 , and it is compared with the original setpoint s based on a classical control strategy by Vanthoor [4] . Although not many solutions dominate the original setpoint s , the original is clearly not Pareto - optim al . O ptimizing with a larger population size of 84 was beneficial 38 despite the added computational cost per generation, as it contained a better distribution of non - dominated solutions with the same simulation time (96 hours). Figure 4 . 2 . Pareto front consisting of the evolved control setpoints compared against the original control setpoints. The worst - case net financial result of the original setpoint and two evolved setpoints is shown. 4.4.2 Validation Step To verify the efficacy of the evolved solutions, we test the output of the economic model when using a new season of estimated weather data from the same locale (2009 - 2010). The results for all four growing seasons are summarized in Table 4 . 7 and show that the evolved setpoints performed reasonably well with 39 Table 4 . 7 . - 2 ×year - 1 - - solution obtained from the Pareto front in Fig. 4. Net financial results (NFR) for all four years are added u p. Original Low Cost High Value Period Crop Value Var. Costs NFR Crop Value Var. Costs NFR Crop Value Var. Costs NFR 2006 - 2007 19.03 10.98 0.19 17.29 8.65 0.79 19.39 10.88 0.66 2007 - 2008 20.69 11.41 1.44 18.72 9.11 1.76 21.10 11.42 1.83 2008 - 2009 17.95 10.97 - 0.88 16.20 8.62 - 0.27 18.29 10.93 - 0.49 2009 - 2010 18.90 10.96 0.09 17.23 8.76 0.62 19.29 10.95 0.49 Total 0.85 2.91 2.49 4.4.3 Sorting Results Table 4 . 8 shows a partial list of the population after it is sorted by the net financial result. Th e larger population size was beneficial, as it was able to find solutions with a superior net financial result with greater frequency. The original setpoints yielded a worst - year NFR of - 0.88, so most of these results are superior all are superior for popu lation size 84, which is clearly preferable. Table 4 . 8 . Worst - - 2 ×year - 1 ) of the nine best evolved solutions (in terms of NFR) in optimization runs with different population sizes. NFR Pop. Size = 84 Pop. Size = 28 - 0.28 - 0.36 - 0.30 - 0.37 - 0.31 - 0.42 - 0.32 - 0.62 - 0.32 - 0.67 - 0.32 - 0.75 - 0.32 - 0.78 - 0.34 - 1.00 - 0.34 - 1.18 40 Table 4 . 9 . - - solution. Parameter Original Low - Co st High Yield T AirVentOn (°C) 23 22.5 22.5 T AirVentOff (°C) 20 26 24.6 RH air_vent_off 0.90 0.70 0.82 CO 2 air_vent_off (ppm) 200 171.6 164.3 T air_boil_on (°C) 16 10 15.7 T out_ThScr_on (°C) 18 16.3 16.7 CO 2 Air_ExtMax (ppm) 850 508.7 585.8 CO 2 Air_ExtMi n (ppm) 365 266.4 112.6 I GlobMax (W×m - 2 ) 500 875.8 206.2 4.4.4 Decision Making Since the worst - case measurements for the net financial result were all negative, these could all be However, these evolved setpoints still outperf orm the original setpoints, and depending on the planning horizon, the grower can consider other seasons that have a positive net financial result and assess whether the risk is worthwhile by considering the ne t financial result over multiple seasons. Fi gure 4 . 3 . High - yield solution control signals over a 24 - hour period. 41 Figure 4 . 4 . High - yield solution microclimate over a 24 - hour period. T_Out denotes the out side air temperature, T_Air denotes the greenhouse air temperature, CO 2 _Air denotes the CO 2 concentration of the greenhouse air and C_Ref denotes the current value of the dynamic CO 2 setpoint. Figure 4 . 5 . L ow - cost solution control signals over a 24 - hour period. 42 Figure 4 . 6 . Low - cost solution microclimate over a 24 - hour period. T_Out denotes the outside air temperature, T_Air denotes the greenhouse air temperat ure, CO 2 _Air denotes the CO 2 concentration of the greenhouse air and C_Ref denotes the curr ent value of the dynamic CO 2 setpoint. 4.5 Discussion In this chapter we showed that multi - objective evolutionary algorithms like NSGA - II can be used to aid in the desig n stage s of greenhouse constructi on by allowing optimiz ation of the control setpoints to enter into the evaluation of the various optional technologies to be deployed . In addition, these setpoints can be evolved between growing seasons as new data become a vailable and as input costs change. We found evolved control se tpoints that outperform the original setpoints in two objectives: maximizing the economic value of the cr op yield a nd minimizing the variable costs , even when using a new set of weather data th at w as no t used during the evolution ary optimization process. U sing estimated weather data as input to the microclimate - crop yield model produced outputs that were mostly similar to those , with s ome exceptions . Historical weat her data should ideally be used for more accurate estimates of the net financial result, but the estimated weather data w ere sufficient for validating the crop yield trends with respect to increasing technology levels, thus the evolved setpoints still prov ided useful information on how to improve the net financial res ult when considering the tradeoffs between the two conflicting objectives . For purposes of this chapter, the search space during the 43 evolution process was limited to 9 integer variables that de fine the setpoints for a fixed control strategy, but later chap ters will define more complex control strategies to evolve, as well as containing metrics to evaluate their performance vis - a - vis other control strategies. 44 5 Using Multi - objective Optimization to Evolve More Sophisticated Controllers T he contents of this cha pter are partially based on our prior published work, and can be found in [43] . The previous chapter covered the use of evolutionary computation to optimize the setpoin ts of a fixed greenhouse control strategy. Although the results show that we can evolve setpoints that dominate the original values that were based on expert knowledge, it assumes a rigid control strategy where the only changes possible are in the values o f the setpoints themselves. This was done to limit the search space during evolution and thus provide faster convergence towards a Pareto - optimal front, but this leaves open the possibility of testing additional incremental changes in complexity to seek im prove ments in performance. In this chapter w e propose a simple change to improve the sophistication of an existing control strategy allow ing it to adjust setpoints based on the time of day. In addition, we explore and discuss notable features present in th e evo lved controllers and propose a performance metric for comparing different evolved controller designs. NSGA - II and model implementation details remain the same as used in Chapter 4 unless otherwise specified. 5.1 Problem F ormulation The economic model inco rpora tes the fixed costs of greenhouse construction elements, the variable costs associated with growing the crop and the value of the crop itself. Based on [4] , the net financial result (NFR) is defined as: where Q CropYield - 2 ×year - 1 ) is the value of the tomato crop, Q Var - 2 ×year - 1 ) consists of the variable costs (costs associated with th e crop, resources used and labor), and Q Fixed - 2 ×year - 1 ) represents the cost of all tangible assets that do not depend on crop growth. 45 Eq. ( 5. 1), divided into two objectives: the economic value of the crop yield and the variable cost s, f 1 (x) and f 2 (x) , respectively. We use the negative of the crop value so that both objectives are treated as minimization problems, subject to a penalty function for solutions that have a net fin ancial result (NFR) that is inferior to the NFR of the orig inal setpoints used in the classical control strategy. In other words, solutions w ill no t be penalized if Original , where NFR Original is the worst - case net financial result of the original setpoints. In order to be able to compare with the orig inal Vanthoor data, we evaluate control strategies over three consecutive growing season s, based on example estimated weather data, which results in a pair of objective values being generated for each season. To determine the final values for each objectiv e, we choose the worst - case objective pair of all three (i.e., the year that yields the worst net financial result). The optimization problem is then defined as follows: where f 1 ( x ) = - Q CropYield and f 2 ( x ) = Q Var as defined in ( 5. 1). Although the optimization problem is unconstrained, solutions with inferior NFR will be penalized according to the following penalty function: Using ( 5. 3) as a scaling factor, the new values for the objectives are f 1 ( x ) = f 1 ( x )/ P ( x ) and f 2 ( x ) = f 2 ( x ) × P ( x ), respectively. Since f 1 ( x ) is minimizing the negative of the crop value, P ( x ) must be applied as a division operation to penalize that objective. Since the goal is to optimize greenhouse control setpoints, the chromosome simply consists of a combination of static setpoint values and the thresholds on climatic v ariables used to calculate the dynamic CO 2 setpoint. T AirVentOn defines the greenhouse air temperature above which roof and side ventilation is always open. Similarly, T AirVentOff defines the greenhouse air temperature below which roof 46 and side ventilation is always closed. RH AirVentOn is the greenhouse air relative h umidity threshold above which the ventilation is turned on. CO 2AirVentOn is the greenhouse air CO 2 concentration below which the ventilation is turned on. T AirBoilOn is the greenhouse air tempe rature below which the boiler heating system is turned on. T Out ThScr O n is the outside air temperature below which the thermal screen is deployed. The dynamic CO 2 setpoint is a function of: CO 2 AirExtMax , which determines the upper bound for the CO 2 setpoint , CO 2 AirExtMin , which determines the lower bound of the CO 2 set point, and I GlobMax , which determines the global radiation threshold above which the CO 2 setpoint reaches its upper bound. Below that, the setpoint decreases linearly with global radiation towa rds its lower bound. The chromosome with its range of values an d desired resolution can be seen in Table 5 . 1 . Table 5 . 1 . Chromosome representation. Values in this range are stored as i ntegers after multiplying by an appropriate factor. Parameter Range Step Size T AirVentOn (°C) [10, 30] 0.1 T AirVentOff (°C) [10, 30] 0.1 RH AirVentOn [0.1, 1] 0.01 CO 2 AirVentOn (ppm) [100, 500] 0.1 T AirBoilOn (°C) [10, 30] 0.1 T Out ThScr O n (°C) [10, 3 0] 0.1 CO 2 AirExtMax (ppm) [500, 1000] 0.1 CO 2 AirExtMin (ppm) [100, 500] 0.1 I GlobMax (W×m - 2 ) [200, 1000] 0.1 Using the controller discussed in Chapter 4 as a basis, we ask the following: if we would like to improve this con troller, would there be a considerable improvement in one or more objectives if we were to split the control strategy in s uch a way as to allow different setpoints based on the time of day? This time partitioning should, in theory, provide a greenhouse con trol strategy the ability to exploit weather patterns present during key parts of the day. For example, dawn is a critical moment for optimizing plant growth in greenhouses due to the transition from nighttime to daytime. Base d on temperature setpoints use d by classical control strategies, as well as existing knowledge of optimal temperature ranges for the tomato 47 crop [4] , i deal n ighttime temperature is significantly lower than the ideal temperature for photosynthet ic activity. To exploit this, we should ideally have setpoints defined that can quickly and efficiently transition between nighttime and daytime conditions, as well as h aving setpoints defined for other times of day that can evolve separately. A summary of such an approach is shown below in Figure 5 . 1 . Figure 5 . 1 . Introducing time partitioning to a greenhouse control strategy . 5.2 Methodology and Results Despite its known shortcomings, a nd because it is not computationally expensive for two - or three - objective problem s, we use the normalized hypervolume [44] as a performance metric for comparing different evolved controllers, choosing a nadir point of [0, 50] based on expected worst - case values. We apply a Mann - Whitney U test [45] with a sample size of n = 5 to determine if the time - partitioned controller is statistically significantly higher in the hypervolume performance metric compared to a 48 controller without a time - partitioning feature. Each sample consists of the resulting hypervolume of the final population after running N SGA - II for 100 generations while starting with a randomly initialized population. E volved solutions were also tested by simulating a new season of estimated weather data from the same loc ale . The results for all four growing seasons are summarized in Table 5 . 2 and show that the Examples of Pareto fronts from both evolved controllers a re shown in Figure 5 . 2 , and they are compared with the performance of classical setpoint s . Both evolved controllers contain solutions that dominate the se classical setpo int s , and the time - partitioned controller obtained better solutions in some regions of its Pareto front relative to the evolved controller without time partitioning. This is due to the time - partitioned controller having a chromosome that is triple in size compa red to the simpler counterpart, requiring more function evaluations to achieve the same performance. On the other hand, we can simply take advantage of the setpoints that the simpler controller uses to seed the time - partitioned controller, allowing us to a chieve better results without relying solely on the genetic algorithm itself (as shown in Figure 5 . 3 ). More details are available in S ection 5.4 . 49 Figure 5 . 2 . Overlapped Pareto fronts consisting of the evolved control setpoints (NTP, red) and the evolved con trol setpoints with time partitioning (TP, green) compared against classical control setpoints (blue). 50 Figure 5 . 3 . Example of control setpoints with time partitioning (TP, green) benefiting from seeding wit h evolved setpoints without time partitioning (NTP, red). The green strate gy. Table 5 . 3 shows a partial list of the populations of both evolved controllers after they are sorted by the net financial result. The original setpoints yielded a worst - year NFR of - 0.88; therefore, these results are superior a negative NFR would reflect that the gre enhouse would operate at a loss for that year. In addition, some of these solutions dominate the original setpoint (see Figure 5 . 2 ), so they are clearly preferable. 51 Table 5 . 2 . - 2 ×year - 1 olution and a s are added up. Original Low Cost High Value Period Crop Value Var. Costs NFR Crop Value Var. Costs NFR Crop Value Var. Costs NFR 2006 - 2007 19.03 10.98 0.19 17.29 8.65 0.79 19.39 10.88 0.66 2007 - 2008 20.69 11.41 1.44 18.72 9.11 1.76 21.10 11.42 1 .8 3 2008 - 2009 17.95 10.97 - 0.88 16.20 8.62 - 0.27 18.29 10.93 - 0.49 2009 - 2010 18.90 10.96 0.09 17.23 8.76 0.62 19.29 10.95 0.49 Total 0.85 2.91 2.49 Table 5 . 3 . Worst - - 2 ×year - 1 ) of the top eight evolved solutions (sorted by decreasing NFR), of a) the evolved controller and b) the evolved controller with time partitioning. Net Financial Result a) b) 0.194 0.387 0.175 0.364 0.167 0.354 0.166 0.347 0.163 0.344 0.154 0.340 0.153 0.328 0.116 0.324 5.3 Decision Making A grower could simply choose the top solution in a list sorted by net financial result (as seen in Table 5 . 3 ) . However, by observing the tradeoffs in a Pareto fr ont the grower has access to additional information to make more informed decisions. For example, a grower may want to opt for solutions that provide greater crop value (which, in this case, provide greater yield), so they can meet unusually high demand fo r a crop even if the current market price does not fully compensate for the increased variable costs. On the other hand, opting for non - dominated solutions with notably low variable costs provides the grower with more environmentally friendly solutions tha t can re duce water and fossil fuel usage. Although not shown, these variable costs may be broken down into their individual components such as 52 water costs, fossil fuel costs, CO 2 costs and labor costs. Examples of these solutions are shown in Table 5 . 4 . Table 5 . 4 . Original setpoints compared with setpoints of two evolved solutions: a low - cost solution and a high - yield solution. Para meter Original Low - Cost High - Yield T AirVentOn (°C) 23 22.5 22.5 T AirVentOff (°C) 20 26 24.6 RH air_vent_off 90 70 82 CO 2 air_vent_off (ppm) 200 171.6 164.3 T air_boil_on (°C) 16 10 15.7 T out_ThScr_on (°C) 18 16.3 16.7 CO 2 Air_ExtMax (ppm) 850 508.7 585.8 CO 2 Air_ExtMin (ppm) 365 266.4 112.6 I GlobMax (W×m - 2 ) 500 875.8 206.2 Figure 5 . 4 . High - yield - solution control signals in a 24 - hour period. 53 Figure 5 . 5 . High - yield - solution microclimate over an example 24 - ho ur period. T_Out is outside air temperature, T_Air is greenhouse air temperature, CO 2 _Air is CO 2 concentration of greenhouse air and C_Ref is current value of the dynami c CO 2 setpoint. Figure 5 . 6 . Low - cost - solution control signals in a 24 - hour period. 54 Figure 5 . 7 . Low - cost - solution microclimate over an example 24 - hour period. T_Out is outside air temperature, T_Air is greenhouse air temperature, CO 2 _Air is CO 2 concentration of greenhouse air and C_Ref is current value of the dynamic CO 2 setpoint. Figure 5 . 8 . Normalized hypervolume for the evolved , non - time - partitioned controller (red), and the evolved, time - part itione d controller (green). Figure 5 . 4 and Figure 5 . 5 show the control signals and greenhouse microclimate for a high - yield solution, while Figure 5 . 6 and Figure 5 . 