Polynomial Mean-Centric Crossover for Directed Mating in Evolutionary Constrained Multi-Objective Continuous Optimization

This paper proposes a mean-centric crossover to improve the effectiveness of the directed mating utilizing useful infeasible solutions in evolutionary constrained multi-objective continuous optimization. The directed mating selects a feasible solution as the first parent and a solution dominating the first parent in the objective space from the population involving infeasible solutions as the second parent. Since infeasible solutions having better objective values than feasible ones have useful variables, it helps to improve the search performance. So far, the commonly used simulated binary crossover (SBX) have been employed to generate offspring from two parents selected by the directed mating. However, it is not clear that the commonly used SBX is appropriate also for parents selected by the directed mating. When the Pareto front exists on the boundary between the feasible and the infeasible regions in the variable space, a mean-centric crossover generating offspring around intermediate area of two parents would be more effective than SBX which is a parent-centric crossover generating offspring around two parents. This work proposes the polynomial mean-centric crossover (PMCX) and combines it with the directed mating. The experimental results show that the proposed PMCX achieves higher search performance than SBX on several test problems.