AN EVOLUTIONARY MULTI-OBJECTIVE APPROACH TO  

SUSTAINABLE AGRICULTURAL WATER AND NUTRIENT OPTIMIZATION 

 
 
 
 
 
 

 
By 

Ian Meyer Kropp 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

A DISSERTATION 

Submitted to 

Michigan State University 

in partial fulfillment of the requirements 

for the degree of 

 

Biosystems Engineering – Master of Science 

 

2018 

 
 
 
 

 

 

ABSTRACT 

AN EVOLUTIONARY MULTI-OBJECTIVE APPROACH TO  

SUSTAINABLE AGRICULTURAL WATER AND NUTRIENT OPTIMIZATION  

By 

Ian Meyer Kropp 

One of the main problems that society is facing in the 21st century is that agricultural production 

must  keep  pace  with  a  rapidly  increasing  global  population  in  an  environmentally  sustainable 

manner. One of the solutions to this global problem is a system approach through the application 

of  optimization  techniques  to  manage  farm  operations.  However,  unlike  existing  agricultural 

optimization research, this work seeks to optimize multiple agricultural objectives at once via 

multi-objective  optimization  techniques.  Specifically,  the  algorithm  Unified  Non-dominated 

Sorting  Genetic  Algorithm-III  (U-NSGA-III)  searched  for  irrigation  and  nutrient  management 

practices that minimized combinations of environmental objectives (e.g., total irrigation applied, 

total  nitrogen  leached)  while  maximizing  crop  yield  for  maize.  During  optimization,  the  crop 

model named the Decision Support System for Agrotechnology Transfer (DSSAT) calculated the 

yield and nitrogen leaching for each given management practices. This study also developed a 

novel bi-level optimization framework to improve the performance of the optimization algorithm, 

employing U-NSGA-III on the upper level and Monte Carlo optimization on the lower level. The 

multi-objective optimization framework resulted in groups of equally optimal solutions that each 

offered a unique trade-off among the objectives. As a result, producers can choose the one that 

best addresses their needs among these groups of solutions, known as Pareto fronts. In addition, 

the bi-level optimization framework further improved the number, performance, and diversity of 

solutions within the Pareto fronts. 

 

 

 

 

 

Copyright by 
IAN MEYER KROPP 
2018 

 

 

 

 

 

 

 

 

 

 

To my family, to whom I owe where I am, and to my fiancé, who keeps me moving forward 

 

iv 

ACKNOWLEDGMENTS 

 

 

This work would not have been possible without my brilliant and dedicated professors, 

coworkers, friends and family. I stand on the shoulders of peers. In particular, I’d like to thank 

my major professor Dr. Pouyan Nejadhashemi for bringing together, mentoring, and efficiently 

running our diverse and prolific laboratory. Also, this research would not be possible without the 

pioneering research by Dr. Kalyanmoy Deb, as well as his patient teaching and mentoring. 

Finally, I thank Dr. Timothy Harrigan for keeping our research headed firmly toward practical 

real-world applications that improve our planet. This research also would not be possible without 

the direct contributions of Gerrit Hoogenboom, Mohammad Abouali, and Proteek Roy. 

Equally important to this research are the intellectual and emotional support from my lab mates: 

Sebastian Hernadez, Melissa Rojas-Downing, Matthew Herman, Mohammad Abouali, Umesh 

Adhikari, Yirigui, Babak Saravi, Nathan Anthony. 

Finally, I would not be where I am today if not for my friends, and family. In particular, my 

fiancée Kaitlyn, my siblings Julia and Emma and my parents are constant sources of inspiration 

and drive. Also, the members of an extremely long list of deep friends deserve significant credit. 

These include, but are not limited to, Andy Low, Barret Hoster, Emma Sanders, Levi Beach, 

Marisa Sandahl, and Mike Fox. 

 

v 

TABLE OF CONTENTS 

 
 
LIST OF TABLES ....................................................................................................................... viii 
 
LIST OF FIGURES ....................................................................................................................... ix 
 
LIST OF ALGORITHMS ............................................................................................................... x 
 
KEY TO ABBREVIATIONS ........................................................................................................ xi 
 
1. INTRODUCTION ...................................................................................................................... 1 
 
2. LITERATURE REVIEW ........................................................................................................... 2 
2.1  Nutrient and Water Management in Agricultural Intensification .................................... 2 
2.2  Optimization Objectives ................................................................................................... 4 
2.2.1  Micro Agricultural Management Applications ......................................................... 5 
2.2.2  Macro Agricultural Management Applications ........................................................ 5 
2.3  Optimization Techniques ................................................................................................. 6 
2.3.1 
Classical and Evolutionary Single Objective Optimization Approaches ................. 6 
2.3.2  Multi-Objective Optimization ................................................................................... 7 
2.3.2.1  Classical Multi-Objective Approaches ............................................................... 8 
2.3.2.2 
Evolutionary Multi-Objective Optimization ....................................................... 9 
2.3.2.2.1  Non-Dominated Sorting Evolutionary Multi-Objective Optimizations ....... 10 
2.3.2.2.2  Other Evolutionary Multi-Objective Optimization Algorithms ................... 13 
2.3.2.2.3  Many-Objective Optimization ...................................................................... 15 
Literature gaps ................................................................................................................ 16 

2.4 

3.4 

 
3. MATERIALS AND METHODS .............................................................................................. 17 
3.1  Modeling process ........................................................................................................... 17 
3.2 
Study area ....................................................................................................................... 20 
3.3  Optimization Platform .................................................................................................... 21 
3.3.1  Objective Function .................................................................................................. 21 
3.3.2  Optimization Algorithm Choice and Setup ............................................................. 23 
3.3.3  Optimization Strategies and Configuration ............................................................ 25 
Post-processing and visualizations ................................................................................. 28 

 
4. RESULTS AND DISCUSSIONS ............................................................................................. 30 
Single-level optimization results .................................................................................... 30 
Strategy 1: Single Level Irrigation Minimization and Yield Maximization ........... 30 
4.1.1 
4.1.2 
Strategy 2: Single Level Irrigation Minimization, Nitrogen Minimization, and Yield 
Maximization ......................................................................................................................... 33 
4.1.3 
Strategy 3: Single Level Irrigation Minimization, Nitrogen Minimization, Leaching 
Minimization and Yield Maximization ................................................................................. 38 
4.2  Bi-level optimization results .......................................................................................... 41 
Strategy 4: Bi-Level Irrigation Minimization and Yield Maximization ................. 41 
4.2.1 
4.2.2 
Strategy  5:  Bi-Level  Irrigation  Minimization,  Nitrogen  Minimization,  and  Yield 
Maximization ......................................................................................................................... 43 

4.1 

vi 

4.2.3 
Strategy 6: Bi-Level Single Level Irrigation Minimization, Nitrogen Minimization, 
Leaching Minimization and Yield Maximization ................................................................. 45 
4.3  Application frequency analysis ...................................................................................... 46 

 
5. CONCLUSIONS ....................................................................................................................... 50 
 
6. CURRENT FINDINGS AND FUTURE RESEARCH ............................................................ 52 
 
7. FUTURE APPLICATIONS ...................................................................................................... 53 
 
APPENDIX ................................................................................................................................... 54 
 
REFERENCES ............................................................................................................................. 56 
 
 

 

vii 

 
 
Table 1. Summary of the optimization strategies ......................................................................... 27 

LIST OF TABLES 

Table 2. Top five (ranked by yield) optimal results compared to best practices (Strategy 1) ...... 32 

Table  3.  Top  five  (ranked  by  yield)  optimal  irrigation  and  nitrogen  results  compared  to  best 
practices (Strategy 2). ................................................................................................................... 37 
 

 

viii 

LIST OF FIGURES 

 
Figure 1. Example of non-dominated sorting in a two objective minimization problem ............. 11 
 
Figure 2. Proposed integrated bi-level and DSSAT framework ................................................... 19 
 
Figure 3. Location of the field of study ........................................................................................ 21 
 
Figure 4. Pareto front for Strategy 1, which maximized yield and minimized irrigation amount 33 
 
Figure 5. Pareto front for Strategy 2. A surface was passed through the solutions to better visualize 
the shape of the front. The color of the surface represents the yield for that given region of the 
front. .............................................................................................................................................. 38 
 
Figure 6. Pareto front for Strategy 3, which maximized yield, minimized nitrogen application, 
minimized  irrigation  application,  and  minimized  nitrogen  leaching.    The  color  of  the  surface 
represents the leaching of the solution .......................................................................................... 39 
 
Figure 7. Strategy 1 results compared to Strategy 4 results .......................................................... 41 
 
Figure 8. Strategy 2 versus Strategy 5 results. Non-dominated Strategy 5 results are the black 
circles and non-dominated Strategy 2 results are red stars ........................................................... 44 
 
Figure 9. Non-dominated Strategy 6 results ................................................................................. 46 
 
Figure  10.  Application  frequency  analysis  a)  Histogram  of  irrigation  application  count  among 
Strategy  4  solutions.  Solutions  are  color-coded  according  to  their  respective  yield  cluster  (see 
section 2.4). b) Box plots of the total irrigation applied in Strategy 4 solutions, divided by the 
number of applications applied along the x-axis. The data is further divided and color coded into 
the clusters as described in section 2.4. ........................................................................................ 47 
 
Figure 11. a.) Histogram of irrigation application count among Strategy 5 solutions. b.) Histogram 
of nitrogen application count among Strategy 5 solutions. Solutions are color coded according to 
their respective yield cluster (see section 2.4). ............................................................................. 49 
 
Figure A.1. Cluster analysis for a) Nitrogen application counts and b) irrigation application counts
....................................................................................................................................................... 55 
 
 

 

ix 

LIST OF ALGORITHMS 

 
 

Algorithm 1: Bi-Level Optimization for Agricultural Optimization…………………………… 26 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x 

 

BMP 

CSM 

DE 

 

 

 

DSSAT 

EA 

 

EMO   

GA 

GP 

MO 

 

 

 

KEY TO ABBREVIATIONS 

Best management practices 

crop simulation model 

Differential evolution 

Decision Support System for Agrotechnology Transfer  

Evolutionary Algorithms 

Evolutionary Multi-Objective Optimization  

Genetic algorithm 

Genetic programming 

Multi-Objective Optimization 

MOCPSO  multi-objective chaos particle swarm optimization  

MOFLP 

Multi-objective Fuzzy Linear Programming 

NP-hard 

Non-deterministic Polynomial-time hard  

NSGA-II 

Non-dominated Sorting Genetic Algorithm II 

NSGA-III   Non-dominated Sorting Genetic Algorithm III 

PSO 

 

SWAT  

UF 

 

Particle swarm optimization  

Soil and Water Assessment Tool  

University of Florida 

U-NSGA-III   Unified Non-dominated Sorting Genetic Algorithm-III  

WSM   

Weighted Sum Method 

xi 

1. 

INTRODUCTION 

One of the major challenges that the world is facing in the coming decades is how to meet growing 

food demand without compromising the integrity of our environment (Mueller et al., 2012). An 

estimate suggests that global food production needs to be increased by 60-110% between 2005 

and 2050 (Pradhan et al., 2015). Even so, by closing the yield gaps, which is the difference between 

attainable  yield  and  actual  yield  in  a  region,  most  countries  are  expected  to  meet  food  self-

sufficiency or to improve their current food self-sufficiency levels (Pradhan et al., 2015). Water 

and nutrient availability are the major production limiting abiotic factors in the regions where the 

yield  gaps  are  high  (Hengsdijk  and  Langeveld,  2009)  and  thus  effective  water  and  nutrient 

management plays a crucial role in food security by closing the yield gaps. In addition, optimizing 

water and nutrient management not only improves crop yield, but also reduces production cost, 

conserves resources, and protects the environment. However, the presence of multiple conflicting 

criteria, expensive simulation routines, nonlinearities in objective functions, and constraints make 

the  optimization  of  such  a  system  very  difficult.    Here,  we  are  proposing  to  evaluate  the 

performance of evolutionary multi-objective optimization methods as an alternative approach for 

addressing these types of socio-economic problems. To test this hypothesis, this thesis seeks to 

address the following research objectives through the utilization of evolutionary multi-objective 

optimization methods: 1) identification of the best irrigation practices to achieve high crop yields 

at minimum water usage, 2) identification of the best irrigation and nutrient management practices 

to achieve high crop yields at lowest environmental cost, 3) evaluate the importance of the number, 

time, and amount of irrigation and fertilizer applications on crop yields.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 

2. 

LITERATURE REVIEW 

The  application  of  optimization  in  agricultural  intensification  has  a  long  and  rich  history. 

Researchers  have  applied  classic  single  objective  optimization  techniques  (e.g.,  linear 

programming, dynamic programming, and genetic algorithms) to a wide range of applications 

since the 1960s (Flinn and Musgrave, 1967). But within the last 25 years, agricultural engineers 

have  embraced  a  new  and  powerful  class  of  optimization  algorithms  know  as  multi-objective 

optimization (MO).  

This literature review seeks to aggregate and analyze the current state of the art applications of 

MO algorithms within the concept of agricultural intensification. In this literature review we first 

introduce  nutrient  and  water  management  in  Nutrient  and  Water  Management  in  Agricultural 

Intensification, and then we summarize currently ubiquitous applications for MO algorithms in 

agricultural  intensification  in  the  Optimization  Objectives  section.  In  the  following  section 

Optimization  Techniques,  the  literature  review  then  describes  and  analyzes  optimization 

techniques within the literature and covers case studies of algorithms and their applications in 

agricultural intensification.  