7 show the control signals and greenhouse microclimate for a low - yield solution. The high - yield solution is characterized by a more aggressive CO 2 enrichment strate gy in which the dynamic CO 2 setpoint reaches its upper bound as soon as the global r adiation is above 206 (in this case) . This increases the value of the crop but also increases the variable costs in the process. The low - 55 cost solution has a significantly l ower setpoint for turning on the boiler, T AirBoilOn , which naturally reduces fossil fuel costs. This is accompanied by a more conservative CO 2 enrichment setpoint caused by a much higher value for I GlobMax , resulting in less frequent use and therefore redu ced variable costs overall. Both low - cost and high - yield solutions have a much highe r value for T AirVentOff , which results in roof and side ventilation remaining closed during hotter weather. Normally this setpoint is used to help conserve heat by sealing the greenhouse during cold weather, but in this case the higher setpoint is used to keep the greenhouse sea led up for longer periods of time, increasing the efficiency of CO 2 enrichment while relying on the fogging system for cooling. Th is process of finding patterns that emerge by means of using an optimization technique is called [46] . Since the non - time - partitioned cont roller has a much small patterns present in high - yield and low - cost solutions. However, this process was not considered for the time - partitioned controller. Auto mating some of the inno vization process would be preferable in this case, though it is beyond the scope of this thesis . Since the worst - case measurements for the net financial result were all positive in Table 5 . 3 , these could all be considere d financially viable solutions. However, even if they were negative, these evolved setpoints can still outperform the original setpoints as long as this value is greater , and depending on the planning hori zon, the grower can consider other seas ons that have a positive net financial result and assess whether the risk is worthwhile by considering the net financial result over multiple seasons. If the grower is obligated to pay the fixed costs for an already b uilt greenhouse , whether or not a crop is planted, it is still clearly advantageous to select the control setpoints that provide the best tradeoff between the two objectives . 5.4 Performance of the Time - Partitioning Feature The rationale for letting a contro ller choose setpoints based on the time of day is relatively straightforward: ideally the control strategy should take advantage of the characteristics that correspond to 56 the time of day i .e., to evolve separate setpoints for the periods in which sunrise, midday and sunset occur. Figure 5 . 2 shows that adding this time - partitioning feature to the evolved controller improves solutions in some regions of the Pareto front. It is trivially possible to eliminate all regions where the n on - time - partitioned controller dominated t he time - partitioned controller, simply by supplying the non - time - partitioned values to the time - partitioned controller for all the partitioned time periods. Time - partitioned solutions dominating the non - dominated s olutions were not discovered in some part s of Figure 5 . 2 because the expensive fitness function did not allow enough function evaluations with the triple - size chromosome to discover those settings. Instead of adding superfluous function evaluations to reach the same resul t , we took advantage of the modular nature of the time - partitioning feature: it was designed such that , if necessary, it can behave like a controller tha t does not change its setpoints based on the time of day by simply using identical sets of values for a l l times of day: morning, midday , and evening. An example Pareto front that takes advantage of this property was shown in Figure 5 . 3 . Despite the significant increase in the search space, the time - partitioned evolved controller ev e ntually outperforms its counterpart based on the hypervolume performance metric, showing solutions that the non - time - partitioned version has not produced (as seen in Figure 5 . 8 ) . This improvement is also reflected in Table 5 . 3 , due to the presence of solutions with greater NFR compared to the other evolved controller, and in Figure 5 . 2 , where we can observe regions where the time - partitioning feature produces solutions that dominate the other evolved controller. By running a Mann - statistica l significance of the difference in hypervolumes that results from adding this time partitioning feature. Results show that the two groups of hypervolume measurem e nts differed significantly ( U = 0, n 1 = n 2 = 5, P < 0.01, two - tailed), and the sample values are summarized in Table 5 . 5 . 57 Table 5 . 5 . Mann - Whitney U test results comparing groups of h y pervolumes, where a) is the no n - time - partitioned controller, while b) uses time - partitioning. Normalized Hypervolume s a) b) 0.347626963 0.352650132 0.347393334 0.351999245 0.346688732 0.351094193 0.346627517 0.350488993 0.346103962 0.349433818 5.5 Dis c ussion We restricted our study to two objectives primarily to ease visualization, but more objectives may be added. For example, tomato quality is a desirable characteristic that could conflict with both yield and energy costs. Moreover, the net financial result could be added as an objective. While sorting the Pareto front based on net financial result is a simple way to aid decision making, by not including this metric as an additional objective, we for e go one of NSGA - h is results in future generations. We also limited the scope of the simulations to using estimated weather data from the same dates and locale used in [4] (followed by an additional year). Future studies should use historical weather data when available and examine the effects of including a larger number of growing seasons during the evolution process as well a s the efficacy of this method for different dates and locales. In addition, other greenhouse design elements commonly used in tomato production should be included, such as pad - and - fan cooling and supplemental lighting. Although it is beyond the scope of t h is thesis , a logical extension of our proposed method is to optimize greenhouse designs alongside their climate control setpoints. Since different greenhouse designs will have different numbers of setpoints associated with them, an alternative multi - objec t ive evolutionary algorithm that supports variable length chromosomes should be u sed. In addition, the greenhouse setpoint optimization problem may be replaced with a more generic control strategy optimization problem. For example, a control strategy could be proposed in which setpoints are replaced by operating regions that 58 can be evo lved, similar to the concept of multi - objective compatible control [47] . Because of the potentially staggering implications in computational time, s ome model reductions in the microclimate - crop model may be necessary to make the se optimization problems practical. A member of the joint MSU - Tongji University Greenhouse Control team, Dr. Yuanping Su, has developed a control optimization strategy using a surrogate model and is currently preparing a manuscript for publication of this work. We have shown in this chapter that multi - objective evolutionary algorithms like NSGA - II can be used to aid the grower in the design stages of greenhouse construction by o ptimizing the control setpoints. These setpoints can be evolved between growing seasons as new data become available and as input costs change. We have found evolved control setpoints that outperform the original setpoints in two objectives: (i) maximizin g the economic value of the crop yield and (ii) minimizing the variable costs, ev en when using a new set of weather data that was not used during the evolutionary optimization process. The non - time - partitioned evolved controller has also been examined in m o re detail, showing some patterns in the feature space that may be useful as desi gn principles for future controller designs. In addition, evolving a set of time - partitioned setpoints has produced non - dominated regions that are better than their counterpar t s, and using their respective hypervolumes as a performance metric shows that th ere is a statistically significant difference between them. Important knowledge about the optimal solutions has also been identified and explained. Although effective for comp a ring two relatively simple control strategies, additional work is needed to test the efficacy of using hypervolume as a performance metric with more sophisticated controllers. 59 6 Analyzing Genotypes of Evolved Controllers 6.1 I ntroduction Th e goal of this chapte r is to explore the behavior exhibited by the evolved versions of the control strategies described in this thesis , discussing any notable properties displayed by these control strategies, and finding key areas for improvement . A total of four strategies ar e examined, each of which was evolved for 100 generations to obtain a population of 80 non - dominated solutions. After examining these four, we examine key changes on the best performing controller (with respect to Pareto - optimal ity) when introducing a crop value penalty for inadequate levels of relative humidit y . The chapte r presents in sequence the following controllers : Section 6.2: Evolved Vanthoor controller Section 6.3: Evolved Vanthoor controller with setpoint partitioning based on time Section 6.4 : Evolved Vanthoor controller with partitioning based on time and fruit set occurrence Section 6.5: Improved controller Section 6.6: Same improved controller with crop value penalty for sub - optimal relative humidity Controller implementation details ar e summarized in Table 6.1. Values that required some assumptions to implement are denoted with an asterisk (*). More information on how greenhouse control strategies are defined and implemented can be found in Chapters 4 and 5 . 60 Table 6 . 1 . General c ontroller implementation and ODE solver details. These values are shared among all controllers described in this chapter unless o th erwise specified. Parameter Description Parameter name/symbol Unit Range Boiler heating U Boil - [0, 1] CO 2 injection system U Ext CO2 - [0, 1] Fogging system U Fog - [0, 0.2]* External shading screen U ShScr - [0, 1] Semi - permanent shading screen (white wa sh) U ShScrPer - [0.5, 1]** Thermal screen U ThScr - [0, 1] Roof and side ventilation system U Roof , U Side , U Vent - [0, 1]*** Controller update interval - Minutes 5 Greenhouse climate simulation step size (initial) - Seconds 10 Greenhouse crop yield si mu lation step size (initial) - Seconds 60 RK4 ODE solver absolute error - - 0.01 RK4 ODE solver relative error - % 1 * Upper bound for U Fog was assumed based on prior strategies established in literature to help reduc e the potential of burns on the cro p leaves due to the salt content of the water supply [42] . This will be enforced unless otherwise spec if ied. ** Although modeled internally as a control va riable, it is assumed that U ShScrPer is always a whitewash that is applied manually based on seasonal needs and the current greenhouse design. This is consistent is variable. Since it acts as a multiplier for the gr overall light transmissivity, it cannot be zero. *** It is assumed that both roof and side ventilation are controlled concurrently whenever ventilation is needed to remain consistent with the de scription and behavior of the control strategy base thesis. The combined value of these window apertures will be referred to as U Vent . 61 The loci shown here are examined against only one objective (the crop yield value) for ease of visualiza ti on. In the figures in this chapter that plot evolve d setpoints and/or variables against their corresponding crop yield value s , solutions which dominate the classical Vanthoor control strategy with default setpoints are marked in green ( * ). The controller s examined in this chapter are presented in order of increasing performance unless otherwise specified , with each one consistently yielding similar Pareto - optimal fronts when using identical NSGA - II configuration settin gs. Figure 6 . 1 contains an example of the Pareto - optimal front that each controller type yields. Figure 6 . 1 . Pareto - optimal fronts for the evolved control strategies in this chapter, with a classical strategy using def au lt setpoints for reference. Red circles represent the classical strategy with evolved setpoints (NTP). Green circles represent t he classical strategy with setp oint partitioning based on time (TP). Blue circles represent a similar strategy that adds setpo in t partitioning based on both time and plant development stage, but also uses sunrise and sunset calculations to transition betw een nighttime and daytime strate gies (TP+). Purple setpoints represent a control strategy with all the previous features, addit io nal control logic, additional nighttime setpoints, and PID control for fogging, heating, and ventilation systems (TP++). 62 6.2 Evolved Classical Controller (No T im e P artitioning) 6.2.1 Introduction This controller is based on a classical control strategy describe d by Vanthoor in his thesis [4] , with the main difference being that most of the setpoints pertaining to greenhouse control are evolved. A summary of the behavior of the cont rol strategy is shown in Figure 6 . 3 . Since this control strategy needs to differentiate between daytime and nighttime to determine whether the thermal screen should be deployed, nighttime has been defined as the absence of global radiation (i.e., I Glob = 0). The chromoso me and its range of values is given in Table 6 . 2 . Figure 6 . 2 . Pareto - optimal front for the control strategy discussed in this section. Solutions from this Pareto front which also do mi nate the classical Vanthoor strategy are marked in green. 63 Figure 6 . 3 . Classical control strategy example. Based on the current greenhouse air temperature, the controller will take different actions to mai nt ain an o ptimal temperature range for the crop, as influenced also by CO 2 concentration and relative humidity in the greenhouse . [4] 64 Table 6 . 2 . Chromosome containing t he setpoints used in the evolved classical controlle r . The genotype cons ists of 9 integer values. Parameter Description Parameter name/symbol Unit Genotype Value Range of Real Values Temperature above which ventilation (U vent ) is turned on T AirVentOn De gr ees (Celsius) [100, 300] [10, 30] Temperature below which ventilation is turned off T AirVentOff Degrees (Celsius) [100, 300] [10, 30] Relative humidity above which ventilation is turned on RH AirVentOn % [10, 100] [10, 100] CO 2 concentration below whic h ventilation is turned on CO 2AirVentOn ppm [1000, 5000] [100, 500] Temperature below which the boiler (U Boil ) is turned on T AirBoilOn Degrees (Celsius) [100, 300] [10, 30] Nighttime temperature below which the thermal screen (U ThScr ) is deployed T OutThS cr On Degrees (Celsius) [100, 300] [10, 30] Upper bound for dynamic CO 2 setpoint* CO 2AirExtMax ppm [2000, 10000] [200, 1000] Lower bound for dynamic CO 2 setpoint* CO 2AirExtMin ppm [1000, 5000] [100, 500] Global radiation above which the dynamic CO 2 setpo in t is maximized* I GlobMax W/m 2 [2000, 10 0 00] [200, 1000] * These variables are used for the calculation of the dynamic CO 2 setpoint, CO 2AirExtOn . See Eq. (6.1) for more details. 65 Figure 6 . 4 . This setpoin t determines the temperature above which the greenhouse controller will keep the ventilation open. 6.2.2 T AirVentOn Figure 6 . 4 shows a relatively wide range of values (between 10 25 degrees Celsius ) that still produce non - dominated sol ut ions. However, the temperature at which the ventilation opens unconditionally is closely tied with its counterpart T AirVentOff in particular, T AirVentOf f can override T AirVentOn when the value is large enough, creating a strategy conditionally which prev en ts the greenhouse from opening based on sub - optimal levels of humidity or CO 2 . T his is because the classical strategy normally contains a temperature gap between T AirVentOff and T AirVentOn ( see Figure 6 . 3 ), but here, these setpoi nt s can evolve in such a way that the gap is eliminated. Without this gap, the greenhouse will remain sealed for longer periods of time, allowing for CO2 injection to occur uninhibited. 66 Figure 6 . 5 . This set po int d etermines the temperature below which the ventilation will always remain closed. 6.2.3 T AirVentOff T he evolved values in Figure 6 . 5 clearly show a trend where increasing the temperature setpoint can produce greater c rop yields at the expense of increased costs. These high - temperature setpoints cause the greenhouse to stay sealed for longer periods of time where CO 2 injection can continue uninterrupted, while relying on active cooling measures (a fogging system in th is case) to maintain the tomato crop within optimal temperature ranges. Since nearly all the Pareto - optimal points are at or near 26 degrees Celsius , it is clear that the added crop yield benefit of keeping the greenhouse closed and injecting CO 2 outweighs t he additional energy cost of the CO 2 and the cooling required. Moreover, all the solut ions which dominate the classical Vanthoor strategy are at or near 26 degrees Celsius . This makes the process of choosing the value for T AirVentOff fairly straightforwa rd , since the same value of 26 degrees Celsius would be used with the notable exception of tradeoff solutions that prioritize lower variable costs (at the expense of lower crop - yield value) , but such strategies are outperformed in terms of net financial re tu rn by the classical Vanthoor strategy. 67 Figure 6 . 6 . This setpoint determines the relative humidity above which ventilation is conditionally turned on. 6.2.4 RH AirVentOn Th is value is only used when the greenhous e air temperature is between T AirVentOff and T AirVentOn , as shown in Figure 6 . 3 , and only when T AirVentOff is also less than T AirVentOn . We can see in Figure 6 . 6 that there is a wide range of values among t he non - dominated solutions. The cause for this lack of pattern is that the setpoints T AirVentOff and T AirVentOn can evolve values in some controllers on the Pareto front that are very close to each ot her, ultimately causing R H AirVentOn to become unutilized due to the lack of the AirVentOff and T AirVentOn . Ordinarily, in real - world greenhouse practice, this setpoint would be af fected by checking for sub - optimal levels of humidity, b ut there is clearly not enough pressure either in the crop model or in the economic model as developed by Vanthoor to maintain optimal humidity levels. Vanthoor addressed this later by proposing quali ty filters on the crop yield with the goal of describing t he impact humidity has on the price and marketability of tomatoes [4] . The effect of such a quality filter on the controller behavior is summarized later in this chapter (see Section 6.6 ). 68 Figure 6 . 