An evolutionary algorithm using two-stage non-dominated sorting and directed mating for constrained multi-objective optimization

When multi-objective optimization problems (MOPs) include several constraints, MOEAs need to introduce a mechanism to obtain feasible solutions from infeasible ones. CNSGA-II, a representative constrained MOEA, evolves infeasible solutions into feasible ones by using the concept of constrain-dominance based on the sum of constraint violation values. However, since the conventional CNSGA-II considers only the sum of constraint violation values in the evolution process of infeasible solutions, objective function values of obtained feasible solutions would be worse. Also, since infeasible solutions have less chance to generate offspring than feasible ones, valuable genetic information of infeasible solutions would not be utilized in the solutions search. To overcome these problems and improve the search performance of MOEAs on constrained MOPs, in this work we propose a novel constrained MOEA introducing a parents selection based on two-stage non-dominated sorting of solutions and a directed mating in objective space. We compare the search performance of the proposed algorithm with CNSGA-II on BNH, SRN, TNK, OSY and μ objectives k knapsacks problems, and we show that the proposed algorithm achieves higher search performance than CNSGA-II on all benchmark problems.