A Dynamic Constraint Relaxation Framework for Constrained Multimodal Multi-objective Optimization

Juan Zou

doi:10.1109/tevc.2026.3727029

A Dynamic Constraint Relaxation Framework for Constrained Multimodal Multi-objective Optimization

2026-08-24

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杨圣祥 (Shengxiang Yang)

DOI：10.1109/tevc.2026.3727029

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Constrained multimodal multi-objective optimization problems (CMMOPs) are highly challenging due to the coexistence of multiple conflicting objectives, complex constraint conditions, and the presence of multiple optimal regions. Solving CMMOPs requires algorithms to simultaneously ensure solution feasibility, maintain diversity to capture various optima, and achieve convergence across conflicting objectives. However, most existing constrained multimodal multi-objective evolutionary algorithms (CMMOEAs) rely on static constraint-handling strategies, which often hinder exploration and fail to balance feasibility and diversity effectively. To address these issues, we propose a dynamic constraint relaxation framework (DCRF) to enhance the performance of multimodal multi-objective evolutionary algorithms (MMOEAs). DCRF introduces two key components: (1) a dynamic constraint relaxation mechanism (DCRM), which dynamically adjusts constraint strictness across different evolutionary stages: promoting global exploration early on, enabling search in narrow feasible regions mid-process, and enforcing strict feasibility for fine convergence in the final stage; and (2) a feasibility-balanced mating selection (FBMS) that leverages an external archive of elite feasible solutions to guide parent selection, compensating for the feasibility loss during relaxation and improving offspring feasibility. Experimental studies on two benchmark sets (i.e., CMMF and CMMOP) and a real-world application (e.g., the location-selection problem) demonstrate that integrating DCRF into three MMOEAs yields competitive performance under the tested settings. In particular, MMOEA/DC+DCRF outperforms seven state-of-the-art CMMOEAs on most evaluation metrics. Further extended experiments indicate that DCRF also achieves promising performance on constrained multi-objective optimization problems (CMOPs).

Keywords:

Constrained multimodal multi-objective evolutionary algorithms

dynamic constraint relaxation mechanism

feasibility-balanced mating selection

diversity

A Dynamic Constraint Relaxation Framework for Constrained Multimodal Multi-objective Optimization

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