7 . This setpoint determines the greenhouse air CO 2 concentration below which ventilation is conditionally turned on. 6.2.5 CO 2AirVentOn S imilar t o Figure 6 . 6 , CO 2 AirVentOn i n Figure 6 . 7 contains a wide range of values among the non - dominated between T AirVentOff and T AirV entO n , or invert the two. However, unlike RH AirVentOn , the effects of CO 2 concentration on the crop are described in detail in the crop model, and this setpoint is meant to be used when the greenhouse air CO 2 concentration can be improved by ventilatin g th e greenhouse with outside air (which would be an unusual occurrence, especially when CO 2 injection is available). 69 Figure 6 . 8 . This setpoint determines the temperature below which the greenhouse contro lle r wi ll turn on the boiler heat ing. 6.2.6 T AirBoilOn This setpoint shows a straightforward trend (in Figure 6 . 8 ) among non - dominated solutions: a higher setpoint will increase cost s while increasing the value of the crop yield. Evolved so lutions do not exceed 20 degre es Celsius for the setpoint, after which those solutions are no longer non - dominated due to excessive crop growth inhibition caused by excessive heating. Solutions which dominate the classical Vanthoor strategy are at or ne ar 15 17 degrees Celsius . The c lassical V anthoor strategy uses 16 degrees Celsius for this setpoint, suggesting that only minor adjustments were needed to achieve better results. 70 Figure 6 . 9 . This setpoint de termines the outside temperatu re below w hich the greenhouse controller will deploy the thermal screen. 6.2.7 T OutThScrOn As seen in Figure 6 . 9 , m ost non - dominated solutions settle with this setpoint between 17 17. 5 d egrees Celsius , so values close to the value used in the classical Vanthoor strategy (18 degrees Celsius ). Since the purpose of the thermal screen is to conserve heat during the nighttime, the ideal value for this setpoint must strike a balance between a) keeping the plants warm enough to stay close to t he ideal instantaneous and 24 - hour mean temperature ranges set by the plant growth model and b) minimizing maintenance respiration caused by said warm temperatures. 71 Figure 6 . 10 . This variable determines the upper bound for the dynamic CO 2 setpoint used during CO 2 injection. 6.2.8 CO 2AirExtMax Figure 6 . 10 shows a wide variety of values among the non - dominated solutions. There is some clust ering near the lower a nd upper bounds defined for th is value, which allow for low - cost and high - yield solutions, respectively. This value is part of the calculation for the variable C O 2 setpoint defined by Vanthoor [4] , and is shown in Eq. ( 6. 1) below: E q. ( 6. 1) shows how the setpoint for opening vents to bring in atmospheric CO 2 is calculated, as a fun c tion of the incident global radiation and the current positioning of the vents. Functions f and g assume their maximum values (at 1.0) when global radiation is at the maximum value for photosynthetic yield and the U V ent is fully closed . At that point, the setpoint CO 2AirExtOn assumes the value CO 2AirExtMax , which maximally inhibits the opening of the air vents (which would move the CO 2 concentration toward atmospheric values) . This makes sense because if global rad iat ion is low, there i s no need to supply m ore CO 2 even if it is relatively low in the greenhouse, and if the vents are mostly closed (so g is near 1), then supplementary CO 2 can be added to greater effect than opening the vents would produce, so the thres hol d for opening the v ents to admit CO 2 sh o uld be raised. Thus, the setpoint for CO 2AirExtOn increases with 72 higher global radiation (I Glob ) and lower ventilation opening (U Vent ). CO 2AirExtMax defines the upper bound for the setpoint (as the difference betw een itself and CO 2AirE xtMin ), and CO 2AirEx t Max defines the lower bound. Therefore, it logically follows that increasing this value will increase the value of the crop yield at the expense of increased costs due to additional CO 2 injection, since raising it ke eps the greenhouse closed more of the t i me, requiring CO 2 addition in order to increase crop value. Figure 6 . 11 . This variable determines the lower bound for the dynamic CO 2 setpoint used during CO 2 inje ction. 6.2.9 CO 2AirExtMin Wi th some exceptions, m ost values in Figure 6 . 11 form a c luster near the lower bound, keeping it consistently low, while CO 2AirExtMax and I GlobMax define whether the strategy is tailored towards a low - cost or hi gh - yield solution. Bas ed on Eq. ( 6. 1) , thi s value ensures that CO 2 injection does not occur in conditi ons where it would be wasteful to do so. Specifically, in cases where evolved values of CO 2AirExtMin are low enough to result in a CO 2 setpoint (i.e., CO 2 AirExtOn ) that is belo w ambient levels, it will lead to CO 2 injection being disabled. 73 Figure 6 . 12 . This variable determines how quickly is maximized, and subsequently contributes to how qu ickly the dynamic CO 2 setpoint (CO 2AirExtO n ) is maximized. 6.2.10 I GlobMax Similar to CO 2AirExtMax , there a re a wide range of solutions for I GlobMax in Figure 6 . 12 that cluster near the lower and upper bounds defined for this value, which also define whether t he control strategy i s tailored towards a low - cost or high - yield solution: a low - cost solution would have a higher I GlobMax , and a high - yield solution would have a low I GlobMax . Solutions that dominate the classical Vanthoor strategy use a value for I GlobM ax that ranges from 2 50 600 W/m 2 (compared to the classical Vanthoor strategy which uses 500 W/m 2 ), suggesting that it i s generally more optimal to use a lower value for I GlobMax , causing the dynamic CO 2 setpoint to be maximized wit h less global radiatio n. 6.2.11 Discussion Overal l , the solutions that dominate the classical unevolved strategy do not form a set pattern other than fitness val ues for the unevolved str ategy are also lo c ated near that region ( s ee Figure 6 . 1 ). The values for CO 2AirVentOn and RH AirVentOn did not form a clear pattern as they were typically not used (due to the presence of many evolved soluti ons where T AirVentOn i s less than T AirVent O ff ). Similarly, T AirVentOn contained a 74 wide range of values that yielded non - dominated solutions without a clear pattern due to T AirVentOff being greater, a situation that res ult s in T AirVentOn being largely unuse d by the control logic . Increasing T AirBoi l On increased the value of the crop yield as expected, but also formed an interesting cut - off point right below 20 °C; increasing the temperature further did not provide any no n - dominated solutions. Finally, the va lues that determine th e dynamic CO 2 setpoi n t show that a grower who wants to calibrate the rate of CO 2 injection towards low - cost solutions sh ould lower CO 2AirExtMax and increase I GlobMax , while the converse is true for high - yield solutions. With some exce ptions, CO 2AirExtMin r emained consistently very low, which helps minimize costs by preventing wasteful CO 2 injection. Based on the controller logic, CO 2 injection is never actually disabled; the setpoint is simp ly adjusted at every time step to determine i f CO 2 injection occurs . Since Eq. ( 6. 1) is reduced to CO 2AirExtMin under the worst conditions (i.e., no global radiation, U Vent > 0.1), the value for CO 2AirExtMin should ideally be low enough that it would never trigger CO 2 injection under these conditions . Pragmatically speaki ng, the values for C O 2AirExtMin were all significantly below atmospheric levels to avoid wasteful CO 2 injection (atmospheric CO 2 values in Almería, Spain exceed 380ppm for the period simula ted in this thesis [48] ). 75 6.3 Evolved Classical Controller ( Added T ime P artitioning ) 6.3.1 Introduction Figure 6 . 13 . Pareto - optimal front for the control strategy dis cussed in this section . Solutions from thi s Pareto front which also dominate the classical Vanthoor strategy are marked in green. This controller is based on a classical co ntrol strategy described by Vanthoor in his thesis [4] , with the main differences b e ing that most of the setpoints pertaining to greenhouse control are evolved. In addition, two additional copies of these setpoints are generated to be used in different tim e periods eac h day , yielding a total of th ree : morning (M) , midd ay (D) , and evening (E) . The names of each variable or setpoint with these types of copies will have the abbreviations for these time periods appended to them (e.g. T AirVentOn becomes T AirVentOnD for the m idday copy of this setpoint). A summary of the chro mosome and its rang e of values is in Table 6 . 3 . With the addition of the three d istinct daytime periods , there are now a total of four time periods (including nighttime). The daytime periods will begin and end at fixed points as de fined in Table 6 . 4 , 76 based on the number o f hours that have passed by since midnight for each day. N ighttime is still defined as the absence of global radiation for purposes of this control strategy (i.e., I Glo b = 0) . Since the ther mal screen is the o n ly greenhouse design element with distinct nig httime setpoints , and the greenhouse controller still needs to check whether boiler heating, fogging or ventilation is needed during nighttime , the greenhouse controlle r will simply choose t he setpoints that a r e needed based on the current time (e.g., if t he current time is 22:30 and the greenhouse controller is checking whether boiler heating is necessary , T AirBoilOn E evening will be used ). 77 Table 6 . 3 . Chromosome containing the setpoints used in th e evolved classical controller with setpoint partitioning based on time of day . The genotype consists of 27 integer values. Parameter Description Parameter name/symbol Unit Genotype Value Ra nge of Real Values Temperature above which ventilation (U vent ) is turned on T AirVentOnM, T AirVentOnD, T AirVentOnE Degrees (Celsius) [100, 300] [10, 30] Temperature below which ventilation is turned off T AirVentOffM, T AirVentOffD, T A irVentOffE Degrees (Ce lsius) [100, 300] [ 1 0, 30] Relative humidity above which ventil ation is turned on RH AirVentOnM, RH AirVentOnD, RH AirVentOnE % [10, 100] [10, 100] CO 2 concentration below which ventilation is turned on CO 2AirVentOnM, CO 2AirVentOnD, CO 2AirVentOnE ppm [1000, 5000] [100, 500] T emperature below which the boiler (U Boil ) is turned on T AirBoilOnM, T AirBoilOnD, T AirBoilOnE Degrees (Celsius) [100, 300] [10, 30] Nighttime temperature below which the thermal screen (U ThScr ) is deployed T OutThSc rOnM, T OutThScrOnD, T O utThScrOnE Degrees ( Celsius) [100, 300] [10, 30] Upper bound for dynamic CO 2 setpoint CO 2AirExtMaxM, CO 2AirExtMaxD, CO 2AirExtMaxE ppm [2000, 10000] [200, 1000] Lower bound for dynamic CO 2 setpoint CO 2AirExtMinM, CO 2AirExtMinD, CO 2Ai rExtMinE ppm [1000, 50 00] [100, 500] Glo b al radiation above which the dynamic CO 2 setpoint is maximized I GlobMaxM, I GlobMaxD, I GlobMaxE W/m 2 [2000, 10000] [200, 1000] 78 Table 6 . 4 . Different times of day as de fined in the greenhous e controller logic i n this section . If the greenhouse controller detects nighttime due to lack of global radiation (i.e., I Glob = 0), either morning or evening setpoints will be used (depending on the current time). Parameter Descript ion Subscript T IME M O RNING PERIOD M 00:0 0 08:59 M IDDAY PERIOD D 09:00 16:59 E VENING PERIOD E 17:00 23:59 Figure 6 . 14 . This setpoint determines the temperature above which the greenhouse controlle r will keep the ventil ation open. 79 6.3.2 T AirVe n tOn Figure 6 . 14 contain s a relatively wide range of values (between 10 28 degrees Celsius , depending on the time of day) that produce non - dominated solutions. S imil ar to the controller de scribed in Section 6.2 , the temperature at which the ventilation opens unconditionally is closely tied with its counterpart, T AirVentOff (d ue to its ability to override T AirVentOn in cases where it evolves to be greater). Howeve r, there is a bias tow ards lower temperat u res during daytime which was not present without the time - partitioning feature. Many of these are overridden by T AirVentOff , but most low - cost, low - crop - yield solutions will use a very low value for T AirVentOnD to ventilate the greenhou se when solar radia t ion is known to be at its highest (therefore contributing to higher greenhouse air temperatures which may require cooling ) . 80 Figure 6 . 15 . This setpoint determines t he temperature below w hich the ventilatio n will always remain closed. 6.3.3 T AirVentOff T he evolved values in Figure 6 . 15 clearly show a trend where increasing the temperature setpoint can produce greater crop yields at the expense of in creased cooling costs . Moreover , the add i tion of the time - partitioning featur e allowed for the evolved setpoints to better exploit the times of day where solar radiation is at its peak. Values for T AirVentOff corresponding to h igh - crop - yield solutions peak at a higher temperatu re during the dayt i me (T AirVentOffD ), while also peakin g at lower temperatures during the evening 81 (T AirVentOffE ), helping reduce plant respiration. Lastly, evolved solutions which dominate the classical Vanthoor strategy all prioritiz e higher temperatures. Figure 6 . 16 . This setpoint determines the relative humidity above which ventilation is conditionally turned on. 6.3.4 RH AirVentOn Figure 6 . 16 shows that, much like with the previous cont roller in Section 6.2 , a wide range of values work reasona bly well for both low - cost and high - crop - value control strategies. The addition of the time - partitioning did not change this tendency, suggesting th at crop yie ld model does not 82 s ufficiently penalize inadequate levels of relative humidity, since we know that, in practice, humidity control is important : if values for RH Air are too low, the high vapor pressure deficit (VPD) associated with it can induce high stomat al resistance and p lant water stress (PWS), while excessively high values for RH Air an d low VPD may reduce growth due to low transpiration (that can lead to physiological disorders), as well as disease if condensation occurs [49] . Figure 6 . 17 . This setpoint determines the greenhouse air CO 2 concentration below which ventilation is conditionally turned on. 83 6.3.5 CO 2 AirVentOn Figure 6 . 17 show s a wide range of values that yield both low - cost and high - crop - value solutions, although this value ends up mostly unused (similar to RH AirVentOn ) , due to the evolved values for T AirVentOff discussed in Section 6.3.3 being grea t er than T AirVentOn in most cases, res ulting in evolved control strategies that disable the logic that checks for this value (see Figure 6 . 3 ). Figure 6 . 18 . This se tpoint determines the temperature below which the greenhouse controller will turn on the boiler heating. 84 6.3.6 T AirBoilOn The evolved setpoint s in Figure 6 . 18 show a similar trend to that of T AirBoilOn in Section 6.2.6 , althou g h there is a clear difference in the upper bound for high - crop yield solutions depending on the time of day . Morning setpoints are significantly lower and do not exceed 16 degrees Celsius . Daytime setpoints are highe r and reach almost 26 degrees Celsius . E vening setpoints are also higher, reaching almost 24 degrees Celsius . These trends show that i t is advantageous to change the boiler setpoint based on different times of day ( a s defined in Table 6 . 4 ) if higher yie lds are desired. M oreover, solutions that dominate the classical Vanthoor strategy have a significantly lower value for this setpoint during the morning and daytime p eriods ( n earing as low as 10 degrees Celsius ). 85 Figure 6 . 19 . This setpoint determines the outside temperature below which the greenhouse controller will deploy the thermal screen. 6.3.7 T OutThScrOn For simulation purposes, nighttime is defined by the absence of solar radiation (i. e. I Glob = 0) so it is possible, though very unlikely, for this setpoint to be used during the day. The values during the morning and evening time periods in Figure 6 . 19 are very similar to those discussed in Section 6.2.7 . Howev er, the values du r ing the midday (D) period are significantly different and predominantly random due to this setpoint having no impact on greenhouse control unless it is nighttime. 86 Figure 6 . 20 . This variabl e determines the u pper bound for the dynamic CO 2 setpoint used during CO 2 injection. 6.3.8 CO 2AirExtMax Figure 6 . 20 shows the evolved values for this variable are largely similar to those discussed in Section 6.2.8 . However, there is a marginal increase in the upper bound for CO 2AirExtMax during the daytime and evening, indicating that it is advantageous to change the upper bound for the dynamic CO 2 setpoint (CO 2AirExtOn ) based on the time of day. 87 Figure 6 . 21 . This variable determines the lower bound for the dynamic CO 2 setpoint used during CO 2 injection. 6.3.9 CO 2AirExtMin Figure 6 . 21 shows the evolved values for this variabl e are largely similar to th ose discusse d in Section 6.2.9 . However, daytime values for CO 2AirExtMin are marginally higher for high - crop - yield solutions , indicating that it is advantageous to change the lower bound for the dynamic CO 2 setpoint (CO 2AirExtO n ) based on the t i me of day. 88 Figure 6 . 22 . This vari able determines how quickly is maximized, and subsequently contributes to how quickly the dynamic CO 2 setpoint is maximized . 6.3.10 I GlobMax Figure 6 . 22 shows the evolved values for this variable are largely similar to those discussed in Section 6. 2. 10 , with daytime values for I GlobMax being overall higher for high - crop - yield solutions. Since i ncreasing I GlobMax will cause the dynamic CO 2 setpoint (CO 2AirExtOn ) to be maximized more slowly (see Eq. 6. 1) , it will reduce the benefits of CO 2 injection o n crop yield . This can be counterproductive for high - crop yield solutions in some cases . However, since the overall crop - yield values are higher, and the 89 overall variable costs are lower (compared to the evolved classical strategy without time - partitioning ), which is more indicative of a control strategy that is producing higher crop yields through ot her means (i.e., better control of optimal temperature ranges, longer periods of time where CO 2 injection is available due to closed ventilation, etc.), rather than a potentially sub - optimal CO 2 setpoint . 