Decomposition-based evolutionary algorithms have been quite successful in dealing with multi-objective optimization problems. Recently, more and more researchers attempt to apply the decomposition approach to solve many-objective optimization problems. A many-objective evolutionary algorithm based on decomposition with correlative selection mechanism (MOEA/D-CSM) is also proposed to solve many-objective optimization problems in this paper. Since MOEA/D-SCM is based on a decomposition approach which adopts penalty boundary intersection (PBI), a set of reference points must be generated in advance. Thus, a new concept related to the set of reference points is introduced first, namely, the correlation between an individual and a reference point. Thereafter, a new selection mechanism based on the correlation is designed and called correlative selection mechanism. The correlative selection mechanism finds their correlative individuals for each reference point as soon as possible so that the diversity among population members is maintained. However, when a reference point has two or more correlative individuals, those worse correlative individuals may be removed from a population so that the solutions can be ensured to move towards the Pareto-optimal front. In a comprehensive experimental study, we apply MOEA/D-CSM to a number of many-objective test problems with 3 to 15 objec-tives and make a comparison with three state-of-the-art many-objective evolutionary algorithms, namely, NSGA-III, MOEA/D and RVEA. Experimental results show that the proposed MOEA/D-CSM can produce competitive results on most of the problems considered in this study.
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