Reference point specification in MOEA/D for multi-objective and many-objective problems

Recently a number of evolutionary multi-objective optimization (EMO) algorithms have been proposed using the framework of MOEA/D (multi-objective evolutionary algorithm based on decomposition). Those algorithms are characterized by the use of uniformly distributed normalized weight vectors from which a set of uniformly distributed reference lines is generated. Their basic idea is to search for a Pareto optimal solution along each reference line. While they are different in various aspects such as fitness evaluation, solution assignment to each reference line, and solution replacement, they share the same basic idea (i.e., to search for a Pareto optimal solution along each reference line). The importance of weight vector specification has been emphasized in the literature. However, the specification of a reference point has not been examined in detail whereas it plays an important role as a starting point of all reference lines. The reference point usually consists of the best value of each objective over the examined solutions, which is an approximation of the ideal point. However, this approximation is not good in early generations where the true ideal point may be much better than the best value of each objective over the examined solutions (even if it is very good in later generations). Based on these discussions, we propose a reference point specification method.