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中文摘要：
解集分布广度评价是多目标进化算法性能评价中的重要研究课题.作者提出了一种在未知Pareto最优面情况下解集分布广度评价方法（Spread Indicator,SI）.不同于已存在的评价方法考虑极端个体,该方法利用边界解集对非支配集分布范围进行评价.对非支配集中边界解的性质和特征进行了详细的分析,讨论了边界解与极端解之间的联系和区别,并根据边界解级数区分不同边界解对分布范围的影响,进而利用低维空间超立方体进行分布范围的估计.另外,引入与质心超体积的比较关系,避免了算法因收敛度不同对分布广度评价结果的影响.实验结果表明了该方法的可行性和有效性.
英文摘要：
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.
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