Plenary: Multimodal, Multiobjective Optimization Problems: Decomposition in Decision and Objective Spaces

Multi-objective optimization problems (MOPs) deal with optimizing multiple conflicting objectives to attain the state of Pareto-optimality, where improving solutions in terms of one objective only leads to deterioration in terms of one or more of the other objectives. Multi-modal MOPs (MMMOPs) are those problems where a many-to-one mapping exists from solution space to objective space. As a result, multiple subsets of the Pareto-optimal Set could independently generate the same Pareto-Front. The discovery of such equivalent solutions across the different subsets is essential during decision-making to facilitate the analysis of their non-numeric, domain-specific attributes. However, algorithms purely designed for MOPs are unable to cater to this requirement as they do not seek multiple solution subsets. In contrast to such algorithms, approaches designed for MMMOPs show good solution diversity in the solution space (often by using crowding distance) at the cost of relatively poor performance (convergence and diversity) in the objective space. In this talk, we will touch upon the basic concepts in MMMOPs, and identify a problem of the existing approaches, which we refer to as the crowding illusion problem due to the usage of crowding distance over the entire solution space. We will then describe a method of solving MMMOPs with a graph Laplacian-based Optimization using Reference vector assisted Decomposition (LORD). Experimental results comparing the performance of LORD with the state-of-the-art algorithms for MOPs and MMMOPs on CEC 2019 multi-modal multi-objective test suite and polygon problems will be presented. The talk will conclude with a mention of some areas of further research in MMMOPs.