Constrained Multiobjective Optimization with Escape and Expansion Forces

Constraints may scatter the Pareto optimal solutions of a constrained multiobjective optimization problem (CMOP) into multiple feasible regions. To avoid getting trapped in local optimal feasible regions or a part of the global optimal feasible regions, a constrained multiobjective evolutionary algorithm (CMOEA) should consider both the escape force and the expansion force carefully during the search process. However, most CMOEAs fail to provide these two forces effectively. As a remedy for this limitation, this article proposes a method called TPEA. TPEA maintains three populations, termed Pop1, Pop2, and Pop3. Pop1 is a regular population, updated with a constrained NSGA-II variant. Pop2 and Pop3 are two auxiliary populations, containing the innermost and outermost nondominated infeasible solutions, respectively. The analysis reveals that these two types of nondominated infeasible solutions can contribute to the generation of escape and expansion forces, respectively. Due to these two forces, TPEA is likely to identify more global optimal feasible regions, which is crucial for constrained multiobjective optimization. Also, a mating selection strategy is developed in TPEA to coordinate the interaction among these three populations. Extensive experiments on 58 benchmark CMOPs and 35 real-world ones demonstrate that TPEA is significantly superior or comparable to six state-of-the-art CMOEAs on most test instances.