An Indicator for Assessing the Spread of Solutions in Multi-Objective Evolutionary Algorithm

Abstract

Spread assessment of Pareto set approximations is an important issue in evaluating the performance of multi-objective evolutionary algorithms(MOEAs).This paper proposes a boundary solution set based spread indicator(SI) without the information of the Pareto optimal front.Unlike the existed indicators which only consider extreme solutions,SI estimates the distribution range of nondominated sets by employing boundary solutions.Specifically,this paper gives a detailed investigation of the characteristics and properties of the boundary solution set and discussed the relations and differences between boundary solutions and extreme solutions.Moreover,SI made a distinction of influence on distribution range of different boundary solutions according to their classes and further evaluated the spread of boundary solutions by using hypervolume in low-dimensional space.Additionally,to avoid the impact of different convergence results,SI introduced the centroid of the considered solution sets.From a comparative study on several test problems,SI is found to be available and effective in assessing the spread of MOEAs.