Balancing exploration and exploitation in dynamic constrained multimodal multi-objective co-evolutionary algorithm

Abstract

Constrained multimodal multi-objective optimization (CMMOPs) involves multiple equivalent constrained Pareto optimal sets (CPSs) matching the same constrained Pareto front (CPF). An essential challenge in solving CMMOPs is how to balance exploration and exploitation in searching for the CPSs. To tackle this issue, a dynamic constrained co-evolutionary multimodal multi-objective algorithm termed DCMMEA is developed in this paper. DCMMEA involves a constraint-relaxed population for handling constraints and a convergence-relaxed population for improving convergence quality. Subsequently, a constraint-relaxed epsilon strategy that considers the constraint violation degree between individuals is designed and applied dynamically in the constraint-relaxed population to develop equivalent CPSs. Similarly, a dynamic convergence-relaxed epsilon strategy that considers the differences between objective values is developed and used dynamically in the convergence-relaxed population. It explores CPSs with high convergence quality and transfers the convergence knowledge to the constraint-relaxed population. Additionally, the constraint- relaxed population size is dynamically increased and the convergence-relaxed population size is dynamically decreased to balance the exploration and exploitation procedures. Experiments are performed on standard CMMOP test suites and validate that DCMMEA obtains superior performance on solving CMMOPs in comparison to state-of-the-art algorithms. Also, DCMMEA is implemented on standard CMOPs and demonstrated good performance in handling CMOPs.