2.1 Nutrient and Water Management in Agricultural Intensification  

As water and nutrients are the limiting abiotic factor in agricultural intensification, they are the 

decision  variables  in  focus  in  this  review.  For  water  specifically,  as  the  sustainability  of 

agricultural  water  use  is  affected  by  competition  from  non-agricultural  water  use  and  climate 

change, there is an increasing interest in minimizing agricultural water use through improving 

water productivity (Morison et al., 2008). Water productivity is defined as crop yield per volume 

of water applied (Kijne et al., 2003). Water applied to the cropped fields can be lost either as a 

productive (transpiration) or as an unproductive (soil evaporation, infiltration, and runoff) water. 

Increasing water productivity entails increasing the productive water use while minimizing the 

2 

unproductive  water  losses.  By  optimizing  the  irrigation  schedule  and  increasing  the  water 

productivity, more amount of crop can be harvested with the same amount of irrigation water. In 

dry  areas  where  cultivated  land  is  limited  by  the  lack  of  sufficient  water,  optimizing  water 

productivity at a farm scale would help bring more area under cultivation by increasing water 

availability.  In  addition,  optimizing  the  operation  of  regional  water  systems  (e.g.,  irrigation 

networks, reservoirs) can increase the area of land under cultivation by assuaging water shortages 

in arid regions and regions with non-agricultural competition.   

Similarly, fertilization is essential for increasing crop productivity; however, over-application or 

incorrect  timing  of  fertilization  may  lead  to  contamination  of  surface  and  groundwater 

(Adesemoye et al., 2008). Focusing on a single nutrient, such as nitrogen, and its over-application 

causes nutrient imbalance, economic loss, and environmental pollution (Goulding et al., 2008), 

while under application leads to poor crop yield. Nutrient management involves managing the 

amount, source, timing and method of nutrient application to minimize nutrient loss and maximize 

plant  uptake  (Gaskin  and  Wilson,  2009).  Nutrient  management  optimization  synchronizes 

fertilization application with plant nutrient utilization, which maximizes crop yield and quality, 

increases profit, conserves resources and enhances soil quality and productivity. This is important 

to ensure long-term food security through a proper balance between increased food production, 

soil health and environmental quality (Lamessa, 2016). 

Furthermore, water and nutrient management together have an even greater impact on agricultural 

intensification. Under a limited water supply, plant nutrient plays an important role in enhancing 

water productivity (Waraich et al., 2011). Under normal water supply condition, transpiration rate 

is increased by fertilization; however, under dry condition, fertilization has been found to result in 

depressed plant growth and higher seedling mortality rate (Li et al., 2009; Rahimi et al., 2013). 

Effective  water  management  improves  nutrient  availability  and  helps  the  transformation  of 

3 

nutrients  in  the  soil  (Li  et  al.,  2009).  Hence,  in  the  regions  where  both  nutrient  and  water 

availability are constraints to crop yield, combined water and nutrient management is essential in 

increasing crop production. Therefore, optimizing nutrient and water management help improve 

food security by closing the yield gap, especially in the developing world. For example, for maize 

in Sub-Saharan Africa, closing the yield gap to 50% of the attainable yield can be achieved through 

nutrient  management,  but  to  close  the  yield  gap  to  75%  of  the  attainable  yield,  simultaneous 

nutrient and water management is required (Mueller et al., 2012). 

To  computationally  optimize  agricultural  intensification,  it  is  necessary  to  develop  efficient 

computation  models  for  these  agricultural  systems.  The  arrival  of  physiologically  based  crop 

growth models allowed researchers to simulate plant growth and yield under varying irrigation and 

fertilizer  supply.  Some  of  the  widely  used  model  such  as  GOSSYM  (Baker  et  al.,  1983), 

CROPGRO  (Boote  et  al.,  1998),  CERES-Maize  (Jones  et  al.,  1986),  CERES-Wheat  (Ritchie, 

1985), SOYGRO (Wilkerson et al., 1983), PNUTGRO (Boote et al., 1992), AquaCrop (Steduto et 

al., 2009) and CropWat (Smith, 1992) have been used and improved in the past few decades. 

Hydrological models such as SWAT (Arnold et al., 2012, Neitsch et al., 2011), TOPMODEL 

(Kirkby, 1975), and MIKE SHE (DHI, 2003) allow researchers to evaluate the environmental 

impact,  agricultural  productivity  and  economic  productivity  of  agricultural  practices  on  entire 

regions. 

2.2  Optimization Objectives 

MO algorithms are currently applied to two broad categories: micro agricultural management and 

macro  agricultural  management.  Micro  agricultural  management  attempts  to  optimize  the 

performance in a single agricultural unit (e.g., a single field or a single farm enterprise), where 

macro  agricultural  management  attempts  to  optimize  the  performance  multiple  individual 

agricultural units at the watershed, county, or regional scales. 

4 

2.2.1  Micro Agricultural Management Applications 

The  less  ubiquitous  micro  agricultural  management  applications  of  MO  include  irrigation 

management (Akbari et al., 2018; García-Vila et al., 2009), and crop planning (Groot et al., 2012; 

Mello Jr et al., 2013; Sarker and Ray, 2009). Even at a smaller scale, agricultural intensification 

problems still pose multiple conflicting objectives at the micro agricultural management scale and 

are therefore are ideal for MO techniques. For example, trying to minimize the levels of nitrogen 

loss in a given field will conflict with the overall yield of the crop (Hengsdijk and Langeveld, 

2009).   

2.2.2  Macro Agricultural Management Applications  

There are abundant examples of MO being applied to macro agricultural management objectives, 

such nutrient tax policy (Whittaker et al., 2017), irrigation network operation (Ashofteh et al., 

2015; Fernández García et al., 2014), land use (Groot et al., 2007), and regional crop planning 

(Sarker and Ray, 2009, 2005; Tan et al., 2017; Wang et al., 2012). MO is a popular choice in macro 

agricultural management because there are large numbers of conflicting objectives on a regional 

scale. For example, producers near a river may over apply nutrients to maximize their output, 

where regional governments may seek to minimize consequent algal blooms in a local reservoir. 

Or  perhaps  the  consistent  hydrologic  head  required  for  hydroelectric  power  generation  is 

interrupted by high irrigation demands in the tropical dry season (Quinn et al., 2018). In addition 

to being multi-objective, macro agricultural management applications are ideal for evolutionary 

algorithms (section 2.3.1). Irrigation scheduling, for example, is an NP-hard problem (Anwar and 

Haq, 2013). The set of NP-hard problems is defined as the set of problems that have not been 

solved  by  algorithms  in  polynomial  time,  and  are  possibly  be  unsolvable  in  polynomial  time 

(Cormen et al., 2009). The difficulty of such irrigation problems renders most simple brute force 

algorithms unrealistic, and evolutionary algorithms are therefore popular choices in the literature.  

5 

2.3  Optimization Techniques  

2.3.1  Classical and Evolutionary Single Objective Optimization Approaches 

In general terms, optimization algorithms search for optimal solutions within a decision variable 

space. Decision variable space is the space containing all the possible choices that a decision-

maker can implement. One example decision space in agriculture would contain all the possible 

combinations  of  irrigation  dates  and  amounts  (between  0  and  50  mm)  for  a  120-day  growing 

season. With 51120 or 8.09∙10'()  different solutions, this decision space is too large for a human 

to reasonably evaluate in its entirety. Under these types of conditions, optimization algorithms can 

be useful tools. Optimization problems are typically defined by one or more decision variables 

(e.g.,  when  to  irrigate)  and  by  one  or  more  objective  functions  that  numerically  define  the 

performance of a given solution (e.g., the seasonal yield for a single irrigation scheme).  

Classical optimization techniques, for this paper, optimize only a single objective function and are 

fully deterministic (Deb, 2009). This class of algorithms typically has excellent performance with 

a  certain  subset  of  optimization  problems  (e.g.,  a  differentiable,  linear,  or  unimodal  objective 

function), and includes, among others, Quasi-Newton, gradient descent, linear programming, and 

golden search section search (Deb, 2009). But outside their narrow scopes of high performance, 

classical optimization techniques struggle to search for optimal solutions in highly non-linear, non-

differentiable, multi-modal, and/or multi-objective problems (Goldberg, 1989).  

Evolutionary  optimization  techniques  offer  a  less  specialized,  and  more  flexible  approach  to 

optimization. Where classical methods solve problems deterministically, evolutionary algorithms 

traverse search spaces with stochastic heuristics inspired by the phenomenon of evolution. Genetic 

algorithms (GA), a widely used subset of evolutionary algorithms, mimic evolution by creating an 

initial random “population” of solutions that evolve towards more and more ideal solutions after 

each generation (Gen and Cheng, 2000). Each individual of a population has a set of “genes” that 

6 

represent the specific decision variables for that given solution, and each solution in a population 

is evaluated and ranked using a fitness function (i.e., objective function). The fittest solutions are 

paired with each other, and their genes are recombined into offspring solutions. Mutation operators 

create further diversity in the population. Ideally, the population as a whole will converge on an 

optimal solution, though there is no way to guarantee a solution is the true optimal solution. Similar 

to DNA, the genes can be coded as binary strings that can br crossed over with the genes of a mate 

solution (Holland, 1975). Alternatively, in real coded GA, genes can also be coded as arrays of 

real numbers and genes are crossed over using a process known as simulated binary crossover 

(Deb and Agrawal, 1995).  

2.3.2  Multi-Objective Optimization  

What differentiates single objective algorithms and MO algorithms is the number of and nature of 

objectives. Single objective algorithms on the one hand search for a solution that satisfies a single 

objective,  and  MO  algorithms  on  the  other  hand  search  for  solutions  that  satisfy  multiple 

conflicting objectives. Conflicting objectives are objectives that cannot be satisfied with a single 

solution.  For  example,  a  hypothetical  producer  wants  to  optimize  his  or  her  urea  application 

practices to a) maximize crop yield and b) minimize nitrogen application totals. The ideal solution 

that maximized crop yield would require generous amounts of urea, while the ideal solution that 

minimized total urea applied would use no urea at all. Therefore, this example has at least two 

equally optimal solutions: a solution that maximizes yield and a solution that minimizes total urea 

application. In other words, an optimization problem with two conflicting objectives will have a 

two-dimensional set of equally optimal solutions, and an optimization problem with n conflicting 

objectives would have an n-dimensional set of equally optimal solutions (Goldberg, 1989).  These 

sets of solutions are known as Pareto fronts, and each member of the Pareto front are known as a 

non-dominated  solution  (Tamaki  et  al.,  1996).  Non-dominated  solutions  are  solutions  in  a 

7 

population  that  are  not  dominated  by  any  other  solution,  where  dominance  is  defined  as 

outperforming a solution in every single objective. In summary, algorithms that can effectively 

search through multi-objective solution space are highly applicable to outstanding agricultural 

engineering problems with conflicting multiple objectives. 

2.3.2.1 Classical Multi-Objective Approaches 

 

During  the  naissance  of  the  MO  field,  algorithms  resolved  conflicting  objectives  by  reducing 

multiple objectives to a single objective. Once reduced to a single objective, a single objective 

optimization technique will find the optimum. These “classical” MO algorithms reduce the search 

space into a smaller region of the Pareto front. Subsequently, MO algorithms often allow for search 

within  different  regions  of  the  Pareto  front.  The  family  of  classical  MO  algorithms  includes 

weighted sum, Tchebyshev (Miettinen, 2012), Benson’s (Benson, 1978), and ε-constraint methods 

(Haimes, 1971). 

Several papers in the literature employ the weighted sum approach. In its most common form, the 

weighted sum approach multiplies an objective vector O of n objectives by a weight vector w, and 

then sums the items of the product vector together into a single objective. 

*+,-./00=2*343
356
7

 

With the multi-objective vector reduced to a single value, a classical single objective technique 

(e.g., GA or Linear Programming) will then use Ooverall as an objective function. The weight vector 

represents  the  importance  given  to  each  objective  by  a  human  decision-maker,  and  relatively 

higher weights endow a given objective more impact on the fitness of a solution.  

There are several applications of the weighted sum method (WSM) in agricultural engineering. 

Nixon  et  al.  (2001)  applied  the  WSM  to  solve  off-farm  irrigation  channel  delivery  schedules. 

8 

Nixon’s framework maximizes “the number of orders that are scheduled to be delivered at the 

requested time” and minimizes “…variations in the channel flow rate.” Behind the WSM lies a 

single objective genetic algorithm. Tan et al. (2017) reduced a multi-objective problem to a single 

objective  fuzzy-robust  linear  programming  problem,  using  relative  membership  grades  as  the 

weights. Sarker and Ray (2009) also used the WSM to validate the results of an evolutionary multi-

objective  optimization  (EMO)  algorithm,  the  Non-dominated  Sorting  Genetic  Algorithm  II 

(NSGA-II), in a crop planning problem. Using WSM is a common validation tool in EMO research 

(Deb, 2009). 

The  epsilon  constraint  method  (Haimes,  1971)  also  converts  a  multi-objective  problem  into  a 

single objective problem but instead uses constraints to reduce the number of objectives. In an n 

objective problem, (n – 1) of the objectives are constrained to a single value, and the remaining 

objective is solved using a single objective method. Consoli et al. (2008) translated a two objective 

problem down into a single objective non-linear programming problem. The researchers, trying to 

1)  minimize  irrigation  deficit  and  2)  maximize  net  economic  benefits,  constrained  the  second 

objective function while minimizing the first objective function. Sarker and Ray (2009) used the 

epsilon constraint method to validate their NSGA-II crop planning optimization.  

Other classical approaches include Genetic Programming, as used by Ashofteh et al. (2015) to 

minimize regional vulnerability to irrigation deficits and to maximize reservoir reliability. Two 

optimization scenarios, one in recent past and one in the near future, produced unique solutions to 

two unique climate scenarios.  

