Evolutionary algorithm with parallel evaluation strategy of feasible and infeasible solutions considering total constraint violation

A new genetic algorithm to search for Pareto-optimal solutions in multi-objective problems with constraints is proposed. This algorithm employs the parallel evaluation strategy in which feasible and infeasible solutions are preserved in separate populations. Feasible solutions are ranked in accordance with the ordinary non-dominated ranking method. On the other hands, infeasible solutions are ranked based on their objective functions and total constraint violation. The total constraint violation is treated as the (M+1)-th evaluation function in addition to M original objective functions used for ranking infeasible solutions. This non-dominated ranking considering both objective functions and total constraint violation is expected to remove infeasible solutions with large constraint violations and preserve useful solutions. Through the present numerical tests, the proposed algorithm without tunable parameters outperforms the existing genetic algorithms considering either objective functions or constraint violations in multi-objective problems with active constraints. Additionally, the proposed algorithm shows better performance than the genetic algorithm using the penalty approach considering the sum of objective functions and total constraint violation. The improvement of Pareto-optimal solution search capability is accomplished by preserving infeasible solutions near the true Pareto-optimal front restricted by active constraints.