6.3.11 Discussion T here is a clear advantage to introducin g the time - partitioning feature to the classical controller. The resulting Pareto - optimal front is consistently superior , particularly when taking advantage of seeding ( as seen in Figure 5 . 3 ), and the loci themselves show some interesting patterns that emerged from this feature. The main benefit provided by time - partitioning is the ability for the greenhouse controller to apply va rious m ethods for saving energy without sacrificing crop yield, particularly when it comes to transitions from nighttime to daytime and vice versa. For example: the boiler setpoint, T AirBoilOn , the temperature below which the boiler is turned on, is much h igher d uring the daytime period when examining high - crop - yield solutions. This results in increased heating costs for that period, but it better exploits the high levels of solar radiation (I Glob ) that are typically present during that time. Conversely, mo rning a nd evening values are much lower, since photosynthetic activity is typically lower during these times, and maintaining optimal temperatures during that period is not as beneficial in comparison. Without time - partitioning, the greenhouse controller i s force d to use a single setpoint that is adequate for all times of day, thus limiting its usefulness. Some setpoints proved to be redundant with the addition of time - partitioning (i.e., T OutThScrOn ). One notable limitation for this controller is that the time of day is static (see definitions for morning, daytime, and evening in Table 6 . 4 ). This leads to evolved controllers that are unable to account for the changes in sunrise and sunset times throughout the year, which can limit their ab ility to accurately transition to daytime and nighttime strategies, respectively. Subsequent controllers in this chapter take this into account by calculating times for sunrise and sunse t as transition points for the controller . Finally, while there are cl ear benefits to adding the time - partitioning feature, this is not just due to exploiting the 90 presence of climate patterns that emerge on a day - to - day basis; it is clearly advantageous to evolve as many copies of a setpoint as possible (as long as it is com putationally feasible). To this end, the next section discusses a controller that also contains setpoints and variables which are evolved separately for two major stages of tomato crop d evelopment; namely, before and after fruit set has occurred. 6.4 Evolved C ontroller ( Additional Features ) 6.4.1 Introduction This controller is similarly based on a classical control strategy described by Vanthoor in his thesis [4] , with the main differences being that most of the setpoints pe rtaining to greenhouse control are evolved. In addition, the following features have been ad ded: 1. Setpoint partitioning based on time of day 2. Setpoint partitioning based on fruit set occurrence 3. Nighttime period is determined by sunrise and sunset calculation s 4. Adjustable time offset to determine transition point between nighttime and daytime strateg ies (e.g. , the thermal screen, T OutThScrOn , is only used during nighttime) Due to the added features, the figures in this section will display up to six copies of o ne setpoint, depending on the time of day and whether or not fruit set has occurred. In addi tion, morning and evening periods will be dynamic: 1) for the morning (M) , the current time for sunrise will determine the start of this period, and 2) for the even ing (E) , the current time for sunset will determine the end of this period. The midday (D) p eriod remains static. Figure 6 . 24 shows an example of how a typical 24 - hour period is partitioned using this method. If a s etpoint or variable contains a copy to be used after fruit set, the corresponding abbreviation (_fr) wi ll be appended to the end of the name, in addition to the abbreviations used to denote the time period (e.g. T AirVentOn becomes T AirVentOnM_fr to denote the morning, post - fruit - set copy of this setpoint). The time offsets (sr_offset, and ss_offset, respect ively) allow the controller to adjust the period in which a nighttime strategy is applied. A flowchart showing how these variables are 91 used can be seen i n Figure 6 . 26 . Lastly, a summary of the chromosome containing these changes can be seen in Table 6 . 5 . Figure 6 . 23 . Pareto - op timal front for the control strategy discussed in this section. Solutions from this Pareto front which also dominate th e classical Vanthoor strategy are marked in green. 92 Figure 6 . 24 . The greenhouse control ler differentiates between daytime and nighttime to determine whether the thermal screen should be deployed, which is only used during nighttime. Both sr_offset and ss_offset are evolved values which will modify the overall length of both nighttime and day time control strategies. These offsets remain fixed for each control strategy, while sunrise and sunset times (shaded region) change over the course of the year. Figure 6 . 25 . Sunrise/sunset tim es and averag e outside air temperatures calculated for the Almería, Spain location in 2006. 93 Figure 6 . 26 . Flowchart describing the process for determining whether daytime or nighttime strategies are used. 94 Table 6 . 5 . Chromosome containing the setpoints used in the evolved classical contro ller, with additional features . The total size of the genotype consists of 58 integer values. Parameter Description Parameter name/symbol Unit Genotype Value Range of Real Values Temperature above which ventilation (U vent ) is on T AirVentOnM, T AirVentOnD, T AirVentOnE, T AirVentOnM_fr, T AirVentOnD_fr, T AirVentOnE_fr Degrees (Celsius) [100, 300] [10, 30] Temperature below which ventilation is off T AirVentOffM, T AirVentOffD, T AirVentOffE, T AirVentOffM_fr, T AirVentOffD_fr, T AirVentOffE_fr Degrees (C elsius) [100, 300] [10, 30] Relative humidity above which ventilation is on RH AirVentOnM, RH AirVentOnD, RH AirVentOnE, RH AirVentOnM_fr, RH AirVentOnD_f r, RH AirVentOnE_fr % [10, 100] [10, 100] CO 2 concentration below which ventilation is on CO 2AirVentOnM, CO 2AirVentOnD, CO 2AirVentOnE, CO 2AirVentOnM_fr, CO 2AirVentOnD_fr, CO 2AirVentOnE_fr ppm [1000, 5000] [100, 500] Temperature below which the boiler (U Bo il ) is on T AirBoilOnM, T AirBoilOnD, T AirBoilOnE, T AirBoilOnM_fr, T AirBoilOnD_fr, T AirBoilOnE_fr Degrees (Celsius) [100, 300] [10, 30] Nighttime temperature below which the thermal screen (U ThScr ) is deployed T OutThScrOnM, T OutThScrOnD, T OutThScrOnE, T OutT hScrOnM_fr, T OutThScrOnD _fr, T OutThScrOnE_fr Degrees (Celsius) [100, 300] [10, 30] Upper bound for dynamic CO 2 setpoint CO 2AirExtMaxM, CO 2AirExtMaxD, CO 2AirExtMaxE, CO 2AirExtMaxM_fr, CO 2AirExtMaxD_fr, CO 2AirExtMaxE_fr ppm [2000, 10000] [200, 1000] Lower bound for dynamic CO 2 setpoint CO 2AirExtMinM, CO 2AirExtMinD, CO 2AirExtMinE, CO 2AirExtMinM_fr, CO 2AirExtMinD_fr, CO 2AirExtMinE_fr ppm [1000, 5000] [100, 500] Global radiation above which the dynamic CO 2 setpoint is maximized I GlobMaxM, I GlobMaxD, I GlobMaxE , I GlobMaxM_fr, I GlobMaxD_fr, I GlobMaxE_fr W/m 2 [2000, 10000] [200, 1000] Amount to subtract from calculated sunrise time sr_offset, sr_offset_fr Minutes [0, 30] [0, 150] Amount to subtract from calculated sunset time ss_offset, ss_offset_fr Minutes [0, 30] [0, 150] 95 Figure 6 . 27 . This setpoint determines the temperature above which the greenhouse controller will keep the ventilation open. 6.4.2 T AirVentOn Figure 6 . 27 shows a relatively wide range of values, depending on the time of day and whether fruit set has occurred (the first three graphs from left to right show solutions for before fruit set , while the last three graphs show solutions for after fruit set has occurred ) . As previousl y discussed, the temperature at which the ventilation opens unconditionally is closely tied with its counterpart, T AirVentOff (due to its ability to override T AirVentOn in cases where it evolves to be greater). However, the addition of distin ct setpoints t o 96 be used before and after fruit set has allowed for more values to be evolved that still retain a gap between T AirVentOff and T AirVentOn . Although this allows RH AirVentOn and CO 2AirVentOn to have more of an impact in greenhouse control (sinc e they will be checked when the greenhouse air temperature falls within this gap), these results do no t suggest that those values themselves are particularly important; rather, it is indicative tilation for p urposes of temperature control. Figure 6 . 28 . This setpoint determines the temperature below which the ventilation will always remain closed. 97 6.4.3 T AirVentOff The values in Figure 6 . 28 sh ow similar trends to those discussed in Section 6.3.3 , the addition of the time - partitioning feature allowed the evolved setpoints to better exploit the times of day where solar radiation is at it s peak. However, the way in whic h this strategy does so differs significantly before and after fruit set: before, the daytime value (i. e., T AirVentOffD ), has a higher overall value while also being lower than its counterpart, T AirVentOnD . This results in t he gap present in the classical Vanthoor strategy where the greenhouse is opened conditionally ( s ee Figure 6 . 3 ). After fruit set (i.e., T AirVentOffD_fr and T AirVentOffE_fr ), we can observe the same overall strategy discussed in Section 6.3.3 , which prioritizes eliminating the gap normally present between T AirVentOff and T AirVentOn by having a value of T AirVentOff_fr that is greater than T AirVentOn_fr . Values for T AirVentOff _fr corresponding to high - crop yield solu tions peak at a higher temperature during the daytime (T AirVentOffD_fr ), while also peaking at lower temperatures during the evening (T AirVentOffE_fr ), helping reduce plant respiration. Lastly, evolved solutions whi ch dominate the classical Vanthoor strate gy all prioritize highe r temperatures, but only after fruit set has occurred. 98 Figure 6 . 29 . This setpoint determines the relative humidity above which ventilation i s conditionally turned on. 6.4.4 RH AirVentOn Simil ar to the trends discus sed in Section 6.3.4 , we see in Figure 6 . 29 that the addition of the time - partitioning (and now distinct setpoints before and after frui t set) did not change the fact that this setpoint has little impact . This further suggests that the crop yield model does not sufficiently penalize inadequate levels of relative humidity, since we know that, in practice, humidity control is impor tant [49] . 99 Figure 6 . 30 . This setpoint determines the greenhouse air CO 2 concentration below which ventilation is conditionally turned on. 6.4.5 CO 2AirVent On S i milar to the trends discussed in Section 6.3.5 , the range of values among the non - dominated solutions is fairly wide despite the addition of time partitioning (and now the distinct setpoints before and after fruit set), sug gesting that thi s setpoint still has little impact overall. 100 Figur e 6 . 31 . This setpoint determines the temperature below which the greenhouse controller will turn on the boiler heating. 6.4.6 T AirBoilOn The evolve d setpoints in Figur e 6 . 31 only show a sim ilar trend to those discussed in Section 6.3.6 after fruit set has occurred (particularly T AirBoilOnD_fr and T AirBoilOnE_fr ). Before fruit set, there is a wide v ariety of values for this setpoint that yield both low - cost and hig h - crop - value solutions , although the morning values (i.e., T AirBoilOnD ) have a cluster of solutions that dominate the classical Vanthoor strategy at around 16 19 degrees Celsius . These re sults suggest that much of the reason for the trends discussed in S ection 101 6.3.6 w ere due to major changes that only occur after fruit set ; namely, the crop - requirements for optimal tomato crop growth, and t he outsi de weather. Thus, there is significant benefit to having setpoints evolved separately for this stage of plant development. Figure 6 . 32 . This setpoint determines the outside temperature below which the gree nhouse controller will deploy the thermal screen. 102 6.4.7 T OutThScrOn Figure 6 . 32 shows trends that are s imilar to those discussed in Section 6.3.7 , where the values are predominantly random when global radiatio n is present due to this setpoint having no impact on greenhouse co ntrol unless it is nighttime. Moreover, before fruit set occur s, we can clearly see that the evolved values for this setpoint did not converge as readily towards 18 degrees Celsius (corresp onding to the classical Vanthoor strategy). However, the expected v alues for T OutThScrOn are clearly present in T OutThScrOnD_fr a nd T OutThScrOnE_fr , respectively. Due to how the nighttime period is defined with this controller ( i.e., beginning at sunset an d ending at sunrise), the static definition for the midday time per iod (i.e., after 9am), and the time of year where fruit set ty pically occurs, T OutThScrOnD_fr was pressured to evolve values that are associated with nighttime deployment of the thermal scr een. In other words, the later times for sunrise typically associat OutThScrOnD more important. 103 Figure 6 . 33 . This variable determines the upper bound for the dynamic CO 2 setpoint used during CO 2 injection. 6.4.8 CO 2AirExtMax The e volved values shown in Figure 6 . 33 show trends that are largely similar to those discussed in Section 6.3.8 . However, before fruit set, there is a marginal decrease in the upper bound of the dynamic CO 2 setpoint during the daytime (i.e., decreasing CO 2AirExtMax D which is then used in CO 2AirExtOn ) , indicating that there is some benefit to changing th is up per bound based on both time of day and plant development stage (in this case, to help reduce costs fro m CO 2 injection). 104 Figure 6 . 34 . This variable determines the lower bound for the dynamic CO 2 setpoint used during CO 2 injection. 6.4.9 CO 2AirExtMin Figure 6 . 34 shows trends that are largely similar to th o se discussed in Section 6.3.9 . However, daytime values for CO 2AirExtMin are marginally higher for high - crop - yiel d solutions, particularly after fruit set. Moreover, t he evening setpoint after fruit set (i.e. , CO 2A irExtMinE_fr ) heavily favors values near 260 ppm, which is overall higher compared to its counterpart before fruit set occurs. 105 Figure 6 . 35 . This variable determines how quickly is maximize d, and subsequently contributes to how quickly the dynamic CO 2 setpoint is maximized . 6.4.10 I GlobMax Figure 6 . 35 shows trends that are largely similar to those discussed in Section 6.3.10 , with some notable ex ceptions . In particular, the mornin g value before fruit set occurs (i.e. , I GlobMaxM ) has a significantly higher lower bound, suggesting that it is advantageous to have a much less aggressive CO 2 injection strategy before fruit set has occurred (since i ncre asing I GlobMax will cause the dynamic CO 2 setpoint to be maximized more slowly ) . In contrast, once fruit set has occurred , we can clearly see that a more 106 aggressive CO 2 injection strategy is preferred (with I GlobMaxD_fr having the lowest values for high - cr op - yield solut ions), suggesting there is a clear benefit to a more straightforward CO 2 injection strategy that aims for a high setpoint for CO 2AirExtOn , rather than a middling value that is used more frequently by keeping the g reenhouse sealed for longer p eriods of time . Figure 6 . 36 . The copies of sr_offset and ss_offset are used to subtract from the current calculated time for sunrise and sunset, respectively. 107 6.4.11 Sunrise and Sunset Offsets ( sr_offset, ss_offse t ) Here in Sec tion 6.4 , we have introduced sunrise and sunset calculations to more accurately determine when the greenhouse controller should transition to daytime and nighttime s trategies, respectiv ely. In addition, we have evo lved offsets to be used for both sunrise and sunset to help the controller determine how long before sunrise and sunset these transitions in control strategy should occur. That is, how long in advance of sun eriod begins is a value evolv ed with the other parameters of the controller, and similarly for the sunset offset and the evening period. Before fruit set occurs, Figure 6 . 36 shows there are a wide range of acceptable values for sr_ offset that yield both low - co st and high - crop - value solutions . This is mainly due to a combination of the warm temperatures present at the start of the growing season (August) , as well as the current plant development stage (i.e. , before fruit set) . Normal ly, one would expect this off that there is an advantage to prolonging or shor tening the period in which a daytime strategy is applied , respectively. However, the vari ety of solutions indicate s th at there is little impact in this case. In contrast, sr_offset_fr heavily prioritizes smaller values. In typical cases , by October , fruit set has occurred ( and thus harvesting begins ) . Around this time, sunrise begins to occur late r, outside air temperatur es begin to drop , and the daytime periods are shorter ( s ee Figure 6 . 25 ). Most of the evolved values for sr_offset_fr reflect strategies that try to conserve heat as much as possible by extending the tim e period in which the thermal screen is used (since it is only deployed as part of the nighttime strategy ). Clearly, the benefits of doing so outweigh th e reduction in photosynthetic activity due to the thermal screen itself reducing the photosynthetically active radiation available t o the plan t during early hours , as well as the reduced amount of CO 2 injection . Most of the evolved values for ss_offset are 95 minutes; thus, nighttime control strategies will begin 95 minutes before the current calculated tim e for sunset. This is the cas e for both low - cost and high - crop - yield value solutions. This sugges t s that, at least before fruit set occurs, it is not worth spending too much energy on maximizing the rate of photosynthesis o f the crop as sunset is approachi ng, even if there is 108 some sun light remaining. In the case of ss_offset_fr, most values are at 150 minutes , therefore signaling an even earlier shift to a nighttime control strategy as sunset approaches. Overall, it shows a similar trend to that of ss_offse t, except the values are larg er overall due to an increased need to conserve heat by using the th ermal screen for longer periods of time during the fall and winter seasons , which coincide with the post - fruit - set timeframe . 