2.3.2.2 Evolutionary Multi-Objective Optimization 

During the 1990s and 2000s, EMO techniques grew in popularity. Evolutionary algorithms (EA) 

are  powerful  tools  for  solving  MO  problems  because  EAs  search  for  populations  of  optimal 

9 

solutions each generation. Therefore, a population-based approach allows an algorithm to search 

for an entire Pareto set of solutions. 

2.3.2.2.1 

Non-Dominated Sorting Evolutionary Multi-Objective Optimizations 

In MO problems, non-dominated sorting is an effective means of ranking solutions in a population 

based on their convergence. Suggested by David Goldberg (1989), non-dominated sorting groups 

solutions into increasingly better non-dominated fronts (Figure 1) in terms of convergence. A non-

dominated front contains solutions that are all non-dominated (i.e., no solution in the set dominates 

another solution within the set). The process starts by finding all of the non-dominated solutions 

in a population. These solutions become the first and highest ranked non-dominated front. The 

front  is  then  removed  from  the  rest  of  the  population,  and  the  second  highest  ranked  front  is 

identified. The process is repeated until all solutions are categorized into ranked non-dominated 

fronts. Once so ranked, an algorithm can quickly identify the dominance relationship between 

members in a population. For example, all solutions in the third highest ranked non-dominated 

front would automatically be chosen for the next generation over a solution from the fourth highest 

ranked non-dominated front.  

10 

 

Figure 1. Example of non-dominated sorting in a two objective minimization problem 

Agricultural  researchers  have  employed  members  of  the  NSGA-II  family  of  algorithms 

consistently  since  the  mid-2000s.  NSGA-II  is  a  powerful,  quick,  and  simple  EMO  algorithm 

developed by Deb et al. (Deb et al., 2002), which uses a combination of non-dominated sorting 

(Goldberg,  1989)  and  crowding  distance  to  rank  the  fitness  of  a  population  of  solutions.  The 

algorithm balances the goals of convergence through non-dominated ranking, and then population 

diversity through crowding distance ranking. NSGA-II performs best with one and two objectives, 

decently with three objectives, and poorly four or more (or “many”) objective problems. NSGA-

II also implements the concept of elitism, in which the parents in one generation, instead of being 

removed from the population after their given generation, have the opportunity to be carried on to 

the following generation (Deb et al., 2002).  

11 

NSGA-II  appears  in  a  wide  breadth  of  papers  in  the  agricultural  engineering  literature.  Its 

popularity  mainly  stems  from  its  ease  of  use,  simple  parameters,  and  balance  of  population 

convergence and diversity. In two papers, Sarker and Ray (2009, 2005) developed and employed 

a variant on NSGA-II to optimize crop-planning practices. Both studies examined an agricultural 

region containing multiple farms and sought to assign crops to each farm optimally. In the first 

paper, the total economic investment in the region was minimized while the regional profit was 

maximized (Sarker and Ray, 2005). For the second paper, the total gross margin was maximized 

while the total cultivation cost was minimized (Sarker and Ray, 2009).  Another research group, 

Darshana et al. (2012), attempted to maximize gross economic output and minimize water usage 

in a region in Ethiopia by changing the cultivars of three different farms in Ethiopia. NSGA-II 

optimized two objectives: an objective to maximize net benefits for farmers and an objective to 

minimize the water requirements from the crops. The research of Perea et al. (2016) optimizes 

pressurized irrigation, specifically sectoring operations. Using a customized version of NSGA-II, 

Perea et al. (2016) minimized the cost of running pumping stations while maximizing farmer’s 

profit in a region in Spain. In another application of NSGA-II, Lalehzari et al. (2016) studied the 

optimal allocation of groundwater and surface water for deficit irrigation. Lalehzari et al. (2016) 

aimed to minimize the total water allocated and maximize the profit relative to the production 

costs. The authors then ran the same multi-objective optimization problem using particle swarm 

optimization.  Most recently, Whittaker et al. (2017) developed a unique bi-level optimization 

routine to determine the optimal fertilizer tax on a watershed. Inspired by the Stackelberg game 

(Von Stackelberg, 2010), they first optimized the spatial distribution of a proposed fertilizer tax 

from the perspective of a policymaker, using NSGA-II to maximize the agricultural output of the 

region and to minimize the environmental impact. This is the upper level of optimization. In the 

lower level of optimization, farmers react to the fertilizer tax and optimize their profits with linear 

12 

programming. The process then repeats with the upper level. A hybrid of chaos algorithm (Jiang 

and  Weisun,  1998)  and  two  MO  algorithms  (NSGA-II  and  MODE)  appears  in  the  work  of 

Arunkumar and Jothiprakash (2017). They applied their modified algorithms to optimize crop 

planning in a multi-reservoir system spanning multiple basins and aim to maximize the net benefits 

and crop production.  

There are many examples that use other algorithms based off of non-dominated sorting. ε-NSGA-

II, a modified version of NSGA-II developed by Kollat and Reed (2006), incorporated the concepts 

of ε-dominance archiving into the NSGA-II. The goal of ε-dominance archiving is to perform a 

more uniform and spread out search within the objective space (Laumanns et al., 2002). ε-NSGA-

II searches for watershed best management practices (BMP) in Liu et al. (2013). The objectives of 

the run are to minimize the cost of the BMP while maximizing the reduction in phosphorus load. 

The Soil and Water Assessment Tool (SWAT) model predicted the phosphorus load for a given 

BMP practice (Arnold et al., 2012, Neitsch et al., 2011). Zhang et al. (2017) also employ ε-NSGA-

II to minimize agricultural water shortages while simultaneously optimizing other competition 

water  requirements  in  a  watershed  and  minimizing  environmental  impact.  The  algorithm 

developed by Groot et al. (2012) incorporates Non-dominated sorting into differential evolution to 

optimize  overall 

farm  management.  The  objectives 

included  minimizing  nitrogen 

leached/denitrified and labor requirements, as well as maximizing economic benefit and organic 

matter balance.  

2.3.2.2.2  Other Evolutionary Multi-Objective Optimization Algorithms  

There are other examples of EMOs applications in the agricultural intensification optimization 

literature. For example, differential evolution (DE) (Storn and Price, 1997) is a popular variant of 

evolutionary  algorithms  in  the  agricultural  management  optimization  literature,  and  a  multi-

objective version of DE (Lampinen et al., 2000; Xue et al., 2003) appears in Groot et al. (2007). 

13 

The study by Groot et al. (2007) optimized land use and hedgerow placement with respects to area 

yield, biodiversity and nutrient loss.  

Some papers use swarm-intelligence-based algorithms. First coined by Beni and Wang (1993), 

swarm intelligence mimics the behavior of swarms of autonomous biological agents (e.g., birds, 

ants,  wolves).  Wang  et  al.  (2012)  employed  a  variant  swarm  intelligence  technique  known  as 

particle swarm optimization (PSO), which searches optimal solutions with a “swarm” of particles 

that act like a flock of birds (Eberhart and Kennedy, 1995). With each iteration, each “individual” 

of the swarm moves to a new position based on its current velocity, its personal best location at 

that time, and a global best location of the entire swarm. However, the variant of PSO, multi-

objective chaos particle swarm optimization (MOCPSO), incorporates a dynamic weighted sum 

optimization within each particle of the swarm to optimize crop planning and water resources in a 

region in China. The objectives included maximizing the regional agricultural output, total grain 

yield, environmental benefit, and water efficiency.  

Genetic Programming (GP) is another family of algorithms that follow evolutionary principles. 

Unlike  GAs,  which  optimize  binary  strings  representing  possible  solutions,  GP  optimizes 

computer programs (i.e., mathematical functions) in the form of parse trees (Koza, 1992). Ashofteh 

et al. (2015) employed a bi-objective MO version of GP to maximize the reliability of reservoir 

irrigation responses and minimize regional vulnerability to irrigation deficits.  

Melody Search (Ashrafi and Dariane, 2013), a variant of Harmony Search (Geem et al., 2007) 

appears in the work of Karami and Dariane (2018). Both Melody and Harmony Search attempts 

to mimic how musicians improvise melodies within a musical ensemble. In Karami and Dariane, 

a Melody Search framework simultaneously optimizes multiple climate scenarios with respects to 

maximizing municipal, instream requirement, agricultural and hydropower reliability.  

14 

2.3.2.2.3  

Many-Objective Optimization  

Many objective problems are multi-objective algorithms that have more than three objectives. 

Many of the first generation of multi-objective algorithms perform poorly after three objectives, 

though a number of many objective algorithms have cropped up in the last ten years, such as 

MOEA/D (Zhang and Li, 2007), Borg (Hadka and Reed, 2013), and NSGA-III (Deb and Jain, 

2014). Many-objective problems have not significantly appeared in the agricultural intensification 

optimization  literature.  Among  the  few  are  Gurav  and  Regulwar  (2012),  who  used  a  Multi-

objective  Fuzzy  Linear  Programming  algorithm  (MOFLP)  to  solve  a  four  objective  irrigation 

planning problem. With MOFLP, irrigation planning in a region in India is optimized with respects 

to maximizing manure utilization, crop production, job creation, and the overall economic benefit. 

The  research  of  Wang  et  al.  (2012),  mentioned  earlier  for  their  PSO  algorithm  MOCPSO, 

optimizes  a  four  objective  crop  planning  and  water  resource  problem.  In  another  publication, 

Karami  and  Dariane  (2018)  overcame  the  difficulties  of  many-objective  optimization  by 

combining Melody Search (Ashrafi and Dariane, 2013) with the concepts of social choice (Arrow, 

1951; de Borda, 1781). With their hybrid optimization algorithm, Karami and Dariane (2018) 

simultaneously maximize reliability for regional municipalities, instream conditions, agricultural 

production, and hydropower operations under four different climate scenarios. Four NSGA-III 

runs, one for each climate scenario, is also used to optimize the aforementioned four objectives 

and to validate the results of the combined melody search and social choice algorithm. Zhang et 

al. (2017) employed ε-NSGA-II (Kollat and Reed, 2006) to solve a five objective regional water 

planning problem, which optimized against the water demands of businesses, agriculture, and the 

environment.  

15 

2.4 

Literature gaps 

There are several gaps in the agricultural intensification optimization literature. Firstly, and to the 

best of our knowledge, there are no micro agricultural management applications that combine both 

nutrient  and  water  management.  As  mentioned  earlier,  simultaneously  optimizing  nutrient 

management and water management outperforms optimizing each objective individually (Waraich 

et al., 2011). Therefore, micro-managing nutrient and irrigation applications on farms would move 

forward the use of state-of-the-art techniques in agricultural intensification. 

Furthermore,  optimizing  only  irrigation  and  nutrient  applications  would  ignore  the  basic 

requirement to make any management practice economically viable. Therefore, simultaneously 

optimizing  irrigation  management,  nutrient  management,  and  crop  yield  would  balance  three 

highly  significant  objectives  in  agricultural  intensification.  Finally,  including  an  objective  for 

environmental  impact  would  add  a  powerful  perspective  on  how  certain  agricultural  practices 

affect the environment as a whole. Adding environmental objectives would determine whether or 

not a practice could be sustainably applied throughout regions.  

Also,  there  is  a  lack  of  good  applications  of  many  objective  algorithms  in  the  agricultural 

intensification optimization literature. Agriculture, with its many conflicting objectives, would be 

an excellent case study for many objective problems. Agricultural systems are highly complex and 

non-linear and could serve to better define the strengths and weakness of the current state of the 

art many objective algorithms.  

 

 

 

 

16 

3. 

MATERIALS AND METHODS 

3.1  Modeling process 

To  maximize  crop  yield  and  simultaneously  optimize  water  and  fertilizer  use  efficiency  with 

limited  environmental  impacts,  we  needed  to  integrate  a  crop  model  with  an  optimization 

technique. The chosen crop model was the Decision Support System for Agrotechnology Transfer 

(DSSAT). DSSAT is a computer model capable of simulating crop growth for various cultivars 

and  species.  DSSAT  considers  the  full  cycle  of  soil-plant-atmosphere  dynamics,  irrigation 

scheduling, and nutrient management planning. The aforementioned characteristics along with the 

speed of the model (the whole growing season simulations taking few seconds) make this model 

ideal for this study. DSSAT can act as the evaluator within a bi-level evolutionary optimization 

framework.  

In the bi-level optimization, one optimization problem is embedded (nested) in another. The outer 

and inner optimization problems are commonly referred to as upper- and lower-level optimization 

problems, respectively. Consequently, the variables of these problems are referred to as upper- and 

lower-level variables. The decision variables include two time-independent and two sets of time-

dependent  variables.  The  time-independent  variables  (xi, 8∈{1,2})  represent  the  number  of 
Irrigation Association and producers, respectively. The time-dependent variables (yj(t), 1≤?≤
∑A3, 1<C<365) determine the amount of irrigation water and nutrient application for each date. 

necessary  irrigation  and  nutrient  applications  within  a  growing  and  are  usually  decided  by  an 

We then evaluate the solution for a number of objectives: 1) maximizing crop yield, 2) minimizing 

irrigation  water  used,  3)  minimizing  the  amount  of  nutrients  applied,  and  4)  minimizing  the 

nutrient loss (through leaching to shallow/groundwater and surface runoff).  

Figure 2 illustrates the linking of the bi-level optimization, decision variables, and DSSAT crop 

model.  The  procedure  starts  with  referencing  the  two  time-independent/upper-level  variables 

17 

(number of irrigation and number of nutrient application events) in the bi-level optimization. A 

Monte Carlo optimizer uses these predefined variables to generate a series of uniformly distributed 

random day combinations within the growing season. For example, given three irrigation and two 

nutrient application events, one of the uniformly distributed random day combinations can be May 

15th, July 18th, and August 1st for irrigation and May 30th and July 18th for nutrient applications. 

