An improved reference point sampling method on Pareto optimal front

Cheng He, Linqiang Pan, Hang Xu, Ye Tian, Xingyi Zhang

Abstract: In this paper, we propose a sampling approach of reference points used for performance metrics of multi-objective evolutionary algorithms. Traditional reference point sampling methods, such as the Das and Dennis method, usually sample the reference points via a set of uniformly distributed weight vectors generated on an ideal hyper-plane in objective space, which however often ignore the geometric shape of a specific Pareto front. Therefore, we propose a novel reference point sampling approach by taking the specific shape of the Pareto optimal front to be tackled into account for measuring the performance of multi-objective evolutionary algorithms. The performance of the proposed reference point sampling method against the other two state-of-the-art sampling methods is tested on six test instances in various conditions, which clearly demonstrate the effectiveness and superiority of the proposed sampling method.