A many-objective evolutionary algorithm combining simplified hypervolume and a method for reference point sampling based on angular relationship

Determining the path for an evolutionary algorithm is crucial for its performance. Current methods for sampling reference points guiding evolutionary algorithms are inadequate for dealing with convex and concave Pareto fronts,and the uniformity of sampling results decreases significantly in high-dimensional spaces. In this paper,we propose a reference point sampling method based on angular relationships to tackle these issue. And we propose the concept of optimally distributed individuals based on the IGD indicator to ensure the distribution of the evolutionary process and prevent the algorithm from converging to local optima. Additionally,we introduce a novel method for calculating individuals’ fitness within the population,ensuring convergence,uniformity,and distribution of the evolutionary algorithm,thereby enhancing selection pressure among non-dominated individuals. Experimental results on diverse benchmark test problems demonstrate that the proposed algorithm competes favorably with six advanced evolutionary algorithms for many-objective optimization.