Decomposition in decision and objective space for multi-modal multi-objective optimization

Multi-modal multi-objective optimization problems (MMMOPs) have multiple subsets within the Pareto-optimal Set, each independently mapping to same Pareto-Front. Prevalent evolutionary algorithms are not purely designed search for solution subsets, whereas, MMMOPs demonstrate degraded performance in objective space. This motivates design of better addressing MMMOPs. The present work identifies crowding illusion problem originating from using distance globally over entire decision Subsequently, an framework, called graph Laplacian based Optimization Reference vector assisted Decomposition (LORD), is proposed, which uses decomposition both and space dealing with Its filtering step further extended LORD-II algorithm, demonstrates its dynamics on multi-modal many-objective problems. efficacies frameworks established by comparing their test instances CEC 2019 suite polygon state-of-the-art other multi- algorithms. manuscript concluded mentioning limitations proposed future directions still source code available at https://worksupplements.droppages.com/lord.