Novel Selection Indexes for Additional Selection of Non-Dominated Sorting Genetic Algorithms

In this paper, we propose two new ranking indexes for solution set in many-objective optimization evolutionary algorithms. A non-dominated ranking allows selection pressure to perform effectively in Many-objective Optimization Problems (MaOPs). NSGA is one of the algorithms that effectively incorporates non-dominated sorting for solving MaOPs. In MaOPs with a large number of objectives, most of the solutions in solution set of NSGA become non-dominated to one another. In such cases, NSGA no longer rank solutions with the non-dominated sorting, and is forced to optimize based only on additional selection indexes, for example, which is crowding distance in NSGA-II. It is well known that the additional selection with crowding distance does not effectively solve MaOP. NSGA-III allows niche selection by means of a large number of uniformly distributed reference points to realize the additional selection. While the niche selection yields high diversity in the solution set and improves the optimization, it requires huge computational cost for calculate the relation ship between the solutions and reference lines. To avoid these problems on conventional NSGAs, this paper proposes a new selection indexes to effectively solve MaOPs with the equivalent computational cost as NSGA-II, where the proposed indexes are based on the hyper volume difference and the hyper conical volume of each point in certain front set. These proposed indexes are implemented with significantly smaller computational costs than the niche selection of NSGA-III. NSGAs with the two proposed selection indexes are applied to several test MaOPs for comparing with the conventional NSGA-II and NSGA-III as numerical experiments. The experimental results showed that NSGA-III has been the most effective, but the proposed indexes demonstrated more effective optimization than NSGA-II.