A region division based decomposition approach for evolutionary many-objective optimization

摘要

A region division based decomposition approach for evolutionary many-objective optimization (denoted as RD-EMO) is proposed in this paper. In the proposed RD-EMO, a set of reference points are generated and the objective space is divided into a set of regions through angle bisectors between adjacent reference lines. Then two attributions of regions are defined, which are region degree and region sparse rate, respectively. Region attributions based select operator is designed to choose solutions in sparse regions of objective space as mating solutions so that new solutions created by mating solutions can be located in sparser regions. In addition, region sparse rate is also applied to the population update process so that solutions in sparse regions of objective space are reserved and those in dense regions are discarded. Hence, two attributions of regions can better guarantee population diversity. Moreover, those solutions with better scalar function values are reserved in the same intensity regions so that population convergence is also guaranteed. In the study of the performance of the proposed algorithm, the performance comparison of RD-EMO with some state-of-the-art algorithms including NSGA-III, MOEA/D-PBI, MOEA/DD, RVEA and MOEA/D-M2M in solving a set of well-known multi-objective optimization problems (MOPs) having 3 to 15 objectives shows that the proposed RD-EMO is superior in converging to approximate Pareto Front (PF) with a standout distribution. We also apply it to solve nine many-objective 0/1 knapsack problems (MKPs), with a good performance obtained.