Using Dominated Solutions at Edges to the Diversity and the Uniformity of Non-dominated Solution Distributions in NSGA-II

Abstract

This paper proposes a method for improving the diversity of the Pareto front and the uniformity of non-dominated solution distributions in a fast elitist non-dominated sorting genetic algorithm (NSGA-II), which is an evolutionary multi-objective optimization algorithm. Conventional NSGA-II has excellent convergence to the Pareto front, but it has been reported that for some test cases, it does not produce a more diverse solution distribution than the strength Pareto evolutionary algorithm 2 (SPEA2). In addition, selection using the crowding distance may cause a bias in the selected solution distribution. To avoid this problem, we propose a method that archives dominated solutions that may be effective in improving diversity in the conventional search process when used for genetic operations, and mates these archived solutions with non-dominated solutions at the edge of rank 1 for each objective function. We experimentally compare this approach with the conventional method on the typical ZDT suite of multi-objective test problems and a two-objective constrained knapsack problem. By evaluating the performance based on Pareto front diagrams, the number of non-dominated solutions, the maximum spread and hypervolume values, we show that the proposed method is effective at improving the diversity at both ends of the Pareto optimal front and the solution distribution.