Dynamical decomposition and selection based evolutionary algorithm for many-objective optimization

Abstract

Decomposition-based many-objective evolutionary algorithms decompose the objective space into multiple subregions, with the help of a set of predefined reference vectors. These vectors serve to guide coevolution between subproblems, and while they show potential for maintaining the diversity of solutions, they have limited exploration capabilities in complex problems and high-dimensional objective space. The main issue is that the predefined reference vectors cannot maintain uniformity of the intersection points between search directions and the irregular Pareto front (PF). To address this problem, this paper proposes a dynamical decomposition and selection strategy (DDS). In DDS, the predefined reference vectors are replaced by solutions themselves and normal-boundary directions (NBI), which guide the population to automatically adapt to the shape of PF. The subregions adapt to divide the objective space to increase diversity. Then, to adjust the relationship between diversity and convergence, a dynamical selection strategy based on the course of evolution is proposed. The process of dynamical decomposition and selection strategy is repeated until the termination condition is met. The proposed algorithm is compared with the state-of-the-art many-objective optimization algorithms on several benchmark problems with 5 to 15 objectives in evolutionary computation. Experimental results show that it outperforms other algorithms in most test instances and is less sensitive to irregular PFs.