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A two-stage multimodal multiobjective evolutionary algorithm using Voronoi diagram and modality detection
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AI
DOI：10.1016/j.swevo.2026.102305.png)
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Abstract
En 中文
In real-world applications, multimodal multiobjective optimization problems (MMOPs), where multiple Pareto optimal sets in the decision space may be mapped to the same Pareto front in the objective space, pose a grand challenge to optimization. In contrast to solving traditional multiobjective optimization problems where the focus is on the convergence and diversity of the solutions in the objective space, it also requires to pay attention to the diversity of the solutions in the decision space in solving MMOPs. To effectively tackle MMOPs, this work proposes a two-stage multimodal multiobjective evolutionary algorithm based on the Voronoi diagram and modality detection, called MMEA/VM. The proposed MMEA/VM consists of a two-stage optimization process, with the first stage focusing on increasing the diversity of the solution set in the decision space and the second stage achieving diversity and convergence in the objective space. As the first-stage search strategy, a Voronoi diagram-based diversity enhancement mechanism is designed to effectively explore the entire decision space by making use of the Voronoi neighbors. Based on a modality detection strategy that identifies the modality to which each candidate is assigned, the second stage adopts a decomposition-based search mechanism for the objective space together with a novel environmental selection method. By seamlessly interleaving the two-stage search processes, MMEA/VM strikes a good balance between exploration and exploitation in both the decision and objective spaces. Experimental studies are conducted on two benchmark suites and a real-world problem. The experimental results on five metrics demonstrate that MMEA/VM has higher competitiveness in comparison with state-of-the-art multimodal multiobjective evolutionary algorithms.
Keywords:
Multimodal multiobjective optimization
Voronoi diagram
modality detection
evolutionary algorithm
Pareto optimal sets
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