Population decomposition evolutionary framework for constrained multiobjective optimization

Abstract

The solution to constrained multiobjective optimization problems (CMOPs) requires both optimizing the objective function and satisfying the constraints. Many studies have demonstrated that multi-population models are effective for solving CMOPs. However, excessive consumption of evaluation times can lead to convergence difficulties in the later stages of population evolution.This article proposes a population decomposition strategy to overcome these drawbacks and enhance the quality of the solution set. Specifically, clustering techniques partition both the main and unconstrained populations in the objective space, yielding $r$ subpopulations and, consequently, $r+1$ subpopulations. A fuzzy selection mechanism is introduced to enhance offspring convergence while preserving population diversity. By reformulating the selection of the optimal individual as a conditional extremum problem within a fuzzy environment, the algorithm’s applicability to CMOPs is significantly improved. Additionally, a novel environmental selection model for unconstrained populations is proposed to ensure both convergence and diversity. In the early stage, this model prioritizes convergence by leveraging the Euclidean distance in the target space. In the later stage, diversity is maintained by incorporating both Euclidean distance and cosine similarity. Finally, comparisons with six state-of-the-art constrained multiobjective evolutionary algorithms on 57 benchmark test functions and 12 real-world problems demonstrate that the proposed algorithm achieves superior performance in terms of both convergence and diversity. The code for PDECMO is https://github.com/YongchaoLucky/PDECMO.git.