Constrained multi-objective optimization assisted by competitive mechanism based reward auxiliary optimization problems

Solving constrained multi-objective optimization problems requires simultaneously satisfying multiple objectives and constraints, presenting a significant challenge for solving tasks. Constructing auxiliary optimization problems to assist the main optimization problem in accelerating convergence is a common approach for constrained multi-objective evolutionary algorithms (CMOEAs). However, this approach may waste computational resources on auxiliary optimization problems that provide little benefit to the main optimization problem at certain stages of the evolution process. Based on the above issue, this paper proposes a constrained multi-objective optimization algorithm to address this issue via competitive mechanism based reward auxiliary optimization problems (RACMO). Specifically, an unconstrained auxiliary optimization problem and a dynamic constrained auxiliary optimization problem are constructed. They are rewarded by the number of solutions provided to the main optimization problem, and the cumulative reward is mapped to the probability to adaptively selecting more valuable auxiliary optimization problems. Moreover, an adaptive stop-update strategy is designed. By controlling the competition between two auxiliary populations and adaptive stop-updating, excellent convergence is guaranteed while significantly saving computational resources. Experimental results demonstrate the competitiveness of RACMO compared to ten advanced CMOEAs on three test suites and eight practical application problems.