From  the  series  of  uniformly  distributed  random  day  combinations,  one  will  be  selected  and 

incorporated into the lower level of the bi-level optimization. The lower level consists of the EMO 

algorithm Unified Non-dominated Sorting Genetic Algorithm-III (U-NSGA-III) (Seada and Deb, 

2015).  The  algorithm  U-NSGA-III  can  be  used  for  single,  multiple,  and  many-objective 

optimization problems alike, thereby allowing us to optimize systematically by starting with the 

most critical objective and then adding other objectives. The incorporated day combination will 

be used to initialize a population of time-dependent variables (irrigation and nutrient application 

amounts). These variables will be assigned to the dates identified in the upper level. For each 

solution in the population, the objective functions (O1 to O4) will evaluate these dates and amounts 

by  calling  the  DSSAT  model  and  retrieving  the  results.  The  population  will  be  tested  against 

termination criteria (e.g., predefined threshold values and maximum number of allowed iterations). 

If the termination criteria are not met, the population (the time-dependent variables) are evolved 

and re-evaluated. This procedure is repeated until the termination criteria are met, which then the 

local Pareto-front for the selected day combination will be stored. After each iteration of the upper-

level of optimization, the new local Pareto is combined with a global Pareto front. In the next step, 

if there are any day combinations left, the above procedure would be repeated for each new day 

combination until all the generated random day combinations are processed.  

18 

 

Figure 2. Proposed integrated bi-level and DSSAT framework 

In order to compare the results from this study with an actual field experiment, the study consisted 

of two phases. In the first phase, we evaluated the efficacy of the lower-level optimization by 

examining the irrigation and nitrogen fertilizer application amounts for a fixed set of dates. The 

fixed set of dates followed the best management practice for high irrigation and high nitrogen 

fertilizer  applications  for  a  field  experiment  conducted  at  the  Irrigation  Research  Park  in 

Gainesville,  Florida.  Using  the  same  application  dates  as  best  practices  enabled  accurate 

comparisons between the performance of the optimization and current best practices. In the second 

phase of the study, we tried to examine whether changing application dates and amounts from the 

fixed dates can further improve the overall performance of the farm considering the predefined 

objectives.    

19 

3.2 

Study area 

The study area is located at the University of Florida (UF) Experimental Station (29° 37.8', -82° 

22.2') known as the Irrigation Research Park in Grasonville, Florida, USA (Figure 3). The study 

area is in a humid subtropical region of southeast of United States, with a wet season starting in 

May and ending in October (Lascody, 2002). The long-term (30 years) average, minimum, and 

maximum temperature of 20.7°C, 27.3 °C, and 14.6 °C, respectively. Meanwhile, the long-term 

total annual precipitation is 1,286 mm (“30-yr Normal Maximum Temperature: Annual,” 2015, 

“30-yr  Normal  Mean  Temperature:  Annual,”  2015,  “30-yr  Normal  Minimum  Temperature: 

Annual,” 2015, “30-yr Normal Precipitation: Annual,” 2015). In 1982 between February 16 and 

May 7, the mean daily maximum temperature was 26.96 C, the mean daily minimum temperature 

was 13.40 C, and the average daily rainfall was 5.07 mm. The dominant soil type of the field is 

Millhopper  Fine  Sand,  which  is  moderately  well  drained.  The  experiment  was  conducted  to 

evaluate the impacts of best management practices for irrigation and nitrogen fertilizer application 

on maximizing maize production (Hoogenboom et al., 2017). The study period occurs over one 

growing season during the spring and summer of 1982. Maize (McCurdy 84aa) was planted on 

February 16 and harvested at maturity on May 7. Among the six treatments in the experiment, we 

focused on treatment 4, which used irrigation and relatively high levels of nitrogen. Given the 

weather  of  1982,  the  best  practices  from  treatment  4  prescribed  16  days  of  furrow  irrigation, 

totaling  to  264  mm  over  the  season.  Nitrogen  best  practices  from  treatment  4  prescribed 

broadcasting ammonium nitrate incorporated at a depth of 10 cm depth six times over the growing 

season, totaling to 401 kg. This simulated experiment yields 11,298 kg/ha of Maize in DSSAT. 

The total seasonal yield, irrigation applied, and nitrogen applied, all act as benchmarks for current 

best practices during the optimization phase of this study.  

20 

Figure 3. Location of the field of study 

3.3  Optimization Platform 

3.3.1  Objective Function  

Optimization problems alter one or more variables to maximize or minimize one or more problem 

objectives. In the case of crop production, producers alter agricultural variables (e.g., irrigation, 

fertilizer) to maximize their profits. This study focuses on the decisions of when to apply irrigation 

and/or nitrogen on a field, and how much irrigation and/or nitrogen to apply.  

Summing the total seasonal irrigation and nitrogen applications provides simple assessments of 

environmental impact but estimating the expected seasonal yield is a more complex challenge. In 

fact, since researchers have dedicated years of research to developing software that can effectively 

model the performance (e.g. yield, nutrient leaching) of cereals and other agricultural staples (e.g. 

CROPGRO  model  (Boote  et  al.,  1998),  CERES-Maize  (Jones  et  al.,  1986),  CERES-Wheat 

(Ritchie, 1985), SOYGRO (Wilkerson et al., 1983), PNUTGRO (Boote et al., 1992)) ,  instead of 

reinventing the wheel and redeveloping a mathematical model for crop yield, it is smarter to use 

an existing crop model as an objective function for yield in an optimization platform.  

21 

There are numerous existing crop models that could act as an optimization objective function. The 

DSSAT model is the clear best choice because it is fast, well validated, and easy to use (Chung et 

al., 2014; Hoogenboom et al., 2012). A user runs the model by defining the soil, weather, cultivar, 

and growing practices within a number of input files. The input files are then fed into the core of 

the DSSAT model, the crop simulation model (CSM). The CSM in return predicts a number of 

performance metrics for that hypothetical season (e.g., yield, nutrient usage, water use, nutrient 

leaching). The CSM itself consists of a highly modular system of sub-models that work together 

as  a  single  unit.  To  name  a  few,  DSSAT  contains  sub-models  that  handle  the  weather,  soil 

(including nitrogen leaching), and numerous cultivars. And because researchers have validated the 

outputs of these sub-modules as a whole under numerous crop, climate, and soil conditions (Jones 

et al., 2003)  Finally, DSSAT has been calibrated to simulate McCurdy 84aa maize growth at our 

study  site  in  Gainesville  Florida,  and  by  extension  is  calibrated  for  the  region  and  climate  of 

Florida.  

Using DSSAT, one can easily design a set of powerful crop production and/or environmental 

objective functions to use in an optimization algorithm, such as in our case:  

[HIA:K,H8L:	N]=PQQRST8U(,…,8WX,8Y(,…,8ZX,[U(,…,[W\,[Y(,…,[Z\]	(1) 

H8L:	^=	∑
H8L:	_=	∑

8W7
X75(
[W`
\`5(

   (2) 

  (3) 

where, Y is yield, L is leaching, I is total irrigation, F is total fertilizer usage, iAn is the irrigation 

amount for date idn, fAm is the nitrogen application for date fdm, j is the total number of irrigation 

applications, and k is the total number of nitrogen applications. The optimization algorithms in this 

study contain combinations of these three objective functions.  

22 

All other variables (e.g., climate, soil, location), save irrigation application amount and nitrogen 

application  amount,  remained  constant  throughout  the  optimization.  The  units  for  irrigation 

applied was millimeter, the units for nitrogen applied was kilogram per hectare, and the units for 

nitrogen leaching is kg/ha. The total amounts of irrigation and nitrogen applied were assumed to 

be  positive  integers.  Applications  contained  no  upper  bound  as  to  allow  the  multi-objective 

optimization algorithm to find the full range of tradeoffs. Finally, all optimization runs used the 

same x1 and x2 values, or in other words, all strategies used the same number of irrigation and 

nitrogen applications. x1 and x2 both come from best field practices, in order to easily compare the 

performance of the optimization to best practices. However, often certain day values go to zero, 

which implicitly reduces x1 and x2 below best practices. 

3.3.2  Optimization Algorithm Choice and Setup 

This  study  optimizes  crop  management  practices  using  multi-objective  (MO)  algorithms.  MO 

algorithms are ideal for problems with conflicting objectives, such as minimizing irrigation and 

maximizing yield. The output of an n-objective MO algorithm is an n-dimensional Pareto set of 

solutions  (Deb,  2009).  These  n-dimensional  Pareto  sets  contain  solutions  that  are  all  equally 

optimal and offer unique tradeoffs for each of the objectives. For example, one solution might 

maximize yield, but waste a lot of irrigation water. A second solution might minimize irrigation 

usage but yield very little product. These two solutions are both optimal with regards to separate 

objectives (irrigation or yield) and are equally optimal. A decision maker, such as a farmer or an 

environmental policy maker, would then choose the solution that best fits their need. 

Building  on  the  concepts  of  MO  algorithms,  EMO  algorithms  incorporate  the  principles  of 

evolutionary  optimization  with  MO  concepts.  Evolutionary  optimization  algorithms  solve 

problems by creating populations of solutions (or individuals), ranking the individuals, and then 

recombining  the  best  solutions  into  a  new  and  ideally  improved  generation  of  solutions. 

23 

Evolutionary algorithms excel at solving complex, nonlinear objectives (Sastry et al., 2014), and 

are therefore a powerful tool for plant and crop optimization. 

The EMO algorithm NSGA-II efficiently sorts individuals by dominance and then by diversity 

(Deb et al., 2002). Given enough generations, it yields maximum convergence (closeness of the 

Pareto front to one or more objectives) and diversity (the spread of the Pareto front) for the given 

problem and seed. NSGA-II’s prioritization of both performance metrics cuts it out among similar 

EMO algorithms. Most decision makers seek the most optimal solutions and equally seek diverse 

choices in their decision-making process. However, NSGA-II performs optimally between one to 

three objectives. Meanwhile, crop production usually requires meeting many objectives, so this 

study  utilized  the  U-NSGA-III  algorithm.  U-NSGA-III  works  similarly  to  NSGA-II,  but  it 

improves the crowding distance calculations of NSGA-II to effectively calculate crowding in one- 

to many-dimensional objective spaces (Deb and Jain, 2014); (Seada and Deb, 2015). 

U-NSGA-III  was  set  to  optimize  with  real  variables;  however,  because  the  variables  in  this 

agricultural optimization system are all integers, the variables were normalized between 0 and 1. 

Zero  represented  zero,  and  1  represented  the  largest  value  of  that  variable  type.  Normalizing 

between these two relatively smaller values reduced the variable search space for U-NSGA-III. 

For example, for irrigation, 0 represented 0 mm of irrigation applied, and 1 represented 50 mm of 

irrigation applied. For nitrogen, 0 represented 0 kg/ha, and 1 represented 150 kg/ha. Software 

within the objective function scales these variables back up and rounds them to the nearest whole 

number for DSSAT.  

The  COIN  Laboratory  at  Michigan  State  University  provided 

the  Java  U-NSGA-III 

implementation,  named  evolib  (Seada,  2017).  At  the  commencement  of  this  research  project, 

evolib was single threaded and to make use of the 24 core processor in our lab computer; we forked 

24 

evolib to include multithreaded evaluation of population (Seada and Kropp, 2018). Additional 

software development efforts included the project DSSAT4j (Kropp, 2018a). Since the DSSAT 

CSM is written in FORTRAN, much of the project focused on writing a Java wrapper for DSSAT 

CSM input and output. The wrapper provides abstracted DSSAT experiments in the form of Java 

objects. For example, a client of the DSSAT4j library might create an experiment object containing 

an array of dates and irrigation amounts. A simple call to a run method returns the yield and/or 

leaching for the given experiment. This allowed simple and elegant integration of DSSAT into a 

U-NSGA-III objective function. DSSAT4j also includes built-in multithreading, which enabled 

quick, multi-threaded U-NSGA-III. DSSAT4j ran DSSAT version 4.7.1 (Git commit d8a977d) 

(Hoogenboom et al., 2017). The final component of the software framework is software that tied 

it all together. This software, named CropOpt (Kropp, 2018b), is a prototype decision support 

framework and optimizes a crop growing scenario provided by a user. The user provides periods 

of irrigation and nitrogen application, along with constraints such as the number of irrigation and 

nitrogen  application,  maximum  and  minimum  amounts  applied  per  application,  and  so  on.  In 

return, the framework optimizes the scenario and returns the results to the user. All results can be 

found in the supplementary data in the DSI website (see data availability). 

3.3.3  Optimization Strategies and Configuration  

The study chose to use a bi-level optimization configuration over single-level optimization because 

of  the  complexity  of  the  problem.  The  number  of  variables  behind  irrigation  and  nutrient 

scheduling are numerous and difficult to optimize. If a hypothetical growing season contains 120 

days, and a farmer has access to 0 to 50 mm of water every day, there are 51120 or 8.09∙10'(), 

different solutions. In its early stages, this study considered every day between February 16 and 

harvested the maize at maturity on May 7 a real variable in the optimization problem. However, 

the optimization runs with this single level optimization configuration failed to match the UF field 

25 

experiment benchmark yield. Therefore, the study sought to reduce the number of variables while 

still optimizing for the 120-day growing season with a bi-level optimization scheme. The upper 

level of the optimization was a Monte Carlo optimization algorithm, which generated random 

combinations of dates to irrigate and/or to apply nitrogen. For each of these combinations, U-

NSGA-III attempted to find the optimal application amounts for each fixed date combination. 

