Investigating the Performance of Evolutionary Algorithms on Constrained Multi-objective Optimization Problems with Deceptive Infeasible Regions

Abstract

When using constrained multi-objective evolutionary algorithms to solve problems, most of them prefer infeasible solutions closer to feasible regions since they have smaller constraint violations. However, they may not work well on some problems which infeasible solutions closer to feasible regions have larger constraint violations than the ones farther away from the feasible regions. This kind of problems has not been explored so far. To help close this research gap, this paper first illustrates it by designing two new constrained multi-objective optimization problems (CMOPs) with deceptive infeasible regions. That is, in the deceptive infeasible regions, solutions farther away from a feasible region has a smaller constraint violation than the ones closer to the feasible region. We have proposed a constraint-handling technique based a set of directed weights (M2M-DW) to solve CMOPs on our previous work. However, it can not be able to solve the CMOPs with deceptive infeasible regions, since the directed weights prefer infeasible solutions with smaller constraint violations, which guides the search to the less promising regions. We improve it to solve the two proposed problems. Another set of benchmark problems, i.e., CTPs, is also used to verify the performance of the compared algorithms. Experimental results show that the proposed algorithm significantly outperforms the algorithms with which it is compared on the two proposed problems and CTPs, in terms of reliability and stability in finding a set of well-distributed optimal solutions.