The typical aim of a multi-objective evolutionary algorithm (MOEA) is to identify a set of well-converged and uniformly distributed Pareto optimal (PO) solutions. This is followed by a multi-criterion decision making (MCDM) step where the decision-maker (DM) has to select a desired solution for further consideration. A convenient and effective MCDM process can be performed when a well-distributed set of Pareto optimal (PO) solutions is provided and the DM is able to visualize, analyze and interpret the solutions. These PO solutions can be associated with unique identifiers - vectors of the same dimension as the Pareto surface. While PO solutions can form arbitrarily complex shapes based on non-domination properties, these identifiers can have simpler properties such as lying on the unit simplex or unit sphere. Since these identifiers inherently capture the properties of the PO frontier, they can be readily used during multi-objective optimization (MOO) to achieve a good distribution of solutions in the corresponding identifier spaces. While most algorithms focus on achieving a good distribution of solutions in the objective space, a good distribution of solutions in the decision-making space can be immensely helpful to the DM. We present and compare several identifier spaces with respect to their properties, and advantages and disadvantages in optimization, visualization and decision-making and propose methods to achieve a superior distribution of solutions in these identifier spaces. We also demonstrate that a combination of these identifiers can be used during optimization to achieve desired distributions for subsequent successful decision-making.The solutions achieved by an MOEA and provided to the DM must provide a comprehensive representation of the PO solutions. These solutions should span the whole PO front while being well-converged and uniformly distributed. However, this cannot be guaranteed in practical scenarios due to the stochasticity of the algorithm and the difficulties associated with the problem itself. A seemingly incomplete Pareto front (PF) is highly problematic during decision-making as the DM might desire more solutions in sparse regions of the current non-dominated (ND) front. Unexpected gaps and discontinuities in the PO front can lead to a lack of trust in the solutions obtained. In this study, we propose a convenient machine learning (ML) assisted multi-criterion decision-making framework that can alleviate some of these issues. We propose to train ML models to map from pseudo-weights to decision variables of PO solutions. These trained models can be used to create solution vectors for any new pseudo-weight vector. We demonstrate that this process can be used to cater to the typical needs of decision-makers, like quickly populating the PF, filling gaps, or extending the PF without further optimization. To deal with constrained problems, we propose an archiving strategy that can be used along with any non-dominated sorting-based MOEA. This archive provides an augmented training dataset that can be used to train ML models to predict the feasibility of newly created solutions before evaluating them, thereby avoiding wasteful evaluations of infeasible solutions. While the previously discussed ML-based MCDM methods can be quick and convenient, they still require iterative solution evaluations in order to confirm the existence of newly created solutions. These MCDM attempts might not be fruitful if the desired solutions do not actually exist. We propose integrating the ML-assisted MCDM concepts into MOEAs as operators to induce confidence in the achieved PF by demystifying the flaws in the PO front. This operator can attempt to answer MCDM concerns, try and fix inherent flaws in the ongoing optimization process, and collect information regarding flaws that could not be fixed. This auxiliary information can be provided to the decision-maker to induce trust in the achieved solutions and can eliminate the need for post-optimal analysis.
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