6.4.12 Discussion Clearly, the features introduced in this controller yielded some improvements over its predecessor ( a s seen in Figure 6 . 1 ). By introducing distinct setpoints to be used before and after fruit set, we hav e allowed the controller to evolve values that are better suited for the needs of the crop in a specific development stage and time of yea r . For example, the pre - fruit - set values used for the dynamic CO 2 setpoint (i.e. , CO 2AirExtMax , CO 2AirExtMin , and I GlobMax ) produce a less aggressive CO 2 injection stra tegy overall compared to the previous controllers described in this chapter. In contrast, the post - fruiting values (i.e. , CO 2AirExtMax_fr , CO 2AirExtMin_fr , and I GlobMax_fr ), generally produce more a more aggressive CO 2 injection strategy. Th e pre - fruit - set values for ventilation - relat ed setpoints (i.e. , T AirVentO ff and T AirVentO n ) do not prioritize maintaining the greenhouse sealed as much as the prior controllers; they instead allow for the greenhouse to be opened conditionally more often by having a gap b etween T AirVentOff and T AirVe ntOn ( a s shown in Figure 6 . 3 ). In contrast, the post - fruiting values prioritize maintaining the greenhouse sealed for longer periods of time . This is especially apparent in T AirVentOffD_fr , where the va lue of the crop yield increas es with higher values on this setpoint, which is typical of control strategies that use a combination of active cooling and heating to maintain optima l temperature ranges while keeping the greenhouse sealed (even in cases where ventilation would be a viabl e method of cooling the greenhouse). It was also clearly beneficial to use sunrise and sunset times to transition between nighttime and daytime contro l strategies (and vice - versa) . This feature allows the length of the daytime strategy periods to change dy namically, thus providing finer control. In addition, both sunrise and sunset times ( decremented by their respective offsets) provide a useful referen ce point: we know these times change daily , which 109 ultimately affects multiple environmental variables (e.g . , the available sunlight, the length of the day , outside air temperature, etc.) . However, this distinction between nighttime and daytime control could be better exploited, as the only control action that occurs during nighttim e is whether the thermal scre en ( T OutThScrOn ) is deployed or not. Some evolved setpoints, such as RH AirVentOn and CO 2AirVentOn , had little impact o n the performance of the controller. In practice, we know that humidity control is important to avoid the ons et of disease on the tomato c rop , and that low levels of CO 2 concentration in the greenhouse air would also ad versely affect the growth of the crop. Since it is unlikely that evolving these values further would yield more useful information, subsequent con trollers will use default val ues for these setpoints that are known to be effective in practice, and in the ca se of the control strategy discussed in Section 6.6 , we also introduce a penalty for sub - optimal levels of relative hu midity in the greenhouse air. 6.5 Improved Controller without Penalty for Inadequate Relative Humidity 6.5.1 Introduction This controller uses a combination of the features from the previous controllers, and makes additional changes based on areas where the results from the previous evolved con trollers suggested there was room for improvemen t : 1. If T AirVentOff > T AirVentOn, additional logic is add ed to the greenhouse controller to improve the handling of this special case (See Figure 6 . 38 ). 2. Ven tilation, boiler, and fogging systems are all assumed to be PID controlled, and their respective gain values are al l evolved. 3. T AirVentOn , T AirVentOff , and T AirBoilOn now contain additiona l copies to be used specifically during the nighttime period. 4. Changes in the greenhouse ventilatio n (U Vent ) caused by PID control will use the mean value of T AirVentOn and T AirVentOff . 110 5. Setpoints and/or variables that were previously evolved, and subsequent ly found to have little impact on either objective were either remove d or had their number of copi es reduced. For example: RH AirVentOn and CO 2AirVentOn have been removed entirely from the chromosome and default values found in literature are used instead , with RH AirVentOn = 0.9 and CO 2AirVentOn = 200 ppm [4] . S etpoints like T OutThScrOn showed no tangible benefit from having additional copies based on the time of day, so the number of copies has been reduced to two (i.e. , one copy is used before fruit set and one after fruit set). F igure 6 . 37 . Pareto - optimal front for the control strategy discussed in this section. Solu tions from this Pareto front which also dominate the classical Vanthoor strategy are marked in green. 111 Figure 6 . 38 . Simple flowchart describing the handling of the special case of T AirVentOff > T AirVentOn . 112 Table 6 . 6 . Chromosome containing the setpoints used in this controller , with additional features . T he total size of the genotype consists of 54 integer values. Parameter Description Parameter name/symbol Unit Genotype Value Range of Real Values Temperature above which ventilation (U vent ) is on T AirVentOnN , T AirVentOnM, T Air VentOnD, T AirVentOnE, T AirVen tOnN_fr , T AirVentOnM_fr, T AirVentOnD_fr, T AirVentOnE_fr Degrees (Celsius) [100, 300] [10, 30] Temperature below which ventilation is off T AirVentOffN , T AirVentOffM, T AirVentOffD, T AirVentOffE, T AirVentOffN_fr, T AirVentOffM_fr, T AirVentOffD_fr, T AirVentOff E_fr Degrees (Celsius) [100, 300] [10, 30] Temperature below which the boiler (U Boil ) is on T AirBoilOnN , T AirBoilOnM , T AirBoilOnD, T AirBoilOnE, T AirBoilOnN_ fr, TAirBoilOnM _fr, T AirBoilOnD_fr, T AirBoilOnE_fr Degrees (Celsius) [ 100, 300] [10, 30] Nighttime temperature below which the thermal screen (U ThScr ) is deployed T OutThScrOn, T OutThScrOn _fr Degrees (Celsius) [100, 300] [10, 30] Proportional, integral and derivative gain values for boiler control PID BoilP , PID BoilI, PID Boi lD, PID BoilP_fr, PID BoilI_fr, PID BoilD_fr (1 × 10 5 ) [10, 100] [10 - 5 , 10 - 4 ] Proportional, integral and derivative gain values for fogging system control PID FogP , PID FogI, PID FogD, PID FogP_fr, PID FogI_fr, PID FogD_fr (1 × 10 5 ) [10, 100] [10 - 5 , 10 - 4 ] Proportiona l, integral and derivative ga in values for ventilation control PID ventP , PID VentI, PID VentD, PID VentP_fr, PID VentI_fr, PID BoilD_fr (1 × 10 5 ) [10, 100] [10 - 5 , 10 - 4 ] Upper bound for dynamic CO 2 setpoint CO 2AirExtMax, CO 2AirExtMax_fr ppm [2000, 10000] [200, 10 00] Lower bound for dynamic CO 2 setpoint CO 2AirExtMin, CO 2AirExtMin_fr ppm [1000, 5000] [100, 500] Amount to subtract from calculated sunrise time sr_offset, sr_offset_fr Minutes [0, 30] [0, 150] Amount to subtract from calculated sunset time ss_offset, ss_offset_fr Minutes [0, 30] [0, 150] Global radiation above which the dynamic CO 2 setpoint is maximized I GlobMax, I GlobMax_fr W/m 2 [2000, 10000] [200, 1000] 113 Figure 6 . 39 . This setpoint determines the tem perature above which the gree nhouse controller will keep the ventilation open. 6.5.2 T AirVentOn Figure 6 . 39 shows that, c ompared to the previous controllers covered in this chapter, there are two addi tional copies of this setpoint to acc ount for the nighttime period : T AirVentOnN and T AirVentOnN_fr . While T AirVentOnN clearly has a wide range of acceptable values that produce both low - cost and high - crop - value solutions , T AirVentOnN_fr prioritizes values at or near 16 degrees Celsius . This v alue is close to temperatures below which a greenhouse would be heated up in practice, so immediately ventilating a greenhouse above 114 such a temperature would not be ideal. However, t he corresponding values of T AirVentOf fN_fr in the next section are slightl y greater and thus override T AirVentOnN_fr . However, even i n cases where a copy of T AirVentOn is overridden by T AirVentOff , it still meaningfully contributes to Pareto - optimal s olutions because of its use when calcula ti ng the reference temperature for the PID - controller - operated venti lation. Figure 6 . 40 . This setpoint determines the temperature below which the ventilation will always remain closed. 115 6.5.3 T AirVentOff Similarly, Figure 6 . 40 shows there are two new copie s of this setpoint: T AirVentOffN and T AirVentOffN_fr . Of these two, T AirVentOffN_fr (i.e., the nighttime, post - fruiti ng setpoint for T AirVentOff ) is noteworthy due to all the solutions being at or slightly above 18 degrees Cels ius . Almost all these values are higher than T AirVentOnN_fr in the previous section , creating a control strategy where the greenhouse remains unco nditionally sealed until the air temperature exceeds the current value of T AirVentOffN_fr . In addition, values for T OutThScrOn _fr (covered below in Section 6.5.5 ) are mostly centered around 17.5 degrees Celsius , which overall shows an emphasis o n maintaining nighttime greenhouse temperatures at around this range . Finally , T AirVentOffM_f r and T AirVentOffD_fr both sh ow a clear t r end in which increasing the value of these setpoints lead s to increased crop yield value. This is consistent with control strategies that prioritize keeping the greenhouse sealed at the expense of increased variabl e costs (from additional cool ing, heating, and CO 2 injection). 116 Figure 6 . 41 . This setpoint determines the temperature below which the greenhouse controller will turn on the boiler heating. 6.5.4 T AirBoilOn Figure 6 . 41 shows that the values for this setpoint are largely random before fruit set, although the nighttime copy, T AirBoilOnN , has a relatively narrow range of values (mostly between 10 18 degrees Celsius ). Naturally, lower temperat ures are preferred during nig httime to reduce plant respiration (as long as these temperatures are not low enough to damage the crop). After fruit set, T AirBoilOnN_fr , T AirBoilOnM_fr , and T AirBoilOnD_fr all show a clear trend in which higher values for thi s setpoint lead to higher cro p yield 117 values (at the expense of higher variable costs). In the case of T AirBoilOnN_fr , any boiler heating that occur s because of this setpoint will be during the nighttime control strategy period, and thus very little to no p hotosynthesis occurs during t his time. Therefore, this setpoint contributes to the value of the crop yield more indirectly: that is, it is reducing crop growth inhibition due to sub - optimal temperatures, rather than helping to maximize the rate of photosyn thesis during the daytime. Figure 6 . 42 . This setpoint determines the outside temperature below which the greenhouse controller will deploy the thermal screen. 6.5.5 T OutThScrOn Figure 6 . 42 shows that evolved values f or T OutThScrOn and T OutThScrOn_fr a re largely consistent with th ose from previous controllers discussed in this chapter , with most values being near 18 degrees Celsius . 118 Figure 6 . 43 . PID gain parameters for boiler heating control. 6.5.6 PID Boiler Figure 6 . 43 shows that b efore fruit set, t he gain parameters for boiler heating have a wide range of values that yield both low - cost and high - crop - value solutions . Nota bly, the integral gain before fruit set (PID BoilerI ) remained consistently low, with most control strategies relying on the proportional gain (PID BoilerP ) to provide an initial value that sufficiently heats the greenhouse air. In contrast, the integr al gai n after fruit set (PID BoilerI _fr ) follow s a clear trend where higher integral gain results in higher crop yield 119 value . In other words , a high integral gain causes the boiler heating value, U Boil , to reach its maximum very quickly. Naturally, this wil l maxi mize the output of the boiler heating at the expense of increased variable costs. Figure 6 . 44 . PID gain parameters for fogging system control. 6.5.7 PID Fog Similarly, Figure 6 . 44 shows th at there are a wide range of parameters which yield both low - cost and high - crop - value solutions . Unlike the boi ler and ventilation 120 systems, the restrictions placed on the output of the fogging syste m force it to operate for limited time periods. Th is translates to many combinations of PID gain parameters being sufficient to meet or exceed that limit . If we could op erate the fogging system uninterrupted for longer periods of time , the evolved gain parameters might show cl ear patterns . Despite the sma ll effect of these fogging system PID parameters, it is well known tha t excessively high levels of humidity can lead to disease in the crop [49] , and salt cont ater reservoir can cause burns on the leaves of the crop [42] . However, s ince these adverse effects ar e not implemented in the combined microclimate - crop - yield model, it is preferable to maintain best practices that aim t o avoid these problems altogether . 121 Figure 6 . 45 . PID gain p arameters for greenhouse vent ilation control. 6.5.8 PID Vent Once again, Figure 6 . 45 shows that parameters which yield both low - cost and high - crop - value solutions . However , most values for PID VentI_fr are on th e lower end (with 10 being the lowest possible value), suggesting that a t least after fruit set occurs there is some benefit to lowering the integral gain, thus somewhat slowing down the rate at which the greenhouse v entilation fully opens. Since most of t he post - fruit - set period takes place during the 122 winter and spring seasons (with accompanying colder outside air temperatures), it stands to reason that there is an advantage to controlling greenhouse ventilation openi ngs more carefully. Figure 6 . 46 . The copies of sr_offset and ss_offset are used to subtract from the current calculated time for sunrise and sunset, respectively. 6.5.9 Sunrise and Sunset Offsets ( sr_offset, ss_o ffset ) Figure 6 . 46 shows values that follow largely similar trends to those discussed in Section 6.4.11 . The offse t applied to the current sunrise time (sr_offset) is largely random, while its post - fruit - set counterpart (sr_offset_f r) is heavily biased towards 0.The offset applied to the current sunset time (ss_offset) has 123 many values at or near 75 minutes, while its post - fruit - set counterpart has most of its values at or near 150 minutes. Despite there b eing three additional setpoin ts with distinct nighttime values compared to previous controllers (i.e., T AirVentOnN , T AirVentOffN , T AirBoilOnN ), the trends shown by the se offsets still reflect an overall strategy that aims to conserve heat as much as possib le by extending the time peri od in which the thermal screen is used (since it is only used during nighttime). Unlike the previous controller in Section 6.4.11 , sr_offset_fr and ss_offset_fr show cluster s of extreme values at 85 minutes and 75 minutes, resp ectively. Both offsets would serve to extend the total duration of the dayt ime control strategy period relative to the other non - dominated solutions. Naturally, extending the time period in which a daytime strategy is applied w ill result in increased varia ble costs (particularly when prioritizing crop yield value), since more act ive cooling and/or heating measures, as well as CO 2 injection, are expected to take place to maximize the rate of photosynthesis of the crop. Figure 6 . 47 . This variable determines the upper bound for the dynamic CO 2 setpoint used during CO 2 injection. 6.5.10 CO 2AirExtMax Figure 6 . 47 shows that, w hile CO 2 AirExtMax has a wide ra nge of value s with no clear pattern, CO 2A irExtMax_fr clearly shows a pattern of increasing crop yield value as it also increases. This shows that the dynamic CO 2 setpoint, CO 2AirExtOn , is being reached many times during the post - fruit - set period and that i ts upper 124 bou nd, CO 2AirExtMax_fr , has a si gnificant impact on the crop yield value . Since most of the post - fruit - set period takes place during the fall and winter seasons, the accompanying lower temperatures (as well as proper evolved values for setpoints p ertaining to temperature control) allow t he greenhouse to remain sealed, allowing for CO 2 injection to occur uninhibited. Figure 6 . 48 . This variable determines the lower bound for the dynamic CO 2 setpoint used during C O 2 injection. 6.5.11 CO 2AirExtMin Si milar to CO 2AirExtMax in Section 6.5.10 , CO 2AirExtMi n in Figure 6 . 48 shows a wide range of values with no clear pattern before fruit set . After fruit set occurs, the crop yie ld generally increases with i ncreasing CO 2AirEx tMin_fr . 125 Figure 6 . 49 . This variable determines how quickly is maximized, and subsequently contributes to how quickly the dynamic CO 2 setpoint is maximized . 6.5.12 I GlobMax Figure 6 . 49 shows that I GlobMax contains a relatively wide ran ge of values that yield both low - cost and hig h - crop - value solutions , although most are within the 600 900 W/m 2 range. Even though a higher valu e for I GlobMax will cause to be maximized more slowly (thus causing the dynamic CO 2 setpoint to be maxim ized more slowly), one would normally ex pect a relatively high value of I GobMax to translate to lower crop yield value and/or lower variable costs due to the reduction in CO 2 injection. However, CO 2 injection does not have enough of an impact o n the crop yield value before fruit set occurs, whic h results in the wide range of values of I GlobMax that yield solutions with both low and high crop y ield value s . After fruit set occurs, most solutions of I Gl obMax_fr follow a trend where a decrease in this variable tends to increase the crop yield value. This is consistent with the other evolved variables used to calculate the dynamic CO 2 setpoint in th is section (CO 2AirExtMax and CO 2AirExtMin ) , in that changi ng these variables to increase the dynamic CO 2 setpoint will tend to increase the value of the cro p yield at the expense of increased variable costs. 126 6.5.13 Discussion One of the main disadvantages of the previous controllers was the lack of distinct setpoints fo r a nighttime strategy, resulting in situations where morning (M) and evening (E) copies of a setp oint needed to contain values that were appropriate for both the time period it was defined for , as well as for a portion of what would be considered nighttim e for purposes of deploying the thermal screen. This is due to how the morning and evening periods are defined ( s ee Table 6 . 