论文标题
在三维目标空间中使用近似最佳分布对质量指标的分析
An Analysis of Quality Indicators Using Approximated Optimal Distributions in a Three-dimensional Objective Space
论文作者
论文摘要
尽管质量指标在基准测试进化多目标优化算法中起着至关重要的作用，但它们的性质仍然不清楚。理解质量指标的一种有希望的方法是使用优化每个质量指标的客观向量的最佳分布。但是，很难获得每个质量指标的最佳分布，尤其是当其理论属性未知时。因此，大多数质量指标的最佳分布尚未得到很好的研究。为了解决这些问题，首先，我们提出了一个问题表述，以在任意帕累托阵线上找到每个质量指标的最佳分布。然后，我们使用拟议的问题制定概述了九个质量指标的最佳分布。我们使用其近似的最佳分布在八种类型的三个目标问题的帕累托阵线上分析了九种质量指标。我们的分析表明，在许多情况下，整个帕累托前沿中均匀分布的目标向量并不是最佳的。每个质量指标都有自己的每个帕累托阵线的最佳分布。我们还检查了九个质量指标之间的一致性。
Although quality indicators play a crucial role in benchmarking evolutionary multi-objective optimization algorithms, their properties are still unclear. One promising approach for understanding quality indicators is the use of the optimal distribution of objective vectors that optimizes each quality indicator. However, it is difficult to obtain the optimal distribution for each quality indicator, especially when its theoretical property is unknown. Thus, optimal distributions for most quality indicators have not been well investigated. To address these issues, first, we propose a problem formulation of finding the optimal distribution for each quality indicator on an arbitrary Pareto front. Then, we approximate the optimal distributions for nine quality indicators using the proposed problem formulation. We analyze the nine quality indicators using their approximated optimal distributions on eight types of Pareto fronts of three-objective problems. Our analysis demonstrates that uniformly-distributed objective vectors over the entire Pareto front are not optimal in many cases. Each quality indicator has its own optimal distribution for each Pareto front. We also examine the consistency among the nine quality indicators.