Formally, the algorithm ran as follows:  

Algorithm 1: Bi-Level Optimization for Agricultural Optimization 

Step 1:  Determine the number of irrigation applications x1 

Step 2:  Determine the number of nitrogen applications x2 

Step 3:  Repeat 

Step 4: 

     Generate x1 random dates for irrigation application 

Step 5: 

     Generate x2 random dates for nitrogen application 

Step 6: 

     Run U-NSGA-III with the application amounts of given irrigation and nitrogen     

     dates as variables 

Step 7: 

     Combine the solutions from step 6 with solutions found in previous iterations 

Step 8: 

     Remove dominated solutions from the combined set of solutions 

 

Here we hypothesized that through bi-level optimization, better management practices could be 

implemented to not only improve crop yield, but to also minimize irrigation application rates, 

minimize fertilizer application rates, and minimize environmental impacts through leaching. To 

verify this hypothesis, different optimization strategies were formulated and evaluated based on 

their ability to improve current best management practices. As a result, each optimization strategy 

maximized yield while minimizing a different combination of environmental impacts, including 

total  irrigation  applied,  total  nitrogen  applied,  and  total  nitrogen  leached.  The  first  three 

26 

optimization strategies use single-level optimization with dates taken from UF best experimental 

field practices, and the last three use bi-level optimization. 

Table 1. Summary of the optimization strategies 
Strategy No.  Optimization Type 

Application Dates 

Objectives 

Max: Yield 
Min: Irrigation applied 

16  fixed 
irrigation  dates 
(dates  from  the  UF  field 
experiment) 
16  fixed 
irrigation  dates 
AND 6 fixed nitrogen dates 
(all dates from the UF field 
experiment) 
16  fixed 
irrigation  dates 
AND 6 fixed nitrogen dates 
(all dates from the UF field 
experiment) 
16 variable irrigation dates  Max: Yield 

Max: Yield 
Min: Irrigation applied  
Min: Nitrogen applied 

Max: Yield 
Min: Irrigation applied  
Min: Nitrogen applied 
Min: Nitrogen leached 

Min: Irrigation applied 

16 variable irrigation dates 
6 variable nitrogen dates  

Max: Yield; 
Min: Irrigation 
Min: Nitrogen applied 

16 variable irrigation dates 
6 variable nitrogen dates  

Max: Yield; 
Min: Irrigation  
Min: Nitrogen applied 
Min: Nitrogen leached 

1 

2 

3 

4 

5 

6 

 

Single Level  
(U-NSGA-III) 

Single Level 
(U-NSGA-III) 

Single Level 
(U-NSGA-III) 

Bi-Level  
(Monte Carlo for 
upper-lever & 
U-NSGA-III 
lower-level) 
Bi-Level 
(Monte Carlo for 
upper-lever & 
U-NSGA-III 
lower-level) 
Bi-Level 
(Monte Carlo for 
upper-lever & 
U-NSGA-III 
lower-level) 

for 

for 

for 

The  various  strategies  are  as  follows.  Strategy  1  kept  all  parameters  from  the  UF  experiment 

constant, including the 16 irrigation dates, but changes the irrigation application rate for each date. 

Keeping all other parameters constant made the results easily comparable to current best practices. 

Strategy 2 similarly kept all parameters constant except for irrigation and nitrogen amounts. Like 

Strategy 1, Strategy 2 uses the same dates of irrigation application and dates of nitrogen application 

as best practices. Strategy 3 was a four-dimensional optimization problem, and contained the same 

variables as Strategy 2, but added an additional objective to minimize nitrogen leaching. Strategy 

27 

4, the first bi-level optimization run, tried to find both the dates for 16 irrigation applications and 

the  amounts  for  each  of  those  irrigation  applications.  The  objectives  of  Strategy  4  mirror  the 

objectives  of  Strategy  1.  Strategy  5,  which  mirrors  the  objectives  of  Strategy  2,  uses  bi-level 

optimization to find the dates and amounts for 16 days of irrigation application and to find the 

dates and amounts for six days of nitrogen application. The final bi-level optimization strategy, 

Strategy 6, which mirrors the objectives from Strategy 3, has the same variables as Strategy 5 

while adding a leaching minimization objective to the problem.  

There are two main stopping criteria employed in the study. In the first stopping criteria, Strategies 

1 through 3 ran until their hypervolumes visually plateaued. A hypervolume is the volume of the 

Pareto front from a reference point (Emmerich et al., 2005). The reference point is typically a 

worst-case scenario value for each objective, and in this study, we chose the following worst-case 

values in our reference points: 1) Yield: 0 kg/ha 2) Irrigation: 1000 mm 3) Nitrogen: 1000 kg/ha 

4) Leaching: 500 kg/ha. Once the hypervolume plateaued, the value with the greatest hypervolume 

was chosen as the best solution. In the second stopping criteria, strategies 4 through 6 ran U-

NSGA-III until a fixed generation. The fixed generation is a predetermined generation at which 

the hypervolumes of Strategies 1 through 3 respectively stopped improving. The study used the 

hypervolume  software  developed  by  Walking  Fish  Group,  which  can  calculate  1  to  many 

dimension hypervolumes (Cox and While, 2016).   

3.4 

Post-processing and visualizations 

Once validated, the study analyzes the solutions within the available Pareto fronts. The first step 

of analysis was to break the Pareto fronts into three clusters. Three clusters effectively break the 

data into three broad categories: high productivity, high environmental efficiency, and even trade-

off. All tradeoffs in every optimization scenario can be broken down in these categories because 

the tradeoffs are all essential bipolar. Yield maximization falls under the productivity pole, and 

28 

irrigation  minimization,  nitrogen  minimization,  and  leaching  minimization  all  fall  under  the 

environmental efficiency pole. The third category attempts to find solutions that are well balanced 

between these poles. This study employs the k-means clustering method to break down the fronts 

into  three  categories  (Arthur  and  Vassilvitskii,  2007).  For  this  study,  the  k-means  algorithm 

separated the solutions based on their normalized objective values. However, other studies could 

weigh the objectives differently according to the needs of a decision maker.  

The study also developed a unique type of histogram to display the clustered data (section 3.3). 

Each bucket in the histogram contains stacked, color-coded bars for each of the clusters. This 

simultaneously represents the total distribution of the Pareto front as well as the distribution of the 

individual clusters in the same front. The application frequency analysis section uses this type of 

histogram.  

Regarding  the  visualization,  Strategy  6  posed  a  challenge.  A  three-dimensional  graph  can 

effectively  display  the  results  of  Strategies  1  through  5  because  each  strategy  contains  2  to  3 

objectives. However, Strategy 6, on the other hand, attempted to optimize four objectives, which 

cannot exist as points on a three-dimensional space. To address this problem, a custom written 

MATLAB script first plots the first three dimensions of the four-dimensional solutions. Then, the 

script  color-codes  the  three-dimensional  points  with  the  values  of  the  fourth  dimension.  This 

method effectively conveys the four-dimensional objective space in a three-dimensional objective 

space.  

29 

4. 

RESULTS AND DISCUSSIONS 

4.1 

Single-level optimization results 

4.1.1  Strategy 1: Single Level Irrigation Minimization and Yield Maximization 

Strategy 1 optimized the simplest set of objectives. It attempted to maximize yield and minimize 

irrigation applied. The optimization found a diverse set of solutions that required significantly less 

irrigation than the UF best practices. The solution with the highest yield matched the output of the 

best practices (11,298 kg/ha) while reducing the required irrigation amount by 45.5% (Table 2). 

However, this solution is arguably not properly Pareto efficient, because the tradeoff of irrigation 

to yield is heavy. Properly Pareto efficient solutions are solutions that are Pareto optimal and offer 

reasonable tradeoff compared to their peers (Geoffrion, 1968). For example, choosing between 

solution A (Figure 4), which yields 11,298 kg/ha with 136 mm of irrigation, and solution B, which 

yields 11,242kg/ha with 130 mm of irrigation, is intuitively simple. Moving from solution B to 

solution A gains just 0.49%  while increasing total irrigation by 4.4%. Therefore, solution A is 

arguably not properly Pareto efficient for many stakeholders. However, the final call of what is 

properly Pareto optimal or not belongs to the stakeholders themselves, and to a farmer who has no 

water  use  limit,  both  are  arguably  properly  Pareto  efficient.  Meanwhile,  the  solution  with  the 

lowest yield produced 2,655 kg/ha with 0 mm of irrigation.  

The  optimization  also  significantly  reduced  the  number  of  irrigation  applications.  In  fact,  all 

solutions  required  13  or  fewer  applications  during  the  season.  The  highest  yielding  solution 

required 11 applications, which is a noticeable improvement over the best practices that required 

16 applications to achieve the same yield (11,298 kg/ha). Farmers with regional restricted temporal 

water  access  would  benefit  using  solutions  that  reduce  the  number  of  applications  while 

maintaining optimal yield (Sampath, 1992). This is an example of how the optimization can shape 

30 

management practices. The number of applications within the Pareto front (ranked in descending 

order by yield) non-monotonically decrease from 11 down to zero.  

Figure  4  illustrates  this  transition  between  high  yielding  solutions  and  highly  water  efficient 

solutions. The more water is conserved between solutions, the more yield decreases. Moving from 

low water solutions to high water solutions at first offers relatively high yield tradeoffs for low 

water tradeoffs. However, approximately halfway through the solutions, unit increases in total 

irrigation cease to offer equal increases in total yield (Figure 4). 

 

 

 

 

 

 

 

 

31 

Table 2. Top five (ranked by yield) optimal results compared to best practices (Strategy 1) 

Yield (kg/ha) 

Number of Applications 

Total Irrigation (mm) 

Best practices 

Optimized results  Best practices  EMO results 

Best practices 

11298 
 
 
 
 
 

11298 
11267 
11242 
11204 
11128 
11075 

16 
 
 
 
 
 

11 
11 
11 
11 
13 
11 

264 
 
 
 
 
 

EMO 
results 

136 
130 
129 
125 
119 
115 

Reduction in 
 irrigation usage 

48.5% 
50.8% 
51.1% 
52.7% 
54.9% 
56.4% 

32 

 

Figure 4. Pareto front for Strategy 1, which maximized yield and minimized irrigation amount  

4.1.2  Strategy  2:  Single  Level  Irrigation  Minimization,  Nitrogen  Minimization,  and  Yield 

Maximization 

Strategy  2  added  an  objective  to  minimize  nitrogen  usage  to  the  objectives  of  Strategy  1  and 

obtained similar reductions in nitrogen and irrigation amounts (Table 3). The best solution with 

respect to yield (top row of Table 3) also matched the yield benchmark from the UF best practices, 

while reducing irrigation by 40.9% and nitrogen by 26.4%. The lowest ranked solution by yield 

applied 3 mm of irrigation and 7 kg/ha of nitrogen and reached 939 kg/ha of yield. This worse case 

(by yield) solution from Strategy 2 performs considerably worse with respect to yield than the 

33 

worst case from Strategy 1 because Strategy 1 used the nitrogen application dates and amounts 

from the best practices, and therefore does not use more or less than 401 kg/ha. Though the yield 

is lower than best practices, this yield is still optimal given harsh irrigation and fertilizer restrictions 

because it is Pareto optimal (Deb, 2009).  

Despite their relatively low yields, examining the lowest solutions by irrigation and nitrogen still 

provides valuable agricultural insights. The lowest ranked solution by nitrogen applied 3 kg/ha of 

nitrogen and 74 mm of irrigation to achieve 1566 kg/ha of yield. The two lowest ranked solutions 

by irrigation both apply 3 mm of irrigation, apply 7 kg/ha and 41 kg/ha of nitrogen respectively, 

and  achieved  989  kg/ha  and  1778  kg/ha  in  yield  respectively.  Both  of  these  cases  offer 

management practices to farmers under severe but common scenarios. A hypothetical farmer who 

wishes to sell organic maize may choose the solution that uses almost no nitrogen, and a farmer in 

an area with strict irrigation restrictions may choose a solution that uses almost no irrigation. In 

both  cases,  the  Pareto  front  offers  the  optimal  yield  found  in  the  optimization  under  such 

restrictions. 

The solutions that contain the highest irrigation and nitrogen usage also offer valuable tradeoffs. 

The highest ranked solution by nitrogen actually applied more total nitrogen (500 kg/ha) than the 

best practices (401 kg/ha) to produce 8,683 kg/ha of yield. However, the solution makes up for its 

heavy nitrogen usage by reducing the irrigation applied. A similarly yielding solution in Strategy 

2 (8,593 kg/ha) uses 68.9% more irrigation while using less nitrogen (123 kg/ha). Therefore, a 

stakeholder may choose to save a great deal of irrigation by choosing the management practice 

that uses a relatively large amount of nitrogen fertilizer. The highest solutions ranked by irrigation, 

using 385 mm of irrigation and 186 kg/ha of nitrogen to yield 10,870 kg/ha, offers a similarly 

unique trade-off. Compared to a similar solution in Strategy 1 that yields 10,859 kg/ha with 401 

kg/ha of nitrogen and 101 mm of irrigation, this solution from Strategy 2 decreases nitrogen usage 

34 

by 56.61% while sacrificing considerable quantities of water. These cases offer unique solutions 

for unique scenarios and give stakeholders the final judgment whether to sacrifice one objective 

to improve two or more other objectives. These results also demonstrate the broadening of options 

in optimizing both irrigation and nitrogen application within the same optimization run. With the 

third objective of nitrogen, stakeholders not only determine the appropriate amount of water but 

also the appropriate amount of nitrogen as well. 