4 ) and the controller still requiring setpoi nts t o be defined for typical greenhouse control purposes during nighttime (e.g. , using boiler heating to heat up the greenhouse). Thus, introducing distinct nig tly f or the time period for which they were defined, leading to overall better results. The most notable effect of introducing distinct nighttime setpoints (wher e applicable) could be observed after fruit set, where T AirVentOnN_fr , T AirVentOffN_fr , T AirBoilOnN_ fr and T OutThScrOn_fr formed many sets of values centered around maintaining temperatures near the T OutThScrOn_fr setpoint . In most cases, for a given value of T OutThScrOn_fr , there is an accompanying pair of values of T AirVentO nN_fr and T AirVentOffN_fr th at are slightly greater , as well as a value of T AirBoilOnN_fr that is lower. This is consistent with the nighttime temperatures that the classical Vanthoor strategy aims to maintain, as well as the setpoint values used to achiev e these results. The additio n of PID control to greenhouse ventilation had some benefits. In particular the post - fruit - set integral gain (PID VentI_fr ) is overall lower compared to its pre - fruit - set counterpart (PID VentI ), indicating that there is some bene fit to slowing down the rate at which the ventilation fully opens after fruit set occurs. While it was not detrimental, a PID - controlled fogging system did not seem to provide a tangib le benefit , mainly due to the restrictions present to prevent the overus e that is known to cause adv erse effects in practice . In the case of boiler heating, it was always PID controlled (with gain parameters pre - determined to approximate the fuel consumpti on of the classical Vanthoor strategy), thus the main change was in allo wing its gain parameters to be evolved . The pre - fruit - set integral gain (PID BoilerI ) prioritized 127 lower values overall, thus slowing down the rate at which the boiler heating is maximiz ed for most solutions. In contrast, the post - fruit - set integral gain (PI D BoilerI_fr ) followed a tren d where higher values for this gain result in increased crop yield value (at the expense of increase d variable costs due to the more aggressive heating that results). One of the disadvantages observed in previous sections was the lack of penalties on eithe r crop growth or crop yield value due to inadequate levels of relative humidity . This is most apparent in the evolved values for the T AirVentOn and T AirVent Off setpoints. In the classical Vanthoor strategy, most o f the humidity control occurs when greenhou se air temperatures are between T AirVentOn and T AirVentOff , ventilating the greenhouse when the greenhouse air is above a relative humidity threshold. Howev er, when these values are evolved, the gap that allows fo r this check to occur is typically eliminat ed. The next section will cover th e same control strategy discussed in this section except that , importantly, a crop value penalty for sub - optimal levels of relative humidity is added. 6.6 Same Improved Controller wit h P enalty fo r Inadequate Relative Humidity 6.6.1 Introduction This control strategy is identical to the one described in Section 6.5 , but a penalty has been intr oduced for sub - optimal levels of relative humidity in the greenhouse air . This aims to reflect the r eal - world valuation of tomato crops, in which tomato growth and development , fungal contamination, and other problems are associated with sub - optimal relati ve humidity . The penalty consists of two trapezoid functions [4] . The first function determines the fraction of first - class tomatoes based on the 24 - hour mean value of the vapor pressure deficit (VPD 24 ) between the canopy and the greenhouse air. The second function determines the fraction of marketable tomatoes b ased on the 48 - hour mean value of the relative humidity ( RH 48 ) of the greenhouse air. This only impacts the resulting crop yield value , and therefore has no effect on the microclimate - crop yield model. However, this still induces significant changes i n evo lved control strategies: if a hypothetical greenhouse controller were to fail to maintain an acceptable range for either VPD 24 or RH 48 , the entire crop coul d end up having no monetary value. I t is expected that 1) using the 128 same evolved solutions as the pr evious section will yield sub - optimal results, and 2) evolving se tpoints once more under a modified economic model should mitigate the effects of the penalt y introduced in this section . Therefore, the main goal of this section is to observe and discuss not able changes in the overall behavior of the evolved controller, r ather than examining the change in magnitude for each objective . Figure 6 . 50 contains the Pareto - optimal front that results from adding this penalty, with the classical Vanthoor strategy also being subject to said penalty. Figure 6 . 50 . Pareto - optimal fron t for the control strategy discussed in this section. Solutions from this Pareto front which also dom inate the classical Vanthoor strategy are marked in green. 6.6.2 T AirVentOn and T AirVentOff The addition of a crop value penalty changed the range of values cons i derably for both T AirVentOn and T AirVentOff . In this section, these setpoints will be plotted togeth er to show the overall change in these pairs of values before and after introducing the crop value penalty. Due to the large number of control strateg ies c o ntained in each Pareto - optimal front, we will only examine solutions which dominate the classical Va nthoor strategy (see Figure 6 . 50 ). In addition, since the behav ior of the controller changes 129 significantly depending on which of t h ese two values are greater (i.e., whether T AirVentOn > T AirVentOff or T AirVentOff > T AirVentOn ), the y will be marked accordingly in Figure 6 . 51 , Figure 6 . 52 , Figure 6 . 53 , and Figure 6 . 54 . Figure 6 . 51 . Evolv ed nighttime setpoints for T AirVentOn and T AirVentOff . The effects of addin g a crop value penalty on the resulting evolved setpoints are examined (right) a n d compared with the same setpoints without the crop value penalty (left). Red values are cases when T AirVentOn is greater than T AirVentOff . 6.6.2.1 Nighttime Setpoints Figure 6 . 51 shows that, w ith the addition of a crop va l ue penalty, the average temperature of the nighttime setpoint s (T AirVentOn and T AirVentOff ) lower ed significantly. In addition, there are significantly more instances in which T AirVentOn is greater than T AirVentOff (red pairs of values on the upper right ) . Many of these pairs of values have relatively large temperature gaps between them which allow th e c ontrol strategy to o p en ventilation conditionally for purposes of humidity control. Based on the classical Vanthoor strategy, a temperature gap of 3 degree s Celsius is typical (T AirVentOn = 23, T AirVentOff = 20), and many of these evolved pairs form sim ila rly sized gaps, with some exceptions. After fruit set occurs, the addition of a crop value penalty cause s the average temperature of the nighttime setpoint s (T AirVentOn_fr and T AirVentOff_Fr ) to increase significantly. Moreover, most solutions develop 130 inst ances in which T AirVentOn is greater than T AirVentOff ( as see n in Figure 6 . 51 , red pairs of values on the lower right). Overall, t he addition of a crop value penalty produced nighttime setpoints which emphasize ventilating the gre enhouse for purposes of reducing the relative humidity of the greenhouse air. T AirVentOn and T AirVentOff had lower average temp eratures which resulted in a control strategy that would ventilate the greenhouse quite often, especially during August where the outside air temperature is much warmer (see Figure 6 . 25 ). After fruit set, T AirVentOnN_fr and T AirVentOffN_fr both emphasize vent i lation for purposes of relative humidity control, although the average temperatures are higher. By t he time this stage of plant development is reached (typically ar ound October), average outside air temperatures will have dropped significantly, and thus v e ntilating the greenhouse will rapidly cool the greenhouse air to sub - optimal temperature ranges for plant growth. Figure 6 . 52 . Evolved morning setpoints for T AirVentOn and T AirVentOff . The effects of addin g a crop value penalty on the resulting evolved setpoints are examined (right) and compared with the same setpoints without the crop value penal ty (left). Red values are cases when T AirVentOn is greater than T AirVentOff . 131 6.6.2.2 Morning Setpoints Figure 6 . 52 shows that, b efore fruit set, the addition of a crop value pen alty increased the both the average temperature and the occurrence of setpoints in which T AirVentOff M is greater than T AirVentOn M , thus resulting in most control strategies n o t ventilating the greenhouse for purposes of humidity control . There clearly is n ot enough of an inc entive to decrease relative humidity during this time period, and the benefits of maintaining the greenhouse closed to take advantage of CO 2 injection in t h e presence of global radiation outweigh the crop value penalties from sub - optimal levels of relative humidity. This can be further exacerbated when outside air temperatures are low enough during this period that using the fogging system is mostly unnecess a ry for cooling down the greenhouse. After fruit set, the addition of a crop value penalty increased the average temperature, with most control strategies containing values in which T AirVentOnM_fr is greater than T AirVentOffM_fr . This results in most of th e control strategies ventilating the greenhouse often for purposes of humidity con trol. In addition, the values for many pairs of T AirVentOnM_fr and T AirVentoffM_fr mirror those of the classical Vanthoor strategy (i.e., T AirVentOn = 23 and T AirVentOff = 20 ) , indicating that, at least for this time period, these values are effective for both high - crop - valu e and low - cost solutions. 132 Figure 6 . 53 . Evolved midday setpoints for T AirVentOn and T AirVentOff . The effec t s of adding a crop value penalty on the resulting evolved setpoints are examined (right) and compare d with the same setpoints without the crop value penalty (left). Red values are cases when T AirVentOn is greater than T AirVentOff . 6.6.2.3 Midday Setpoints Figure 6 . 53 shows that, b efore fruit set, the addition of a crop value penalty incr eased the average temperature s for both T AirVentOnD and T AirVentOffD , with most pairs o f values allowing ventilation of the greenhouse for humidity control . Pairs of values which did not allow this kind of humidity control had lower temperature setpoints o verall, suggesting that in the absence of the ability to open the greenhouse ventilatio n conditionally based on humidity levels, a lower temperature setpoi n t for opening the greenhouse ventilation unconditionally can work as an alternative. After fruit set , the addition of a crop value penalty decreased the average temperatures for both T AirVentOnD_fr and T AirVentOffD_fr . Most of these pairs of values do not allow ventilating the greenhouse for humidity control, instead opting for opening (and closing) gree nhouse ventilation unconditionally at a relatively low setpoint of around 17 degrees Celsius . Despite the cooler outside temperatures present after fruit s e t occurs, t hi s results in some ventilation during the midday period (particularly when global radiat ion is at its peak), while keeping the greenhouse sealed and its air temperature as close to 17 degrees Celsius as possible otherwise. At a setpoint of aro u nd 17 degrees Celsius , this is slightly below the 133 optimal 24 - hour mean canopy temperature range for the crop, which is 18 22 degrees Celsius [4] . However, due to the higher average temperature se tpoints during t h e nighttime, morning, and evening periods ( coming up in Section 6.6.2.4 ) , the 24 - hour mean canopy temperature remains at or above 18 degrees Celsius , helping prevent tomato crop growth inhibition. Figure 6 . 54 . Evolved evening setpoints for T AirVentOn and T AirVentOff . The effect s of adding a crop value penalty on the resulting evolved setpoints are examined (right) and compared with the same setpoints without the crop value penalt y (left). Red values are cases when T AirVentOn is greater than T AirVentOff . 6.6.2.4 Evening Setpoints Figure 6 . 54 shows that, b efore fruit set, the addition of a crop value penalty significantly increased the instances in which these setpo i nts allowed ventilation of the greenhouse for purposes of humidity control. Most of these setpoints allow the controller to open the greenhouse ventilation unconditionally at a lower temperature compared to its midday counterpart (i.e., T AirVentOnD and T A i rVentOffD ) which suggests that, in most cases, it is beneficial to open the greenhouse ventilation m ore frequently once the levels of photosynthetically active radiation a nd outside air temperatures begin to drop (since the costs associated with CO 2 injec t ion and managing higher canopy temperatures for maximizing photosy nthesis become an unacceptable tra deoff ). 134 After fruit set, the addition of a crop value penalty also significantly increased the instances in which greenhouse ventilation occurs for purpose s of humidity control. However, most of these setpoints form a narrow temperature range that allows f or this to occur, around 17 18 degrees Celsius . In contrast, the values for its midday counterpart (i.e., T AirVentOnD_fr and T AirVentOffD_fr ) only allow f or the greenhouse ventilation to unconditionally open and close when above and below 17 degrees Cels ius , res pectively , in most cases. This suggests that, once the evening period begins during the post - fruit - set period, it is beneficial to start reducing t h e frequency with which a control strategy opens the greenhouse ventilation, albeit by a very slight amount. Based on the post - fruit - set nighttime setpoints displayed in Figure 6 . 51 we can see that this culminates in a n evening - to - n ighttime transition during which the se nightti me temperatur e setpoints (i.e., T AirVentOnN_fr and T Ai rVentOffN_fr ) increase significantly to conserve heat by reducing overall ventilation, while still maintaining a temperature range in which ventilation ca n still occur for purposes of humidity control. 135 Figure 6 . 55 . This setpoint determines the temperature below which the greenhouse controller will turn on the boiler heating. 6.6.3 T AirBoilOn Figure 6 . 55 shows that, b efore fruit set, t he evolved values for this setpoint did not change cons iderably with the addition of a crop value penalty, with a wide range of values producing both high - crop - v alue and low - cost solutions. Most notably, the mi d day setpoint (i.e., T AirBoilOnD ), has a narrower range of around 16 24 degrees Celsius compared to these same setpoints evolved without the crop value penalty (around 10 28 degrees Celsius ). Due to the high average outside air temperatures present bef o re fruit set (see Figure 136 6 . 25 ), even a relatively high setpoint for the boi ler was not correlated with increased crop yield value and/or variable costs. After fruit set, the evolved values for this setpoint show largely similar tr e nds to those discussed in Section 6.5.4 : that is , in creasing the nightti me, morning, and midday setpoints also tends to increase the value of the crop yield (at the expense of increased variable costs), suggesting that introduc i ng the crop value penalty did not significantly alter the role of this setpoint overall. Figure 6 . 56 . This setpoint determines the outside temperature below which the greenhouse controller will deploy the t hermal screen. 6.6.4 T OutThScrOn Figure 6 . 56 shows that t he evolved values for T O utThScrOn and T OutThScrOn_fr are largely consistent with those from previous controllers discussed in this chapter, although T OutThScrOn contains values wh i ch are lower on average compared to those discussed in Section 6.5.5 . 137 Figure 6 . 57 . PID gain parameters for boiler h eating control. 6.6.5 PID Boiler Figure 6 . 57 shows that, b efore fruit set, the gain parameters for boiler heating show largely similar trends, ex cept for the integral gain (i.e., PID BoilerI ) which contains much larger values on average compared to its counterpart in Section 6.5.6 . While the introduction of a crop value penalty did not affect the overall t he evolved gain parameters , t his difference in the integral gain values suggest that a wider range of values for the integral gain were acceptable when in c onjunction with the evolved values 138 for T AirVentOn and T AirVentOf f discussed earlier in Section 6.6.2 (since changes in the setpoints for greenhouse ventilation will also affect the frequency and output necessary for the boiler h e ating to maintain optimal temperature ranges for the tomato crop). After fruit set, most control st rategies favor a stronger proportional response compared to its counterpart without the crop value penalty (see Section 6.5.6 ). This is especially true for solutions which dominate the classical Vanthoor strategy, with very few control strategies using a value of PID BoilerP_fr that is below 50. The integral gain (i.e., P ID BoilerI_fr ) follows a largely similar trend even with the i n troduction of a crop value penalty, indicating that increasing the rate at which the output of the b oiler is maximized also increases the value of the crop yield (at the expense of increased var iable costs). 139 Figure 6 . 58 . PID gain parameters for fogging system control. 6.6.6 PID Fog Figure 6 . 58 shows that, b efore fruit set, the gain parameters for the fogging system show largely similar trends to their counterpart s without the crop value pe n alty in Section 6.5.7 , with the exception of the proportional gain (i.e. , PID FogP ) . Most of these proportional gain values became significantly lower with the introduction of a crop value penalty, indicating that in many cases, a slower initial response from the fogging system was needed as a result . 140 After fruit set, both prop ortional and integral gain (i.e., PID FogP_fr and PID FogI_fr ) increased overall with the introduction of a crop value penalty ; therefore , a control strategy in which the fogging system maximizes its output very quickly is preferred. Figure 6 . 