An evolutionary constrained multi-objective optimization algorithm with parallel evaluation strategy

Abstract

This paper proposes an improved evolutionary algorithm with parallel evaluation strategy (EAPES) for solving constrained multi-objective optimization problems (CMOPs) efficiently. EAPES stores feasible solutions and infeasible solution separately in different populations, and evaluates infeasible solutions in an unusual manner, such that not only feasible solutions but also useful infeasible solutions will be used as parents to reproduce the populations for the next generation. The EAPES proposed in this paper ranks infeasible solutions based on the scalarizing function named constrained penalty-based boundary intersection (C-PBI), which is determined by objective function values and a total constraint violation value. Then, this paper investigates the performance of the C-PBI-based EAPES to search for Pareto-optimal solutions compared to the non-dominated sorting genetic algorithm II (NSGA-II) and the previous EAPES without using C-PBI. The C-PBI-based EAPES with a well-tuned parameter is most capable to explore Pareto-optimal solutions with good diversity, spread, and convergence to the true Pareto front. The C-PBI-based EAPES assigns bad rank to the infeasible solutions that are expected away from an unknown Pareto front, and does not store such solutions. Thus the C-PBI-based EAPES exhibits a higher searching capability than the previous EAPES by evaluating infeasible solutions in an appropriate balance between objective functions and total constraint violation.