A Constraint-Handling Technique for Decomposition-Based Constrained Many-Objective Evolutionary Algorithms

To solve the constrained many-objective optimization problems (CMaOPs), the tradeoff among convergence, diversity, and feasibility is a crucial and challenging task. This article proposes a new constraint-handling technique tailored for decomposition-based many-objective evolutionary algorithms to deal with the CMaOPs effectively. Specifically, the proposed method, namely, constrained penalty boundary intersection (CPBI), is an improved aggregation function based on the penalty boundary intersection. In CPBI, the normalized overall constraint violation (CV) is embedded to pursue feasibility. In this way, by the optimization of CPBI, convergence, diversity, and feasibility can be optimized simultaneously. Furthermore, the weight of the normalized overall CV is adjusted adaptively based on the feasible ratio of the current population. To evaluate the performance of CPBI, it is combined with three decomposition-based algorithms. Ten benchmark problems with $50$ instances are chosen as the test suite. In addition, the proposed method is compared with nine advanced algorithms. Experimental results have demonstrated the promising performance of CPBI for different problems.