59 . PID gain parameters for greenhouse ventilation control. 6.6.7 PID Vent Figure 6 . 59 shows that, b ef o re fruit set, the introduction of a crop value penalty significantly increased both proportional and integral gain parameters (i.e., PID Vent P and PID VentI ) on average. This results in 141 control strategies which maximize the greenhouse ventilation openings a l most immediately, and that such behavior is preferred now indicates that the crop value penalty intr oduced a need for much more frequent ven tilation for purposes of humidity control. After fruit set, the gain values show largely similar trends, with the i n tegral gain (i.e., PID VentI_fr ) showing a more narrow range of values (around 15 45) compared to i ts counterpart without the crop value pe nalty in Section 6.5.8 (around 10 70). Similarly, it shows that most control strategi e s favor a slower rate at which ventilation openings are maximized. 142 Figure 6 . 60 . The copies of sr_offset and ss_offset are used to subtract from the current calculated time for sunrise and sunset, respectiv e ly. 6.6.8 Sunrise and Sunset Offsets (sr_offset, ss_offset) Figure 6 . 60 shows tha t, b efore fruit set, most of the evolved values for sr_offset and ss_offset contain similar trends to those discussed in Section 6.5.9 , where there are a wide range of values which produce both high - crop - yield and low - cost solut regions (e.g., ss_off set with the crop value penalty has a large number of values near 30 m i nutes, while ct on the overall 143 control strategy (i.e., setpoints for T AirVentOn and T AirVentOff th at prioritize humidity control) required these offsets to change to so m e extent to maximize their efficacy. After fruit set, the evolved values for sr_offset_fr and ss_off set_fr show trends that are nearly identical to those discussed in Section 6.5.9 even with the introduction of a crop value pen a lty, suggesting that the overall strategy of reducing the time in which morning and evening setpoint s are used remains effi cient for this stage of plant development. Moreover, reducing the value of ss_offset_fr to as low 95 minutes can result in a margina l increase in crop yield (at the expense of increased variable costs). Figure 6 . 61 . This variable determines the upper bound for the dynamic CO 2 setpoint used during CO 2 injection. 6.6.9 CO 2AirExtMax Figure 6 . 61 shows that, b efore fruit set, the evolved values for CO 2AirExtMax did not change significantly with the addition of the crop value penalty and shows a wide range of values that produce both high - crop - value and low - cost solutions. Thi s trend is expected , as most of the strategies discussed in earlier sections did not typically me et the upper bound for the CO 2 setpoint due to the frequency in which ventilation is needed during this warmer period. T he introduction of a crop value pen a lty only reinforces this trend due to the additional ventilation that occurs for purposes of humidit y control. 144 After fruit set, the evolved values for CO 2AirExtMax_fr show a similar trend to the one described in Section 6.5.10 , where an increase in this value also tends to increase the value of the crop yield. However, this tr end is much less pronounced, and suggests that the increase in ventilation that occurred thanks to the crop value penalty limits th e ability of the greenho u se controller to find the right conditions to enable CO 2 injection, as well as reaching the upper bo und of the CO 2 setpoint defined by CO 2AirExtMax_fr when CO 2 injection does occur. Figure 6 . 62 . This vari a ble determines the lower bound for the dynamic CO 2 setpoint used during CO 2 injection. 6.6.10 CO 2AirExtMin Figure 6 . 62 shows that t he evolved values for this variable are consistent with those of previous controllers discussed in this ch a pter. After fruit set occurs, CO 2AirExtMin_fr shows a significantly less pronounced trend of increas ing as the value of the crop yield also increases , similar to CO 2AirExtMax_fr as described in Section 6.6.9 . 145 Figure 6 . 63 . This variable determines how quickly is maximized, and subsequently contributes to how quickly the dynamic CO 2 setpoint is maximized . 6.6.11 I GlobMax Figure 6 . 63 shows that, b efore fruit set, the addition of a crop value penalty significantly reduced the ev olved values for I GlobMax , with most of them being at or near 350 W/m 2 . This indicates that, in the presence of increased ventilation requirements for humidity c ontrol (and subsequently, a reduction in the frequency in which CO 2 injection is possible), max imizing the dynamic CO 2 setpoint (i.e., CO 2AirExtOn ) at lower levels of global radiation is preferable. After fruit set, the evolved values for I GlobMax_fr refl ect nearly identical trends to those described in Section 6.5.12 , w here a decrease in this variable tends to increase the crop yield value (at the expense of increased variable costs). 6.6.12 Discussion Overall, a crop value penalty resulted in some major differences in the genotypes of the evolved control strategies , especially after fruit set occurs . Most of these differences translated into control strategies that prioritize opening the greenhouse ventilation conditionally based on su pra - optimal levels of relative humidity. Some time periods did not evolve setpoints that provi de as much humidity control as one would 146 normally expect (e.g., T AirVentOnD_fr and T AirVent OffD_fr ), and instead rely on the other time periods to perform more aggressive humidity control to compensate. This provides an opportunity for the greenhouse to re main sealed more often during the midday period, thus providing more chances for CO 2 inject ion to occur uninhibited in times where global radiation is expected to be at its peak. Other genotype values evolved to accommodate the overall increase in ventilat ion required for producing Pareto - optimal solutions (e.g., I GlobMax evolved values that are overall lower). Based on the crop value penalty that was introduced, there were distinct changes that were observed in the control strategies discussed in Section 6.6 . Relative humidity management became a lot more important, although the results show that evolved control strategies did not always need to check for sub - optimal levels of relative humidity to do so: it is also possible to s imply choose temperature set points that are low enough that the greenhouse ventilation will open unconditionally. In addition, given the current model for crop value penalty, there were control strategies that simply allow some of the midday periods to hav e sub - optimal levels of rela tive humidity in exchange for a higher rate of photosynthesis (by keeping the greenhouse sealed and injecting CO 2 ), and only doing tighter relative humidity control during the nighttime, morning or evening periods. 6.7 Conclusions The goal of this chapter was fulfill ed, which is to explore the behavior exhibited by the evolved control strategies described in this thesis, as well as to obtain useful information from the evolved genotypes. The control strategies described in this sect ion are initially based on t he classical Vanthoor strategy described in his thesis [4] , with each iteration adding complexity to the controller logic itself. This iterative process was valuable in determining the e ffects and overall efficacy of certain features (e.g., time - based partitioning). Using the classical Vanthoor strategy as reference, evolving the setpoints instead of using the default values yielded some improvements. This much is expected, as this classi cal Vanthoor strategy is no t presented as an optimal strategy; rather, it is a control strategy that would be typical of the locale that was 147 chosen (Almería, Spain) that worked sufficiently well for their study involving the optimization of greenhouse desi gn elements , rather than gr eenhouse operating parameters . Without making any changes to the controller logic itself, this essentially serves as a method to recalibrate setpoints based on historical weather data. While this clearly has its benefits, it is a lso extremely computational ly intensiv e , as it requires around 24 hours to optimize these setpoints for 100 generations using the current ly available resources , which allows us to run 40 instances of the microclimate - crop - yield model in parallel. This mak e s it impractical to use in an online setting (i.e., for optimizing setpoints in an already deployed greenhouse). Therefore, this is better suited for greenhouse control optimization to aid the grower in early stages of planning before committing to making significant financial inves tments. Allowing for setpoints to change based on the time of day was clearly beneficial. Although ideal conditions for the tomato crop are a well - studied subject, obtaining a greenhouse control strategy that can efficiently reac h and maintain these condit ions is still extremely difficult , and is further exacerbated by the unpredictability of the weather. By dividing the setpoints into several distinct copies based on the time of day, we allow these setpoints to evolve into values which are better suited fo r these time periods. Despite the unpredictability of the weather, we can still surmise that there are several major time periods in which we can expect a shift in control strategy: nighttime, morning, midday, and evening. The re sults in Figure 6 . 1 show that adding this time - partitioning feature yields superior Pareto - optimal solutions overall compared to control strategies without that feature. Allowing distinct setpoint s based on two main stages of plant development (i.e., before and after fruit set) provided significant benefits. Before fruit set, some of the main requirements of the tomato crop include m aintaining an acceptable level for the 24 - hour mean canopy temperature and reaching the temperature s um threshold for fruit set to occur. After fruit set, the greenhouse controller must maintain acceptable levels for both instantaneous and 24 - hour mean can opy temperatures, as well as increasing the canopy temperature sum up to a maximum amount (after whic h the rate of fruit growth will be maximized). Failure to meet these canopy temperature requirements will result in complete crop growth inhibition in 148 extr eme cases (by halting all carbohydrate generation from photosynthesis). Although these requirements a re similar before and after fruit set, the addition of sub - optimal instantaneous canopy temperatures as a source of crop growth inhibition after fruit set (as well as seasonal weather differences) still create distinct enough conditions that evolving separ ate values for this stage of plant development was justifiable. Introducing sunrise and sunset calculations, as well as offsets for each of these calculati ons, was also beneficial. The less complex controllers discussed in this chapter used fixed transitio n points between nighttime and daytime (and vice versa) and could not account for basic weather patterns that could normally be exploited. Ideally, these o ffsets should have the ability to be dynamic as well (based on current environmental conditions or ot her properties of the greenhouse controller) , but these offsets were still beneficial in their current state due to allowing for control strategies to adju st the overall duration of nighttime and daytime control strategies. Prior to adding to the controlle rs the capability to evolve boiler PID gain values, the boiler would operate under fixed, predetermined gain values in order to approximate the fuel consum ption of the classical Vanthoor strategy. Whe n allowed to evolve, many control strategies had gain va lues which provided a noticeable improvement in ability to maintain optimal temperature ranges for the crop , thus improving the value of the c rop yield. This naturally comes with a respective increase in variable costs (associated with fuel co nsumption) but creating distinct copies of these values based on whether fruit set has occurred or not helped to minimize the impact of this variable cost increase. By introducing PID - controlled behavior to both ventilation and fogging systems, we observed significant differences in the overall behavior compared to their original operating modes (i.e., fully on or fully off). In addition, having distinct cop ies of these values based on whether fruit set has occurred or not allowed for the behavior of these development stage. However, since the benefits were not as substantial when compared to evolving the osts associated with adding this PID - controlled functionality may affect its economic viability. 149 It was clearly beneficial to adjust the transition points of nighttime control strategies to daytime strategies (and vice versa) based on sunrise and sunset ti mes. Further improvements could likely be achieved by allowing the other transition points (i.e., morning to midday, and midday to evening) to be dynamic a s well . Lastly, much like the dynamic CO 2 setpoint (CO 2AirExtOn ) described in Eq. (6.1), other setpoi nts may be improved by allowing them to change dynamically based on current environmental conditions. The overall behavior displayed by the evolved control strategies in this chapter can be a useful starting point to determine their development, although c aution is still needed to make sure any novel control strategies do not violate known best practices for humidity control during all stages of plant growth . 150 7 Metrics for Decision Making 7.1 I ntroduction The goal of this chapter is to briefly summarize various p erformance metrics for narrowing down the number of control strategies that may suit the needs of a grower . Due to the multi - objective optimization approach used in this thesis, the number of solutions available can be unwieldy and challenging to interpret , so various methods are proposed for narrowing the choices down among a set of Pareto - optimal solutions. In addition, we briefly discu ss a method for comparing the performance of newly developed control strategies against other ones by calculating their h ypervolume s . For purposes of this chapter, the crop value penalty described in Section 6.6 is not included in the economic model output , since it does not affect the methodology behind the performance metrics described in the f ollowing sections . The sections are presented as follows: Section 7.2: N et Financial Result (NFR) Section 7.3: Normalized Hypervolume Between Controllers Section 7.4: Robustness Against Unknown Weather Data Section 7.5: Robustness Against Genotype Perturba tions 151 Figure 7 . 1 . Example Pareto fronts of all the control strategies described in this thesis , compared with the classical Vanthoor strategy. All control strategies were evolved for 100 generations. 7.2 Net Fi nancial Result (NFR) The most strai ghtforward method to filter out results from a Pareto front for this problem is to use a scalarization that aggregates the results of the two objectives into a single number, net financial result (NFR). Defined in Eq. (5. 1), t his consists of the sum of the fixed costs and the two objectives used for multi - objective optimization throughout this thesis (i.e., the variable costs and crop yield value /crop yield economic return ). Table 7 . 1 . Economic model output fo r the four main greenhouse controller types described in this thesis . Control Strategy Type Mean NFR (euros/m 2 × year) Median NFR Standard Deviation Highest NFR Lowest NFR NTP - 1.351 - 1.125 0.235 - 1.059 - 1.948 TP - 1.183 - 1.162 0.324 - 0.786 - 1.891 TP+ - 0.584 - 0.424 0.5 - 0.089 - 1.947 TP++ 0.055 0.407 0.747 0.783 - 1.853 152 Based on Table 7 . 1 , it is clear that the last control strategy (TP++) is preferable: most of the available solutions will be prof itable, and solutions with the same NFR as less complex controllers will provide b etter tradeoff s between the two main objectives; that is, for a given NFR, the more complex controller can provide higher crop value yield or lower variable costs, as seen in Figure 7 . 1 . There are some clear drawbacks to this method. Since the two objectives are into a single objective, useful information can be lost in the process. Broadly speaking, it can be beneficial to consider whethe r the resulting NFR is due to control strategies producing an exceptionally high crop yield value at the expense of increased variable costs (or, conversely, exceptionally low variable costs while sacrificing some crop yield value). This economic model als o does not consider constraints a grower might encounter in practice. For example, minimum (or maximum) crop yield requirements for meeting current demands are not considered, and it is assumed that any quantity/quality of crop yield is acceptable (unless the cr op value penalty in Section 6.6 is used, in which case a percentage of the crop yield will be rendered unmarketable if relative humidity control is inadequate ). All o ther factors that contribute to v ariable costs , such as fossil fuel, CO 2 , water, and labor are also not limited. It would be possible to break these factors apart and make this a many - objective optimization problem; it would also be possible to do a sensit ivity analysis of how these factors influence the crop y ield value/variable cost tradeoffs. However, both are beyond the scope of the current work. Despite these drawbacks, a grower could circumvent them with sufficient knowledge of the available resources to invest in a greenhouse. This way, constraints can be defined for all components that make up the variable costs and/or crop yield value can be included in the economic model . Since much of the information necessary to apply these constraints will be hi ghly dependent on the location, greenhouse design, as we ll as myriad other factors, a more generic approach was presented here instead. 153 7.3 Normalized Hypervolume Between Controller Types Figure 7 . 