A Diversity-Enhanced Tri-Stage Framework for Constrained Multiobjective Optimization

Achieving a tradeoff between convergence, feasibility, and diversity is critical for solving constrained multiobjective optimization problems (CMOPs). Existing constrained multiobjective evolutionary algorithms (CMOEAs) primarily focus on constraint-handling techniques to balance constraint satisfaction and objective optimization. However, individual diversity is generally considered to be low. Owing to the insufficient enhancement of diversity, CMOEAs are unable to disperse well in the objective space to enhance the search for the constrained Pareto front (CPF) when handling CMOPs with complex constraints. To address this limitation, this study develops a diversity-enhanced tri-stage framework with three different evolutionary stages. First, sufficient convergence is enabled to move the population across the infeasible regions. Afterward, an angle-domination strategy is designed, aiming to spread the population evenly in the objective space while maintaining the achieved convergence. Third, we propose a minimum neighborhood-based domination strategy to ensure that the population searches the CPF by pursuing an even distribution in the objective space. Moreover, a weight vector preselection strategy is proposed to reduce computational overhead by avoiding ineffective searches in regions that do not include the CPF. Extensive experiments with 48 benchmark instances and 25 real-world instances validate the effectiveness of our approach over nine state-of-the-art methods.