A decomposition based evolutionary algorithm with angle penalty selection strategy for many-objective optimization

Evolutionary algorithms (EAs) based on decomposition have shown to be promising in solving many-objective optimization problems (MaOPs). First, the population (or objective space) is divided into K subpopulations (or subregions) by a group of uniform distribution reference vectors. Later, subpopulations are optimized simultaneously. In this paper, we propose a new decomposition based evolutionary algorithm with angle penalty selection strategy for MaOPs (MOEA-APS). In the environmental selection process, in order to prevent the solutions located around the boundary of the subregion from being simultaneously selected into the next generation which will affect negatively on the performance of the algorithm, a new angle similarity measure (AS) is calculated and used to punish the dense solutions. More precisely, after selecting a good solution x for a sub population, the solutions whose angle similarity with x exceeding η or pareto dominated by x will be directly punished. Moreover, The threshold η is not fixed, but decided by the distribution of the solutions around x. This mechanism allows to improve diversity of population. The experimental results on DTLZ benchmark test problems show that the results of the proposed algorithm are very competitive comparing with four other state-of-the-art EAs for MaOPs.