Push and Pull Search for Solving Constrained Multi-objective Optimization Problems

This paper proposes a push and pull search (PPS) framework for solving constrained multi-objective optimization problems (CMOPs). To be more specific, the proposed PPS divides the search process into two different stages, including the push and pull search stages. In the push stage, a multiobjective evolutionary algorithm (MOEA) is adopted to explore the search space without considering any constraints, which can help to get across infeasible regions very fast and approach the unconstrained Pareto front. Furthermore, the landscape of CMOPs with constraints can be probed and estimated in the push stage, which can be utilized to conduct the parameters setting for constraint-handling approaches applied in the pull stage. Then, a constrained multi-objective evolutionary algorithm (CMOEA) equipped with an improved epsilon constraint-handling is applied to pull the infeasible individuals achieved in the push stage to the feasible and non-dominated regions. Compared with other CMOEAs, the proposed PPS method can more efficiently get across infeasible regions and converge to the feasible and nondominated regions by applying push and pull search strategies at different stages. To evaluate the performance regarding convergence and diversity, a set of benchmark CMOPs is used to test the proposed PPS and compare with other five CMOEAs, including MOEA/D-CDP, MOEA/D-SR, C-MOEA/D, MOEA/DEpsilon and MOEA/D-IEpsilon. The comprehensive experimental results demonstrate that the proposed PPS achieves significantly better or competitive performance than the other five CMOEAs on most of the benchmark set.