On the effect of reference point in MOEA/D for multi-objective optimization

Abstract Multi-objective evolutionary algorithm based on decomposition (MOEA/D) has continuously proven effective for multi-objective optimization. So far, the effect of weight vectors and scalarizing methods in MOEA/D has been intensively studied. However, the reference point which serves as the starting point of reference lines (determined by weight vectors) is yet to be well studied. This study aims to fill in this research gap. Ideally, the ideal point of a multi-objective problem could serve as the reference point, however, since the ideal point is often unknown beforehand, the reference point has to be estimated (or specified). In this study, the effect of the reference point specified in three representative manners, i.e., pessimistic, optimistic and dynamic (from optimistic to pessimistic), is examined on three sets of benchmark problems. Each set of the problems has different degrees of difficulty in convergence and spread. Experimental results show that (i) the reference point implicitly impacts the convergence and spread performance of MOEA/D; (ii) the pessimistic specification emphasizes more of exploiting existing regions and the optimistic specification emphasizes more of exploring new regions; (iii) the dynamic specification can strike a good balance between exploitation and exploration, exhibiting good performance for most of the test problems, and thus, is commended to use for new problems.