Controlling selection area of useful infeasible solutions and their archive for directed mating in evolutionary constrained multiobjective optimization

As an evolutionary approach to solve constrained multi-objective optimization problems (CMOPs), recently a MOEA using the two-stage non-dominated sorting and the directed mating (TNSDM) has been proposed. In TNSDM, the directed mating utilizes infeasible solutions dominating feasible solutions to generate offspring. Although the directed mating contributes to improve the search performance of TNSDM in CMOPs, there are two problems. First, since the number of infeasible solutions dominating feasible solutions in the population depends on each CMOP, the effectiveness of the directed mating also depends on each CMOP. Second, infeasible solutions utilized in the directed mating are discarded in the selection process of parents (elites) population and cannot be utilized in the next generation. To overcome these problems and further improve the effectiveness of the directed mating in TNSDM, in this work we propose an improved TNSDM introducing a method to control selection area of infeasible solutions and an archiving strategy of useful infeasible solutions for the directed mating. The experimental results on m objectives k knapsacks problems shows that the improved TNSDM improves the search performance by controlling the directionality of the directed mating and increasing the number of directed mating executions in the solution search.