Global and local feasible solution search for solving constrained multi-objective optimization

Constrained multi-objective optimization problems (CMOPs) are challenging due to the complexity of feasible regions caused by constraints, especially when facing small feasible ranges, multiple feasible regions, and complex distribution of feasible regions. Existing algorithms struggle to balance population convergence, diversity, and feasibility. This paper proposes a constrained multi-objective evolutionary algorithm framework based on global and local feasible solutions search to address this issue. The proposed framework is divided into three stages, and an adaptive method is proposed to decide when to switch the search state. In the first two stages, the evolution of the population is relatively free and not subject to constraint restrictions. Feasible solutions in the population are saved in the FeasiblePool for environmental selection during these two stages. The FeasiblePool does not affect the evolving population during these stages. In the first stage, the framework uses global search operator to fully explore the decision space and determine the rough range of feasible solutions in the decision space. In the second stage, the framework uses local search operator to enhance the diversity of FeasiblePool within this determined range. In the last stage, the framework reuses these excellent feasible solutions information to guide population evolution while considering constraints. The proposed framework has been compared with four state-of-the-art constrained multi-objective algorithms on four benchmark suites and three real-world applications. The complete experimental results show that the proposed framework has high competitiveness for solving CMOPs.