The above tradeoffs are visually present in the Strategy 2 Pareto front in Figure 5. The top of the 

front, where water and nitrogen are highest, contains the highest yields, but as you conserve more 

nitrogen and water, the yield decreases at the skirts of the front.  

The  number  of  nitrogen  applications  in  Strategy  2  does  not  decrease  as  dramatically  as  the 

irrigation applications in Strategy 1. When the data is broken into high, medium and low yield 

clusters (using k-means clustering), all the high yield solutions were within 4 to 6 applications. 

Furthermore, the solutions using 4 to 5 applications were outside of the interquartile range of the 

high yield cluster. Even for the medium and low clusters, all solutions between the first quartile 

and the maximum were between 3 and 6 applications (Figure A.1 in the Supplementary Materials). 

This suggests that solutions using under three nitrogen application have a higher risk of being 

dominated by other solutions. Also, the fact that the median, the third quartile, and the maximum 

are all the same value in the high yield cluster (Figure A.1) suggest that solutions with more than 

six  nitrogen  applications  may  contain  competitive  contributions  to  the  existing  Pareto  front. 

However, this paper focuses on the optimization problem using a maximum of six possible days 

to keep in line with the UF benchmarks field experiment and seeks to keep the nitrogen application 

count within realistic bounds. Until the economic impacts of increasing the number of nitrogen 

applications above 6 can be taken into account in future studies, we assume that the maximum 

number of nitrogen application is six.  

35 

The number of irrigation applications does not appear to directly affect yield as strongly as the 

number of nitrogen applications (Figure A.1). In fact, in the high yield cluster, the range is very 

wide (4 applications to 16 applications), though the middle 50% of the solutions fall between the 

narrower range of 9 to 14 applications. The medium yield cluster has slightly a wider range (3 

applications to 16 applications) and a higher middle 50% range (13 applications to 5 applications), 

and the low yield cluster has a similar range and inner quartile range (2 to 15 applications and 5 to 

12 applications respectively). These increasing ranges suggest that the effects of the number of 

irrigation applications have a diminishing effect on the yield as the target yield decreases.  

Similar to Strategy 1, the number of irrigation applications on the highest-ranking solution by yield 

uses fewer irrigation applications than best practices (14 instead of 16). However, 21 solutions still 

required 12 to 16 applications. The added complexity of six additional variables and one additional 

objective  from  Strategy  1  might  explain  the  presence  of  these  solutions  with  high  application 

counts. Adding more variables increases the dimensionality of the decision space and adding more 

objectives increases the dimensionality of the objective space. Both cases increase the difficulty 

of finding optimal solutions (Deb, 2009). Alternatively, perhaps more irrigation applications are 

optimal when simultaneously optimizing nitrogen and irrigation.  

Another interesting finding in Figure 5 is that there is an upward trend in yield from low irrigation 

and nitrogen application to high irrigation and nitrogen application. The trend dictates that with 

every horizontal cut, along the yield axis, there is one trade-off solution that can be used to help 

farmers to make better decisions. For example, if we extract the green shade from the figure, we 

have a two-dimensional Pareto front with respects to irrigation and nitrogen. Along this Pareto 

front, there is a point known as the knee point, which offers a trade-off solution among irrigation 

and nitrogen application. Similar points can be created at different yield levels and can be presented 

to farmers to simplify the decision-making process.  

36 

 
Table  3.  Top  five  (ranked  by  yield)  optimal  irrigation  and  nitrogen  results  compared  to  best 
practices (Strategy 2). 

Yield (kg/ha) 

Best 
practices 
11298 
 
 
 
 

 

EMO 
results 
11298 
11208 
11142 
11106 
11102 

 

Total Irrigation  
(mm) 
Best 
practices 
264 
 
 
 
 

EMO 
results 
156 
223 
127 
291 
164 

Irrigation 
Reduced 

40.9% 
15.5% 
51.9% 
-10.2% 
37.9% 

Total 
(kg/ha) 
Best 
practices 
401 
 
 
 
 

Nitrogen 

Nitrogen 
Reduced 

EMO 
results 
295 
219 
325 
203 
281 

26.4% 
45.4% 
19% 
49.4% 
29.9% 

37 

Figure 5. Pareto front for Strategy 2. A surface was passed through the solutions to better 

visualize the shape of the front. The color of the surface represents the yield for that given region 

of the front. 

4.1.3  Strategy  3:  Single  Level  Irrigation  Minimization,  Nitrogen  Minimization,  Leaching 

Minimization and Yield Maximization 

Strategy  3  includes  the  effects  of  a  direct  environmental  impact:  nitrogen  leaching.  Nitrogen 

leaching occurs when nitrogen-based fertilizers infiltrate the soil and ultimately the groundwater. 

38 

Figure 6. Pareto front for Strategy 3, which maximized yield, minimized nitrogen application, 

minimized irrigation application, and minimized nitrogen leaching.  The color of the surface 

represents the leaching of the solution 

 

To incorporate this environmental metric, Strategy 3 included four objectives: minimize nitrogen 

application, minimize irrigation application, minimize nitrogen leaching, and maximize yield.  

The optimization results accurately reflect the literature on leaching. The results with relatively 

high irrigation application and maximum nitrogen applications yielded the most maize, but also 

the most leaching. However, the results provide solutions that reduce dangerous leaching levels 

by simply reducing the yield by approximately 100 kg/ha. Knowing this information is important 

39 

for decision-makers to incentivize farmers to avoid over-fertilizing their fields, and thus reducing 

leached nitrogen in water supplies. 

The  yield,  water,  and  nutrient  usage  among  high  yielding  solutions  vary  only  slightly  from 

Strategy 1 and Strategy 2. The best Pareto front of the run contained solutions yielding up to 

11,281 kg/ha (17 kg/ha lower than the highest yielding solutions from Strategy 1 and Strategy 2). 

Also, the same solution that achieved 11281 kg/ha used more considerably more irrigation than 

the highest yielding solutions in Strategy 1 and Strategy 2. Specifically, Strategy 1 and Strategy 

2 both yielded 11,298 kg/ha with 134 mm of irrigation and 156 mm respectively, where Strategy 

3 needed 180 mm of irrigation to achieve 11,281 kg/ha. The amount irrigation appears to trend 

upwards  with  each  additional  objective  added,  with  the  Strategy  3  solution  using  the  most. 

However, neither the Strategy 1 solution nor the Strategy 2 solution dominates this Strategy 3 

solution because the Strategy 3 solution outperforms both of them in total nitrogen applied and 

leaching.  Strategy  3  achieves  11,281  kg/ha,  approximately  the  same  yield  as  Strategy  1  and 

Strategy 2, but with only 285 kg/ha of nitrogen applied and 65. 6 kg of nitrogen leached. The 

corresponding solutions from Strategy 1 and Strategy 2 applied 401 kg/ha (from best practices) 

and 295 kg/ha of nitrogen respectively and leached 75.2 kg/ha and 92.6 kg/ha respectively. This 

demonstrates the utility in adding additional objectives to the optimization. The more objectives 

included in our optimization platform, the nuanced the possible management practices become.  

The remaining value ranges were in most ways similar to Strategies 1 and 2. Yield ranged from 

1,252 to 11,281 kg/ha. Leaching ranged from 21.99 to 119.5 kg/ha. Irrigation applications ranged 

from 8 mm to 276 mm, and nitrogen applications ranged from 9 kg/ha to 558 kg/ha. The number 

of irrigation applications ranged from 2 to 16 applications, but unlike Strategy 1 and 2, the number 

of nitrogen applications ranged from 4 applications to 6 applications. This suggests that when 

40 

treating leaching as an objective, solutions with 0 to 3 nitrogen applications are dominated by 

their 4 to 6 application counterparts.   

4.2 Bi-level optimization results 

4.2.1  Strategy 4: Bi-Level Irrigation Minimization and Yield Maximization 

Figure 7. Strategy 1 results compared to Strategy 4 results 

The combined Pareto front of the 372 separate optimization runs, consisting of 119 Pareto optimal 

solutions, outperformed the optimization from Strategy 1. Firstly, the hypervolume (using 0 kg/ha 

of  yield  and  1,000  mm  of  irrigation  as  a  reference  point)  for  the  bi-level  optimization  was 

11,027,186, where the hypervolume for the single level was 10,998,189. The larger hypervolume 

suggests better overall convergence and diversity from the bi-level results over the single level 

41 

results  (Deb,  2009).  This  improvement  is  visually  present  in  Figure  7.  Secondly,  the  middle 

segment of the Strategy 4 Pareto front is significantly more convergent than the middle of the 

Strategy 1 Pareto front. More convergence in a Pareto front means more points are closer to the 

ideal of maximizing irrigation and minimizing irrigation (Figure 7) (Rudolph, 1994).  However, it 

worth  noting  that  Strategy  1  solutions  dominate  10%  of  Strategy  4  solutions,  and  Strategy  4 

solutions dominate 88% of Strategy 1 solutions. But as Figure 7 illustrates, the dominated Strategy 

4 solutions only marginally derivate from their Strategy 1 neighbors.  

There are possible explanations to why Strategy 1 still dominates a few Strategy 4 solutions, and 

why Strategy 4 solutions dominate the vast majority of Strategy 1 solutions. The overall trend is 

that the single level run from Strategy 1 marginally dominates in high yielding areas of the front, 

where Strategy 4 solutions dominate the most dramatically in the middle of the front. Strategy 1 

holds out in high yielding areas of the Pareto front because Strategy 1 already has dates chosen by 

experts to maximize yield. Therefore, it excels in finding solutions in this reduced search space. 

On the other hand, Strategy 4 likely outperforms Strategy 1 in the middle of the front because it 

opens the search space to date combinations that better suit median yield values. Both Strategy 4 

and Strategy 1 performed similarly in the lower yielding solutions at the bottom of the Pareto 

because minimizing yield simply involves reducing irrigation levels to zero for every date. These 

runs clearly demonstrate the usefulness of this bi-level optimization strategy. The Monte Carlo 

optimization layer widens the narrow manual optimization of dates beyond yield maximization 

and provides stakeholders with more refined management practices to their particular cases, from 

low to high yield, and low to high irrigation availability. 

42 

4.2.2  Strategy  5:  Bi-Level  Irrigation  Minimization,  Nitrogen  Minimization,  and  Yield 

Maximization 

Like Strategy 4, Strategy 5 found a better Pareto front than the single level optimization Pareto 

front. Firstly, the number of solutions in the front increased dramatically. Maintaining a running 

bank of non-dominated points after each generation and after each run resulted in a 2,971 solution 

Pareto front after 137 runs. This differs significantly from the 119 solutions found in Strategy 4 

and  is  due  to  the  additional  dimension  in  objective  space  (nitrogen  application  amount 

minimization). Offering more optimal solutions to decision makers allows them to make decisions 

that are more refined after optimization. Secondly, the solutions from Strategy 5 dominated the 

vast majority of single-level irrigation, nitrogen and yield optimization solutions from Strategy 2. 

In fact, 98% of solutions from Strategy 2 are dominated by Strategy 5, and only 0.2% of Strategy 

5 solutions were dominated by Strategy 2 solutions. Finally, the hypervolume of the single level 

optimization, with a reference point at 0 kg/ha of yield, 1,000 mm of irrigation, and 1000 kg/ha of 

nitrogen, is 1.01(cid:1)1010. The hypervolume of the bi-level optimization, using the same reference 

points, is slightly larger at 1.03(cid:1)1010, which suggests better over convergence and/or diversity of 

the front from Strategy 5 compared to the front from Strategy 2. 

An interesting difference between the two objective bi-level optimization run (Strategy 4) and the 

three objective bi-level optimization run (Strategy 5) is in how they respectively outperformed the 

single level optimization runs. The single level solutions from Strategy 1 that outperformed the bi-

level results from Strategy 4 were mainly focused on in the high yield region of the Pareto front. 

However, when an additional objective is added in Strategy 5, the only single level solutions from 

Strategy 2 that outperforms bi-level results from Strategy 5 are two seemingly random spots on 

the Pareto front. Another major difference between the performance of Strategy 4 and Strategy 5 

is the number of runs necessary to overcome their single level strategies. Strategy 5 was able to 

43 

dominate a greater amount of Strategy 2 with fewer runs (137 runs) than Strategy 4 did in 372 

runs. One explanation for these differences is that since Strategy 2 had one more objective than 

Strategy 1 and thus had a more complex objective space to traverse. Therefore, Strategy 2 struggled 

to converge on the potential optimum within a considerably large search space, and could not 

compete with the solutions from the bi-level optimization from Strategy 5. This demonstrates the 

power of the bi-level Monte Carlo and U-NSGA-III optimization that aids in avoiding local optima 

during optimization and increases the breadth of the Pareto front of management practices at the 

end of optimization. 

Figure 8. Strategy 2 versus Strategy 5 results. Non-dominated Strategy 5 results are the black 

circles and non-dominated Strategy 2 results are red stars 

 

44 

4.2.3  Strategy  6:  Bi-Level  Single  Level  Irrigation  Minimization,  Nitrogen  Minimization, 

Leaching Minimization and Yield Maximization 

Strategy 6 continued the trend of Strategy 4 and 5: it took fewer runs (101) to dominate even more 

of its corresponding single level run (Strategy 3). Strategy 6 dominated all but one the solutions 

from Strategy 3, and the single non-dominated Strategy 3 solution only dominated 0.2% of the 

Strategy 6 solutions. Again, the single level optimization version of this four-objective problem 

(Strategy 3) was ill-equipped to converge on the full front found by Strategy 6. The addition of the 

fourth objective and the 6 additional variables for leaching (compared to Strategy 1 and 4) is the 

source of the additional complexity. One final benefit of Strategy 6 is even a greater number of 

solutions (6,198) found caused by the additional fourth dimension of objective space. The large 

number of solutions better defines the shape of the Pareto front than Strategy 3. Strategy 3 lacks a 

well-defined shape, but Strategy 6 reveals that the tradeoffs of the four-objective optimization 

problem are very similar to the tradeoffs of the three-objective problems in Strategy 2 and Strategy 

5. However, the shape of the Strategy 6 Pareto front adds additional insights into environmental 

agricultural optimization.  No solutions exist at the top of the front, where irrigation approximately 

exceeds 150 mm and nitrogen application roughly exceeds 250 kg/ha. The very sharp, near 90-

degree-shaped boundary suggests that past a certain amount of combined irrigation and nitrogen 

application,  no  optimal  solutions  exist.  This  piece  of  knowledge  could  aid  farmers  and 

policymakers  in  making  decisions  that  avoid  both  adversely  affecting  the  environment  and 

adversely affecting the yield of the crop.  

