Feedback Tracking Constraint Relaxation Algorithm for Constrained Multi-Objective Optimization

In practical applications, constrained multi-objective optimization problems (CMOPs) often fail to achieve the desired results when dealing with CMOPs with different characteristics. Therefore, to address this drawback, we designed a constraint multi-objective evolutionary algorithm based on feedback tracking constraint relaxation, referred to as CMOEA-FTR. The entire search process of the algorithm is divided into two stages: In the first stage, the constraint boundaries are adaptively adjusted based on the feedback information from the population solutions, guiding the boundary solutions towards neighboring solutions and tracking high-quality solutions to obtain the complete feasible region, thereby promoting the population to approach the unconstrained Pareto front (UPF). The obtained feasible solutions are stored in an archive and continuously updated to promote the diversity and convergence of the population. In the second stage, the scaling of constraint boundaries is stopped, and a new dominance criterion is established to obtain high-quality parents, thereby achieving the complete constrained Pareto front (CPF). Additionally, we customized an elite mating pool selection, an archive updating strategy, and an elite environmental selection truncation mechanism to maintain a balance between diversity and convergence. To validate the performance of CMOEA-FTR, we conducted comparative experiments on 44 benchmark test problems and 16 real-world application cases. The statistical IGD and HV metrics indicate that CMOEA-FTR outperforms seven other CMOEAs.