A decomposition-based multi-objective optimization approach considering multiple preferences with robust performance

In this paper, we propose a decomposition-based multi-objective optimization approach considering multiple preferences, expressed by means of reference points, and with robust performance (mprMOEA/D). This algorithm is able to find multiple preferred regions in a single run, and its performance is robust with respect to different problems. The proposed algorithm utilizes a subpopulation (SP) for each reference point to search for the corresponding preferred region. An external population (EP) is maintained to selectively preserve solutions from all the SPs, and it can be revisited when producing new solution for each SP. The proposed collaboration mechanism between the SPs and EP is helpful in convergence and diversity preserving. In order to obtain robust performance, local crossover coordinate systems, which coincide with the local manifold of the Pareto set, are introduced into mprMOEA/D for the crossover operator of differential evolution, alleviating the influence of the overall Pareto set shape. The effects of these adopted techniques on the proposed algorithm are discussed, and the robust performance of the proposed approach is validated using numerical functions in comparison with four existing approaches. Experimental results show that the proposed algorithm outperforms the other algorithms.