2 . Example of normalized hypervolumes for each evolved controller des cribed in this thesis, calculated every generation. Given a theoretical ideal point and anti - ideal (or nadir) point, we can calculate the hypervolume for a given Pareto front : for two objectives, it is the area of the two - dimensional polygon created betwee n a Pareto front and the nadir point. This provides a method to s ummarize the overall efficacy of a population of evolved control strategies. However, t his can have similar drawbacks to relying on NFR like in Section 7.2 , and un lik e NFR, it does not provide a value that can easily tell a decision maker whether a particular control strategy is viable or not. That said , this can still be a valuable tool for comparing different types of greenhouse controller s , particularly to determ ine whether or not a feature introduced in a novel controller is currently outperforming (or can eventually outperform) older and/or simpler controllers. It is one means of quantifying the differences between two Pareto fronts i.e., comparing their hypervo lum es. 154 Figure 7 . 2 shows one instance in which each controller type in this thesis is evolved for 100 generations. The hypervolume is computed after each generation of evolu tion and appears as the vertical axis. Clearly, TP++ shows the best performance overall by this metric , and the rate at which the hypervolume increases for each controller slows down considerably long before 100 generations are reached . Sometimes , evolved controllers whose logic is less complex and which are known to be outperformed can still appear to be superior initially (as seen in earlier chapters in Figure 5 . 8 ) due to all populations of control strategies being initialized with random values. This underscores the importance of allowin g each controller to evolve for many generations, as well as having a large enough sample size to observe a statistically significant difference in hypervolume. In Section 5.4 , a Mann - test showed that a sample size o f 5 with 100 generations each was sufficient to show a statistically significant difference in hypervolume between the NTP and TP controller types. If a novel controller is unable to produce hypervolumes that are on - par with or superior to other controller s within 100 generations, it may indicate that it is cu rrently unviable. This is especially true if computational resources are limited, and significantly increasing the number of generations in which a controller is evolved is prohibitively expensive. As an alternative to changing a seemingly unviable control ler, other NSGA - II configuration parameters, as well as other MOEAs , may be explored to obtain better results with a similar investment in computational time. 155 7.4 Robustness Against Unknown Weather Data T able 7 . 2 . E xample of e conomic model output ( euro s × m - 2 × year - 1 ), comparing the classical Vanthoor strategy with the same strategy with evolved setpoints . Weather data for the 2009 2010 season was only used to evaluate control strategies after the optimization step was completed . The fogging system is assumed to have no restrictions in this example to illustrate how some weather seasons can be economically unviable (due to negative NFR), but still have an overal l positive result if multiple weather seasons are consi dered. Original Low Cost High Value Period Crop Value Var. Costs NFR Crop Value Var. Costs NFR Crop Value Var. Costs NFR 2006 - 2007 19.03 10.98 0.19 17.29 8.65 0.79 19.39 10.88 0.66 2007 - 2008 20.69 11.41 1.44 18.72 9.11 1.76 21.10 11.42 1.83 2008 - 2009 17.95 10.97 - 0.88 16.20 8.62 - 0.27 18.29 10.93 - 0.49 2009 - 2010 18.90 10.96 0.09 17.23 8.76 0.62 19.29 10.95 0.49 Total 0.85 2.91 2.49 One approach to narrow down potential solutions is to simply test evolved control strategies against unknown weather data. By using multiple seasons of weather data , we evolved control strategies that adapt to more general weather patterns associated with the locale. To test the efficacy of these evolved c ontrollers, a new weather season was used to measure their fitness . This approach was covered earlier in Chapter 5 , and an example of the outputs of said approach is in T able 7 . 2 . Naturally, control stra tegies that provide the highest NFR against unknown weather data would be preferred in these cases and are One drawback is that simulating additional weather seasons adds considerable computational co st. While it is not as costly to add multiple unknown weather seasons as a post - optimization step, each additional weather season added during the optimization pro cess as part of the fitness calculation can be prohibitively expensive. Moreover, it is possi ble that too many seasons of weather data will cause an a ch allenging problem in and of itself that should b e used for evolving control strategies will depend on many factors, including but not limited to: the available 156 computational resources, the weather patterns in a locale, and the availability of historical weather data. Such a study is beyond the scope of this thesis, and it was assumed that three weather seasons was sufficient for evolving control str ategies ( with one additional, unknown weather season as a post - optimization step to help filter results ). 7.5 Robustness Against Genotype Perturbations The goal i n this section is to present a method to examine the robustness of a control strategy against pert urbations of its genotype. This may be used for obtaining solutions that are also robust in practice, but modeling such perturbations (e.g., inaccurate read ings in temperature sensors) would require extensive knowledge specific to a greenhouse implementa tion, such as the tolerance values pertaining to the greenhouse sensors, how they are deployed inside such a greenhouse, weather conditions, a nd myriad other factors. In this cas e , we use d a simple model to generate these perturbations to show how this me t ric can be used to filter out undesirable control strategies from a Pareto front , as the effect of systematic biases in sensors can mimic the effect of a non - optimal setting of an evolved setpoint. One of the earliest examples bringing attention to the iss ue of robustness in MOEAs was described by Deb et al. [46] , noting that in practice a decision maker may not always be interested in a global optim al solution; rather, solutions that are robust to small pertu rbations in its genotype may be preferred . Based on this study, we propose using the following var iation: 1. All the values in a genotype have perturbations applied to them for every sample. 2. For each original solution in the Pareto front, every locus L at ind ex i of its genotype will have perturbations applied to it, assuming a normal distribution with a mean = L i , and variance 2 = 0.1 × L i . - 100 samples are generated for each original solution , and their fitness functions are calculated . 3. Each original solution is assigned a value based on the area of the convex hull c reated by the outer points among all the sa mples. 157 - Original solutions with smaller convex hull area are considered more robust. Based on this method, the output provides a single value that can be easily sorted to quantify the sensitivity of each solution. While this procedure has similar drawbacks to that of NFR in Section 7.2 , it provides additional information that NFR does not provide, and the convex hulls themselv es can be easily visualized to better interpret these results (see Figure 7 . 3 ). Figure 7 . 3 . Example output of the proposed metric. A solution from the original Pareto front (black) is sampled 100 times with random perturbations, and their fitness function is calculated for each new samp le (red). The outer points of these new solutions are used to obtain the convex hul l (red shaded region). 158 Figure 7 . 4 . Example Pareto front showing the effects of adding perturbations to each solution. The g rey region shows the union of all the polygons generated by the perturbed samples o f the Pareto front. The least sensitive solutions tend to be low - variable - cost solutions (blue region), while high - crop - value solutions can be extremely sensitive (green reg ion). Table 7 . 3 . Partial list of evo lved solutions sorted by increasing convex hull area . Convex Hull Area Crop Yield Value (euros × m - 2 × year - 1 ) Variable Costs (euros × m - 2 × year - 1 ) Original NFR (euros × m - 2 × year - 1 ) Mean NFR (euros × m - 2 × year - 1 ) 0.58 9 16.44 1 8.449 0.141 - 0.153 0.82 6 14.747 8.078 - 1.181 - 1.181 0.908 17.034 8.733 0.451 0.19 9 0.986 15.493 8.225 - 0.582 - 0.814 1.22 6 17.10 9 8.853 0.40 6 0.092 1.439 16.563 8.506 0.206 - 0.06 4 1.47 3 17.33 4 9.029 0.454 0.06 7 1.971 18.13 3 9.807 0.47 6 0.133 2.05 1 17.442 9.166 0.426 0.05 7 2.064 17.695 9.369 0.476 0.181 Based on Table 7 . 3 , we can see that a small convex hull area associated with a solution does not guarantee that the mean and/or ori gina l NFR will be positive. However, it is still a useful tool to filter out 159 undesirable results, as an excessively high convex hull area will lead to unviable NFR values that are, on average, far inferior to the classical Vanthoor strategy (e.g., the gree n sh aded region in Figure 7 . 4 is partially dominated by the classical strategy). In addition, based on the results we can see a tendency for high - crop - value solutions to be highly sensitive to genotype perturbations . If robust solu tions are desired that are viable with respect to having a positive NFR, solutions near the low - variable - cost region of the Pareto front are superior. Solutions that provide good values on both obj ectives are slightly more sensitive (e.g., the red shaded r egion in Figure 7 . 4 ), but can still provide positive mean NFR values despite the perturbations. In addition, these types of solutions dominate the classical Vanthoor strategy, with their perturbed versions becoming non - dominated on ly in their worst cases, and, of course, that is when comparing them to an unperturbed classical Vanthoor strategy. 160 8 Summary and Conclusions I n this chapter we will briefly summarize the results in this thesis, discuss some of the challenges encountered dur ing research, as well as p ossible directions this research could continue to further improve existing methods for optimizing greenhouse control. Based on the results and discussion from the previous chapters, the goal of this thesis was fulfilled. We used an existing microclimate - crop - yield model [4] , which was originally developed with greenhouse design optimization in mind . We then modif ied this methodology for optimizing and developing control strategies instead, using MOEAs as the primary tool for doing so . Using a classical control strategy as a basis, we developed three new versions, each of which improved upon the previous controller by providing better tradeoffs between the two main objectives: maximizing cro p yield value and minimizing variable costs . In addition, we were able to observe some interesting properties in these evolved controllers which provided valuable information on how to iteratively improve control strategies, as well as identified potential limitations of the microclimate - crop - yield model. One of the biggest challenges was overcoming the large amount of computational resources required to apply MOEAs for this type of optimization problem . Early attempts at addressing this issue included modi fying the differential equations that describe the microclimate - crop - yield model (see Chapter 3 ) in order to reduce the stiffness of these equations (and thus improv e the overall speed of the ODE solver by allowing larger simula tion step sizes that are still within acceptable margins of error) . This approach showed some promise , but it ultimately proved to have considerable challenges for validation of results, including providing insufficient crop yields to match those reported in existing literature. As an alternate solution to the pre vious problem, implementing a subset of the microclimate - crop - yield model described by Vanthoor (as described in Chapter 4 ) was sufficient to achieve the main goal o f t his thesis . This model was originally developed to be modular in nature, considering the possibility of many different greenhouse design configurations, which made this approach possible. This subset of the microclimate - crop - yield model describes a rela tiv ely complex greenhouse design while still having 161 acceptable simulation times, which allowed us to adequately explore and optimize challenging greenhouse control problems . However, there is clear room for improvement in this regard , as there are many gre enh ouse design elements that were not considered, including but not limited to: retractable shading screens, supplemental lighting, passive greenhouse heating, mechanical/pad and fan cooling, direct air heating, etc. Such greenhouse design elements should ide ally be considered in future studies for greenhouse control optimization as this would improve the practicality of our optimization method , but doing so requires examining existing models that incorporate these greenhouse design elements, and potentiall y m odify ing these models to improve simulation speeds to the extent that optimization with MOEAs can still remain feasible. Moreover, these model modifications would require independently validating the results obtained in a real greenhouse to verify their ef ficacy and/or make corrections to the model, as needed , which is beyond the scope of what we could attempt here. Despite introducing various distinct controller types in this thesis (in Chapters 5 and 6 ) , each with increasing complexity, we did not reach a point where the computational resources we re the primary bottleneck when developing and evolving more complex control strategies . This is mostly due to the focus of this thesis being on iteratively i mproving existing controller types (as seen in Chapter 6 ): using the classical greenhouse control strategy as a starting point, we gradually increased its complexity, observed the overall behavior these new control strategies pr oduced, and subsequently used those r esults to find useful properties to improve further (or features that were detrimental and therefore removed). While it would be trivial to present a control strategy whose genotype takes considerably longer to evolve, meaningfully interpreting the results of such a controller would take considerable time without additional techniques to aid in this process. Ideally, this should be streamlined by at least partially automating the process with which key properties, rules, and/or design principles can be extr acted from the Pareto fronts generated by each new controller type that is introduced. Multi - objective optimization e attempts have been made in the past to present viable approaches for automated innovization [50, 51] . 162 The results in Section 6.6 show that while the current microclimate - crop - yield mod el is adequate for simulating tomato crop growth in a greenhouse setting, inadequate humidity control is not sufficiently penalized in cases where a model - based optimization approach is used to improve control strategies (e.g., this dissertation). The trap ezoid functions that make up the crop value penalty primarily affect the post - fruit - set stage of plant growth, since these penalties are only applied after harvest begins . This penalty still has an effect on the overall behavior of the control str ategy bef ore fruit set, due to maintaining a 24 - hour mean value of the vapor pressure deficit (VPD 24 ) between the canopy and the greenhouse air, as well as a 48 - hour mean value of the relative humidity (RH 48 ) of the greenhouse air. However, this would have a margin al effect overall before fruit set, since the pre - fruit - set control strategy only needs to yield an acceptable range of both VPD 24 and RH 48 shortly before fruit set begins. Values like RH 48 were proposed to model the effect of the onset of the fun gus Botry tis cinerea on the crop, but this type of fungal infection is not limited to affecting the yield of marketable tomatoes, and can infect all the plant tissue [52] . Ideally, the microclimate - crop yield model should penalize sub - optimal levels of relative h umidity a t all stages of plant growth to better reflect the real - world effects of fungal infections and other diseases on the tomato crop. It was assumed that no additional costs would be incurred from the implementation of these control strategies (other than the costs of any resources they utilize) , and that the features described in each controller in this section would already be available to use. Although an effort was made to avoid major greenhouse design changes, both fixed and variable costs associa ted with the development of additional controller logic and upgrades to greenhouse design elements should be included (when applicable). Depending on their real - world cost, these may affect the viability of more complex control strategies. Both objectives , the var iable costs and crop yield value, may also be divided into individual components that can be treated as their own separate objective s (thus turning this into a many - objective optimization problem , as opposed to two - objective). Assuming that the ap propriate computational resources are 163 comprise the variable costs and crop yield value, which may be of interest to a decision maker in practice. Finally , the metr ics for decision making presented in Chapter 7 allow a user to significantly narrow down solutions that may be of interest. When using both net financial result (NFR) and the convex hull area (as seen in Section 7.5 ) as performance metrics, we are able to narrow down potential solutions quickly while visualizing the overall robustness (with respect to genotype perturbations) when picking a specific solution. The method proposed for measuring robustness against genotype pe rturbations assumes that these perturbations can be modeled using a simple normal distribution, and as such does not reflect the inconsistencies that one would encounter in practice. However, such a method could still be applied if ther e is sufficient know ledge of a greenhouse implementation to model these perturbations , providing a 164 LITERATURE CITED 165 LITERATURE CITED [1] G. van Straten, G. van Willigenburg, E. van He nten, and R. van Ooteghem, Optimal Control of Greenhouse Cultivation . Boca Raton, Florida, USA: CRC Press, 2010, p. 326. [2] K. Fernandez - Stark, P. Bamber, G. Gereffi, G. Ahmed, S. J. Heil, and C. Root, "The frui t and vegetables glob al value chain: Economi c upgrading and workforce development," Center on Globalization, Governance & Competitiveness (CGGC), Duke University, North Carolina, USA, 2011. [3] K. J. Boote and J. M. S. 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