A point crowdedness based evolutionary algorithm for many-objective optimization

Abstract It is well known that many-objective optimization problems (MaOPs) are difficultly to be balanced diversity and convergence in the search process due to the high dimension of the objective spaces. The method of evaluating the diversity of the solution set can directly affect the final performances of the algorithms. In this article, we propose a point crowding-degree (PC) strategy to evaluate the diversity of solution sets in view of the characteristics of high dimension and fewer sampling points of MaOPs in the high-dimensional objective space, which propose a point crowding-degree based evolutionary algorithm (PCEA) for many-objective optimization problems. Specifically, the proposed PC strategy not only considers the distance between any two points as large as possible, but also considers the gap between each dimension component as large as possible, and ponders the influence of surrounding neighbor points on the diversity of this point, which obtain a better diversity solution set. At the same time, the selection of evolutionary operators balance convergence and diversity, and further points the search to the feasible region. The PCEA is compared experimentally with several state-of-the-art algorithms on the CEC2018 many-objective benchmark functions with up to 15 objectives and the experimental results show that the proposed PCEA algorithm has strong competitiveness and better overall performance. In addition, the proposed PC strategy is integrated into other advanced MaOPs methods. The results show that it is beneficial to improve the performance of other MaOEAs algorithms.