45 

Figure 9. Non-dominated Strategy 6 results  

4.3 

Application frequency analysis  

Once Strategies 4 through 6 found Pareto optimal fronts for their respective scenarios, the study 

categorized and analyzed trends within the results of each strategy. As discussed in section 2.4, 

the k-means clustering method partitioned the results into three regions: high yielding solutions, 

environmentally efficient solutions, and even trade-off solutions. The distribution of application 

counts required within each cluster is a powerful tool for developing management practices. For 

example,  if  a  farmer  only  has  access  to  five  applications  of  irrigation  in  a  season,  he/she  can 

estimate the expected yield in the season and how he/she can implement the practice. It can also 

help reduce the complexity of future optimization problems. For example, if a farmer seeks to 

46 

achieve a yield within the medium trade-off cluster, and still wants to optimize irrigation usage, a 

new  optimization  routine  would  only  need  6  irrigation  variables  instead  of  16.  Reducing  an 

optimization problem from 16 to 6 would significantly reduce the complexity and run time of an 

optimization routine (Deb, 2009). 

Figure 10. Application frequency analysis a) Histogram of irrigation application count among 

Strategy 4 solutions. Solutions are color-coded according to their respective yield cluster (see 

section 2.4). b) Box plots of the total irrigation applied in Strategy 4 solutions, divided by the 

number of applications applied along the x-axis. The data is further divided and color coded into 

the clusters as described in section 2.4. 

The results of the aforementioned frequency analysis on Strategy 4 appear in Figure 10. Figure 

10.a presents Strategy 4 application counts in the histogram format. The histogram at first appears 

to be bi-modal overall, but each of the three clusters actually has its own unique mode. The high 

yield cluster has a mode of 8 applications, the even trade-off solution cluster has a mode of 5 

applications, and the water efficient solutions have a mode of 4 applications. Again, knowing the 

47 

distribution of each cluster can aid farmers in developing best irrigation management practices by 

choosing  the  right  number  of  irrigation  applications  to  schedule  in  a  season.  Figure  10.b 

summarizes the statistics of the total amount of irrigation per season for each of the histogram 

buckets from Figure 10.a as boxplots. As Figure 10.b demonstrates, the variance of the water 

efficient solutions increases with the number of applications, and the variance of the even trade off 

cluster increases and then decreases as application count increases. Finally, the variance of the 

high  yield  solutions  also  initially  increases  with  the  number  of  applications,  but  then  sharply 

decreases after 13 applications.  

The histogram in Figure 11 describes the total irrigation (upper figure) and nitrogen (lower figure) 

application count across the three clusters from Strategy 5. The irrigation histogram for Strategy 5 

is also bi-modal, with peaks at 4 applications and 6 applications. Individually, the high cluster has 

a mode at 7 applications, the even trade-off solutions have a mode of 4 applications, and the water 

efficient solution has a mode of 3 applications. This central tendency towards solutions between 4 

and 6 suggests that farmers restricted to 6 applications of irrigation in a season can still achieve 

high yielding solutions. This is another example of how EMO algorithms can help with developing 

management practices. The distribution of nitrogen applications is a bit more complicated. The 

histogram appears truncated at 6 days and cuts out of at the mode of the distribution.  This suggests 

that Pareto optimal solutions with more than 6 days of nitrogen application exist, and in future 

optimization  routines,  more  than  six  nitrogen  application  variables  may  yield  more  optimal 

solutions. Finding more optimal solutions beyond 6 nitrogen application variables may develop 

new, better management practices for maize growth in the future.   

48 

Figure 11. a.) Histogram of irrigation application count among Strategy 5 solutions. b.) 

Histogram of nitrogen application count among Strategy 5 solutions. Solutions are color coded 

according to their respective yield cluster (see section 2.4).  

 

 

 

 

 

 

 

 

 

49 

5. 

CONCLUSIONS 

The EMO algorithm U-NSGA-III is thus proven to be a powerful and useful tool in developing 

agricultural best management practices. Strategy 1 can provide a wide Pareto front of possible 

management practices, which not only work contain optima by yield, but also optima by water 

usage. Therefore, decision-makers can find the exact optimum for their particular agricultural use 

case.  Strategy  2  further  refined  the  results  from  Strategy  1  by  optimizing  both  irrigation  and 

nitrogen  application  at  the  same  time,  which  better  equips  decision  makers  with  management 

practices for their particular access to irrigation and nitrogen supplies. Strategy 3 also added an 

objective that directly affects the environment, leaching. 

Meanwhile, bi-level optimization runs (Strategies 4 through 5) built upon the first three strategies 

by searching beyond the fixed set of days and found more convergent and diverse population. The 

bi-level optimization technique also provided more solutions, which enrich the options of decision 

makers. The bi-level method also broke out of local optima that thwarted Strategies 1 through 3. 

Finally, examining the Pareto results of the bi-level results produces useful knowledge on the 

nature of application counts and their effect on other objectives. 

One major limiting factor to note on this paper is the weather. The approximately 50% reduction 

in irrigation from Strategy 1 appears to be an extraordinary reduction in irrigation (Table 2), but 

these  results  present  the  optimal  obtainable  output  possible  in  that  given  season.  In  order  to 

generate viable solutions for farmers on the ground, a decision support tool would predict the 

weather of an incoming season, and the tool would then run a robustness analysis on the Pareto 

solutions generated. In MO, robustness describes as how sensitive a solution is to slight changes 

in variables such as weather (Deb and Gupta, 2005). In future research papers, prioritizing robust 

solutions that perform well over different weather scenarios would yield more realistic Pareto 

optimum sets for a given season. 

50 

Finally, optimizing agricultural practices entails optimizing conflicting objectives, such as total 

irrigation and total yield, against each other. EMO is a powerful tool that searches for sets, or 

Pareto  fronts,  of  optima  within  conflicting  objective  space.  Decision  makers  (e.g.,  farmers, 

policymakers) can then choose the particular optimum that offers the best trade-off in their use 

case. The EMO algorithm U-NSGA-III, using the crop-modeling suite DSSAT as the optimization 

objective  function,  found  innovative  and  novel  solutions  to  irrigation  and  nitrogen  fertilizer 

application planning. In addition, a novel bi-level optimization scheme (U-NSGA-III and Monte 

Carlo optimization) mitigates the difficulties of the unmanageably large variable space. 

 

 

 

 

 

 

 

 

 

 

51 

6. 

CURRENT FINDINGS AND FUTURE RESEARCH  

In the coming century, societies must dramatically increase food production without furthering the 

irreversible  damage  to  the  environment.  One  means  of  balancing  these  two  objectives  is 

sustainable  intensification.  Sustainable  intensification  entails  increasing  the  yield  of  existing 

agricultural lands while minimizing negative impacts on the environment. With these goals in 

mind, we sought to optimize irrigation and fertilizer scheduling on the farm level with respects to 

crop yield and environmental impact. Since no solution exists that maximizes yield and minimizes 

environmental impact, multi-objective optimization techniques were used to obtain a set of optimal 

solutions  that  collectively  represent  the  tradeoffs  between  the  conflicting  objectives.  Decision 

makers can then rank and select their optimal trade-off from the global set of optimal solutions. 

The following are the main conclusions from this research: 

•  Multi-objective optimization can help with sustainable agricultural intensification process 

by  identifying  solutions  to  irrigation  scheduling  and  nitrogen  application  that  are 

significantly more efficient than current best practices.  

•  Multi-objective optimization gives the power of prioritizing conflicting objectives into the 

hands of human decision makers by providing the Pareto front of optimal solutions  

•  Examining the common traits among a group of Pareto optimal solutions allows producers 

to improve their existing management practices 

•  Our bi-level optimization framework further improves the efficiency of solutions, as well 

as  the  number  of  Pareto  optimal  solutions  by  introducing  the  irrigation  and  nitrogen 

application dates in addition to the application amounts 

 

 

52 

7. 

FUTURE APPLICATIONS  

This study integrated U-NSGA-III based multi-objective optimization platform with DSSAT crop 

model. The objective function of U-NSGA-III enables the platform to optimize against a myriad 

of  soil,  crop,  and  climate  types.  With  our  platform,  we  were  able  to  produce  solutions  that 

maximize yield while reducing water usage by 48.48%, nitrogen usage by 26.4%, and nitrogen 

leaching by 51.48%. Despite these promising results, more work needs to be done to improve the 

over processes in agricultural intensification. The following are areas that can be expanded from 

this work in future research: 

•  The  current  research  only  used  the  climate  information  from  one  growing  season. 

However, by quantifying the uncertainty of weather, future optimization will be able to 

find solutions that are more robust and applicable in the field 

•  Running optimization under different conditions (e.g., management practices, crop types, 

soils) can identifying deeper universal characteristics among optimal agricultural solutions 

• 

Incorporating economic objectives (e.g., net profit) and economic uncertainty (e.g., market 

costs, materials costs) can help producers to identify more feasible solutions 

•  A public online decision support tool that provides producers with highly accurate day-to-

day management recommendations against multiple agricultural objectives that can be a 

game changer by closing the yield gaps 

 

 

 

53 

 

 

 

 

APPENDIX 

54 

 

 

 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Appendix 

Figure A.1. Cluster analysis for a) Nitrogen application counts and b) irrigation application 

 

counts 

 

 

 

 

 

 

 

 

 

 

 

55 

 

 

 

 

 

 

 

 

 

REFERENCES 

56 

 

 

 

 

 

 

 

 

 

 

 

REFERENCES 

30-yr Normal Maximum Temperature: Annual [WWW Document], 2015. . Prism Clim. Group, 

Oregon State Univ. 

 
30-yr Normal Mean Temperature: Annual, 2015. . Prism Clim. Group, Oregon State Univ. 
 
30-yr Normal Minimum Temperature: Annual, 2015. . Prism Clim. Group, Oregon State Univ. 
 
30-yr Normal Precipitation: Annual [WWW Document], 2015. . Prism Clim. Group, Oregon 

State Univ. URL http://prism.oregonstate.edu 

 
Akbari, M., Gheysari, M., Mostafazadeh-Fard, B., Shayannejad, M., 2018. Surface irrigation 
simulation-optimization model based on meta-heuristic algorithms. Agric. Water Manag. 
201, 46–57. 

 
Anwar, A.A., Haq, Z.U., 2013. Genetic algorithms for the sequential irrigation scheduling 

problem. Irrig. Sci. 31, 815–829. https://doi.org/10.1007/s00271-012-0364-y 

 
Arrow, K., 1951. Social Choice and Individual Values John Wiley and Sons New York Google 

Scholar. 

 
Arthur, D., Vassilvitskii, S., 2007. k-means++: The advantages of careful seeding, in: 

Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms. pp. 
1027–1035. 

 
Ashofteh, P.-S., Haddad, O.B., Loáiciga, H.A., 2015. Evaluation of Climatic-Change Impacts on 

Multiobjective Reservoir Operation with Multiobjective Genetic Programming. J. Water 
Resour. Plan. Manag. 141, 04015030. https://doi.org/10.1061/(ASCE)WR.1943-
5452.0000540 

 
Ashrafi, S.M., Dariane, A.B., 2013. Performance evaluation of an improved harmony search 
algorithm for numerical optimization: Melody Search (MS). Eng. Appl. Artif. Intell. 26, 
1301–1321. https://doi.org/10.1016/j.engappai.2012.08.005 

 
Baker, D.N., Lambert, J.R., McKinion, J.M., 1983. GOSSYM: A simulator of cotton crop 

growth and yield. South Carolina. Agric. Exp. Station. Tech. Bull. 

 
Beni, G., Wang, J., 1993. Swarm intelligence in cellular robotic systems, in: Robots and 

Biological Systems: Towards a New Bionics? Springer, pp. 703–712. 

 
Benson, H.P., 1978. Existence of efficient solutions for vector maximization problems. J. Optim. 

Theory Appl. 26, 569–580. https://doi.org/10.1007/BF00933152 

 
Boote, K.J., Jones, J.W., Hoogenboom, G., 1998. Simulation of crop growth: CROPGRO model. 
 
Boote, K.J., Jones, J.W., Singh, P., 1992. Modeling growth and yield of groundnut. 
 

57 

Chung, U., Gbegbelegbe, S., Shiferaw, B., Robertson, R., Yun, J.I., Tesfaye, K., Hoogenboom, 
G., Sonder, K., 2014. Modeling the effect of a heat wave on maize production in the USA 
and its implications on food security in the developing world. Weather Clim. Extrem. 5, 67–
77. https://doi.org/10.1016/j.wace.2014.07.002 

 
Consoli, S., Matarazzo, B., Pappalardo, N., 2008. Operating Rules of an Irrigation Purposes 

Reservoir Using Multi-Objective Optimization. Water Resour. Manag. 22, 551–564. 
https://doi.org/10.1007/s11269-007-9177-9 

 
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C., 2009. Introduction to Algorithms. MIT 

Press. https://doi.org/10.1108/S0749-742320160000019022 

 
Cox, W., While, L., 2016. Improving the IWFG algorithm for calculating incremental 

hypervolume, in: 2016 IEEE Congress on Evolutionary Computation (CEC). pp. 3969–
3976. https://doi.org/10.1109/CEC.2016.7744293 

 
de Borda, J., 1781. Mathematical derivation of an election system. Isis 44, 42–51. 
 
