Competition-based two-stage evolutionary algorithm for constrained multi-objective optimization

In recent years, the emergence of constrained multi-objective evolutionary algorithms (CMOEAs) has made it increasingly difficult to balance between the diversity and convergence of algorithms. To address this challenge, this paper proposes a competition-based two-stage evolutionary algorithm, named CP-TSEA, for constrained multi-objective problems. In the first stage, a $\varepsilon$ constraint boundary relaxation learning mechanism was applied to the auxiliary population. This mechanism not only improved the diversity of the population but also enhanced the global search capability by relaxing the constraints, allowing infeasible solutions with higher fitness rankings to participate in the evolution. In the second stage, an equal-probability competitive strategy was used to select high-quality parents from the elite mating pool to ensure that the population could converge quickly to the optimal solution. The two-stage approach not only improved the exploration ability of the algorithm, but also was able to select higher quality solutions and prevent them from falling into local optima. Additionally, the solution selection in the elite environment employed a three-criteria ranking method to maintain a balance between population diversity and convergence. In terms of experiments, CP-TSEA was compared with seven advanced CMOEAs across five test suites, and the comprehensive data showed that CP-TSEA significantly outperformed its competitors. In addition, CP-TSEA also achieved the best values in six real-world problems, which further confirmed its scalability in real-world applications.