A dual dynamic constraint boundary based constrained multi-objective evolutionary algorithm for small feasible regions

Addressing constrained multi-objective optimization problems (CMOPs) with small feasible regions presents a significant challenge, as existing algorithms often struggle to balance feasibility, diversity, and convergence within the population. To overcome this challenge, we propose a dual dynamic constraint boundary-based constrained multi-objective evolutionary algorithm, referred to as TPDCB. In TPDCB, the original CMOP is transformed into two dynamic CMOPs using a dual dynamic constraint boundary strategy to better identify feasible solutions. Specifically, for the two dynamic CMOPs within the constraint relaxation boundary, the first dynamic CMOP primarily focuses on multi-objective optimization, while the second dynamic CMOP equally emphasizes both multi-objective optimization and constraint satisfaction to enhance individual diversity. Furthermore, an auxiliary problem without constraints is introduced by treating constraint violations as an additional optimization objective, which improves the algorithm's global convergence. Finally, a tri-population co-evolution framework is proposed to simultaneously tackle all three constructed problems. The algorithm's performance is evaluated on 22 benchmark problems and three real-world applications, and compared to seven state-of-the-art algorithms. Experimental results demonstrate that TPDCB is competitive in solving CMOPs with small feasible regions.