An Evolutionary Algorithm Based on Dynamic Grid Search for Constrained Multimodal Multiobjective Optimization
TL;DR
A dynamic grid search-based evolutionary algorithm (DGSEA) for CMMOPs that assigns a dynamic grid space to each solution, which expands as the evolution progresses, and achieves a better balance among feasibility, convergence, and diversity.
Abstract
Constrained multimodal multiobjective optimization problems (CM-MOPs) widely exist in real-world applications and are characterized by the coexistence of constraints and multimodality. Solving CMMOPs requires identifying multiple feasible Pareto-optimal solutions with identical objective values. However, many existing algorithms tend to converge prematurely to local feasible regions and fail to discover all equivalent Pareto-optimal solutions. To address this issue, this paper proposes a dynamic grid search-based evolutionary algorithm (DGSEA) for CMMOPs. DGSEA assigns a dynamic grid space to each solution, which expands as the evolution progresses. In the early stage, a small grid promotes effective exploration of discrete feasible regions while maintaining a well-distributed set of candidate solutions. In the middle and later stages, the expanded grid helps eliminate redundant solutions and achieves a better balance among feasibility, convergence, and diversity. Moreover, a grid-based density metric is incorporated into mating and environmental selection to generate and select offspring with good distribution. Experimental comparisons with state-of-the-art algorithms demonstrate that DGSEA achieves superior performance in solving CMMOPs.