Deb, K., 2009. Multi-objective Optimization Using Evolutionary Algorithms. John Wiley and 

Sons, Chichester, UK. 

 
Deb, K., Agrawal, R.B., 1995. Simulated Binary Crossover for Continuous Search Space. 

Complex Syst. 9, 115–148. https://doi.org/10.1.1.26.8485Cached 

 
Deb, K., Gupta, H., 2005. Searching for Robust Pareto-Optimal Solutions in Multi-objective 

Optimization, in: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (Eds.), 
Evolutionary Multi-Criterion Optimization. Springer Berlin Heidelberg, Berlin, Heidelberg, 
pp. 150–164. 

 
Deb, K., Jain, H., 2014. An Evolutionary Many-Objective Optimization Algorithm Using 

Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With 
Box Constraints. IEEE Trans. Evol. Comput. 18, 577–601. 
https://doi.org/10.1109/TEVC.2013.2281535 

 
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T., 2002. A fast and elitist multiobjective genetic 

algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6, 182–197. 
https://doi.org/10.1109/4235.996017 

 
Eberhart, R., Kennedy, J., 1995. A new optimizer using particle swarm theory. MHS’95. Proc. 

Sixth Int. Symp. Micro Mach. Hum. Sci. 39–43. https://doi.org/10.1109/MHS.1995.494215 

 
Emmerich, M., Beume, N., Naujoks, B., 2005. An EMO Algorithm Using the Hypervolume 

Measure as Selection Criterion, in: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. 
(Eds.), Evolutionary Multi-Criterion Optimization. Springer Berlin Heidelberg, Berlin, 
Heidelberg, pp. 62–76. 

 
 
 

58 

Fernández García, I., Moreno, M.A., Rodríguez Díaz, J.A., 2014. Optimum pumping station 

management for irrigation networks sectoring: Case of Bembezar MI (Spain). Agric. Water 
Manag. 144, 150–158. https://doi.org/10.1016/j.agwat.2014.06.006 

 
García-Vila, M., Fereres, E., Mateos, L., Orgaz, F., Steduto, P., 2009. Deficit Irrigation 

Optimization of Cotton with AquaCrop. Agron. J. 101, 477. 
https://doi.org/10.2134/agronj2008.0179s 

 
Geem, Z.W., Kim, J.H., Loganathan, G. V., 2007. A New Heuristic Optimization Algorithm: 

Harmony Search. https://doi.org/10.1177/003754970107600201 

 
Gen, M., Cheng, R., 2000. Genetic algorithms and engineering optimization. John Wiley & Sons. 
 
Geoffrion, A.M., 1968. Proper efficiency and the theory of vector maximization. J. Math. Anal. 

Appl. 22, 618–630. https://doi.org/10.1016/0022-247X(68)90201-1 

 
Goldberg, D.E., 1989. Genetic algorithms in search, optimization, and machine learning. 

Addison-Wesley, Boston. 

 
González Perea, R., Camacho Poyato, E., Montesinos, P., Rodríguez Díaz, J.A., 2016. 

Optimization of Irrigation Scheduling Using Soil Water Balance and Genetic Algorithms. 
Water Resour. Manag. 30, 2815–2830. https://doi.org/10.1007/s11269-016-1325-7 

 
Groot, J.C.J., Oomen, G.J.M., Rossing, W.A.H., 2012. Multi-objective optimization and design 

of farming systems. Agric. Syst. 110, 63–77. https://doi.org/10.1016/j.agsy.2012.03.012 

 
Groot, J.C.J., Rossing, W.A.H., Jellema, A., Stobbelaar, D.J., Renting, H., Van Ittersum, M.K., 
2007. Exploring multi-scale trade-offs between nature conservation, agricultural profits and 
landscape quality-A methodology to support discussions on land-use perspectives. Agric. 
Ecosyst. Environ. 120, 58–69. https://doi.org/10.1016/j.agee.2006.03.037 

 
Gurav, J.B., Regulwar, D.G., 2012. Multi Objective Sustainable Irrigation Planning with 

Decision Parameters and Decision Variables Fuzzy in Nature. Water Resour. Manag. 26, 
3005–3021. https://doi.org/10.1007/s11269-012-0062-9 

 
Hadka, D., Reed, P., 2013. Borg: An Auto-Adaptive Many-Objective Evolutionary Computing 

Framework 21, 231–259. 

 
Haimes, Y. V, 1971. On a bicriterion formulation of the problems of integrated system 

identification and system optimization. IEEE Trans. Syst. Man. Cybern. 1, 296–297. 

 
Hengsdijk, H., Langeveld, J.W.A., 2009. Yield trends and yield gap analysis of major crops in 

 
Holland, J.H., 1975. Adoption in Natural and Artificial Systems. University of Michigan. Ann 

the world. 

Arbor. 

 
 

59 

Hoogenboom, G., Jones, J.W., Traore, P.C.S., Boote, K.J., 2012. Experiments and data for model 

evaluation and application, in: Improving Soil Fertility Recommendations in Africa Using 
the Decision Support System for Agrotechnology Transfer (DSSAT). Springer, pp. 9–18. 

 
Hoogenboom, G., Porter, C.H., Shelia, V., Boote, K.J., Singh, U., White, J.W., Hunt, L.A., 
Ogoshi, R., Lizaso, J.I., Koo, J., 2017. Decision Support System for Agrotechnology 
Transfer (DSSAT) Version 4.7. 

 
Jones, C.A., Kiniry, J.R., Dyke, P.T., 1986. CERES-Maize: A simulation model of maize growth 

and development. Texas A& M University Press. 

 
Jones, J., Hoogenboom, G., Porter, C., Boote, K., Batchelor, W., Hunt, L., Wilkens, P., Singh, 
U., Gijsman, A., Ritchie, J., 2003. The DSSAT cropping system model. Eur. J. Agron. 18, 
235–265. https://doi.org/10.1016/S1161-0301(02)00107-7 

 
Karami, F., Dariane, A.B., 2018. Many-Objective Multi-Scenario Algorithm for Optimal 

Reservoir Operation Under Future Uncertainties. Water Resour. Manag. 32, 3887–3902. 
https://doi.org/10.1007/s11269-018-2025-2 

 
Kijne, J.W., Barker, R., Molden, D.J., 2003. Water productivity in agriculture: limits and 

opportunities for improvement. Cabi. 

 
Kirkby, M., 1975. Hydrograph modelling strategies. IN Peel, R., Chisholm, M. & Haggett, 

P.(Eds.) Processes in Physical and Human Geography. 

 
Kollat, J.B., Reed, P.M., 2006. Comparing state-of-the-art evolutionary multi-objective 

algorithms for long-term groundwater monitoring design. Adv. Water Resour. 29, 792–807. 
https://doi.org/10.1016/J.ADVWATRES.2005.07.010 

 
Koza, J.R., 1992. Genetic programming: On the programming of computers by means of natural 

selection. MA. 

 
Kropp, I., 2018a. DSSAT4j. 
 
Kropp, I., 2018b. CropOpt. 
 
Lampinen, J., Zelinka, I., others, 2000. On stagnation of the differential evolution algorithm, in: 

Proceedings of MENDEL. pp. 76–83. 

 
Lascody, R., 2002. The onset of the wet and dry seasons in east central Florida-A subtropical 

wet-dry climate? Natl. Ocean. Atmos. Adminstration/National Weather Serv. Forecast Off. 
Melbourne, FL. 

 
Laumanns, M., Thiele, L., Deb, K., Zitzler, E., 2002. Combining Convergence and Diversity in 

Evolutionary Multiobjective Optimization. Evol. Comput. 10, 263–282. 
https://doi.org/10.1162/106365602760234108 

 
 

60 

Mello Jr, A. V, Schardong, A., Pedrotti, A., 2013. Multi-Objective Analysis Applied to an 

Irrigated Agricultural System on Oxisols. Trans. ASABE 56, 71–82. 

 
Miettinen, K., 2012. Nonlinear multiobjective optimization. Springer Science & Business Media. 
 
Nixon, J.B., Dandy, G.C., Simpson, A.R., 2001. A genetic algorithm for optimizing off-farm 

irrigation scheduling. J. Hydroinformatics 3, 11–22. 

 
Quinn, J.D., Reed, P.M., Giuliani, M., Castelletti, A., Oyler, J.W., Nicholas, R.E., 2018. 
Exploring How Changing Monsoonal Dynamics and Human Pressures Challenge 
Multireservoir Management for Flood Protection, Hydropower Production, and Agricultural 
Water Supply. Water Resour. Res. 54, 4638–4662. 

 
Ritchie, J.T., 1985. Description and performance of CERES wheat: A user-oriented wheat yield 

model. ARS wheat yield Proj. 159–175. 

 
Rudolph, G., 1994. Convergence Analysis of Canonical Genetic Algorithms. IEEE Trans. Neural 

Networks 5, 96–101. https://doi.org/10.1109/72.265964 

 
Sampath, R.K., 1992. Issues in irrigation pricing in developing countries. World Dev. 20, 967–

977. https://doi.org/10.1016/0305-750X(92)90124-E 

 
Sarker, R., Ray, T., 2009. An improved evolutionary algorithm for solving multi-objective crop 

planning models. Comput. Electron. Agric. 68, 191–199. 
https://doi.org/10.1016/j.compag.2009.06.002 

 
Sarker, R., Ray, T., 2005. Multiobjective Evolutionary Algorithms for solving Constrained 

Optimization Problems. 

 
Sastry, K., Goldberg, D.E., Kendall, G., 2014. Genetic Algorithms BT  - Search Methodologies: 
Introductory Tutorials in Optimization and Decision Support Techniques, in: Burke, E.K., 
Kendall, G. (Eds.), . Springer US, Boston, MA, pp. 93–117. https://doi.org/10.1007/978-1-
4614-6940-7_4 

 
Seada, H., 2017. evolib. 
 
Seada, H., Deb, K., 2015. U-NSGA-III: A Unified Evolutionary Optimization Procedure for 

Single, Multiple, and Many Objectives: Proof-of-Principle Results. Springer, Cham, pp. 34–
49. https://doi.org/10.1007/978-3-319-15892-1_3 

 
Seada, H., Kropp, I., 2018. evolib (multi-threaded). 
 
Smith, M., 1992. CROPWAT: A computer program for irrigation planning and management. 

Food & Agriculture Org. 

 
Steduto, P., Hsiao, T.C., Raes, D., Fereres, E., 2009. Aquacrop-the FAO crop model to simulate 

yield response to water: I. concepts and underlying principles. Agron. J. 101, 426–437. 
https://doi.org/10.2134/agronj2008.0139s 

61 

Storn, R., Price, K., 1997. Differential Evolution – A Simple and Efficient Heuristic for global 

Optimization over Continuous Spaces. J. Glob. Optim. 11, 341–359. 
https://doi.org/10.1023/a:1008202821328 

 
Tamaki, H., Kita, H., S, K., 1996. Multi-objective optimization by genetic algorithms: a review. 

Diversity. https://doi.org/10.1080/02680939.2013.782512 

 
Tan, Q., Zhang, S., Li, R., 2017. Optimal use of agricultural water and land resources through 

reconfiguring crop planting structure under socioeconomic and ecological objectives. Water 
(Switzerland) 9, 488. https://doi.org/10.3390/w9070488 

 
Wang, Y., Wu, P., Zhao, X., Jin, J., 2012. Water-Saving Crop Planning Using Multiple 
Objective Chaos Particle Swarm Optimization for Sustainable Agricultural and Soil 
Resources Development. CLEAN – Soil, Air, Water 40, 1376–1384. 
https://doi.org/10.1002/clen.201100310 

 
Waraich, E.A., Ahmad, R., Ashraf, M.Y., Saifullah, Ahmad, M., 2011. Improving agricultural 

water use efficiency by nutrient management in crop plants. Acta Agric. Scand. Sect. B-Soil 
Plant Sci. 61, 291–304. 

 
Whittaker, G., Färe, R., Grosskopf, S., Barnhart, B., Bostian, M., Mueller-Warrant, G., Griffith, 

S., 2017. Spatial targeting of agri-environmental policy using bilevel evolutionary 
optimization. Omega (United Kingdom) 66, 15–27. 
https://doi.org/10.1016/j.omega.2016.01.007 

 
Wilkerson, G.G., Jones, J.W., Boote, K.J., Ingram, K.T., Mishoe, J.W., 1983. Modeling soybean 

growth for crop management. Trans. ASAE 26, 63–73. 

 
Xue, F., Sanderson, A.C., Graves, R.J., 2003. Pareto-based multi-objective differential evolution. 

2003 Congr. Evol. Comput. CEC 2003 - Proc. 2, 862–869. 
https://doi.org/10.1109/CEC.2003.1299757 

 
Zhang, C., Li, Y., Chu, J., Fu, G., Tang, R., Qi, W., 2017. Use of Many-Objective Visual 

Analytics to Analyze Water Supply Objective Trade-Offs with Water Transfer. J. Water 
Resour. Plan. Manag. 143, 5017006. 

 
Zhang, Q., Li, H., 2007. MOEA/D: A multiobjective evolutionary algorithm based on 

decomposition. IEEE Trans. Evol. Comput. 11, 712–731. 

 

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