Controlling selection areas of useful infeasible solutions for directed mating in evolutionary constrained multi-objective optimization

As an evolutionary approach to solve constrained multi-objective optimization problems (CMOPs), recently an algorithm using the two-stage non-dominated sorting and the directed mating (TNSDM) was proposed. In TNSDM, the directed mating utilizes infeasible solutions dominating feasible solutions in the objective space to generate offspring. The directed mating significantly contributes to the search performance improvement in evolutionary constrained multi-objective optimization. However, the conventional directed mating has two problems. First, since the conventional directed mating selects a pair of parents based on the conventional Pareto dominance, two parents having different search directions may be mated. Second, the directed mating cannot be performed in some cases especially when the population has few useful infeasible solutions. In this case, the conventional mating using only feasible solutions is performed instead. Thus, the effectiveness of the directed mating cannot always be achieved depending on the number of useful infeasible solutions. To overcome these problems and further enhance the effect of the directed mating in TNSDM, in this work we propose a method to control the selection area of useful infeasible solutions by controlling dominance area of solutions (CDAS). We verify the effectiveness of the proposed method in TNSDM, and compare its search performance with the conventional CNSGA-II on discrete m-objective k-knapsack problems and continuous mCDTLZ problems. The experimental results show that the search performance of TNSDM is further improved by controlling the selection area of useful infeasible solutions in the directed mating.