论文标题
关于具有多个性能指标的MOEAS的统计分析
On Statistical Analysis of MOEAs with Multiple Performance Indicators
论文作者
论文摘要
当我们广泛测试一组MOEAS并旨在确定其适当的排名时，评估多目标进化算法（MOEAS）的经验性能至关重要。在报告实验数据时，经常应用多个性能指标，例如，世代距离和超量，通常将每个指标上的数据独立于其他指标分析。这种治疗在汇总所有性能指标上的结果时会带来概念上的困难，如果性能指标的边际分布重叠，则可能会发现算法之间的显着差异。因此，在本文中，我们建议进行多元$ \ Mathcal {E} $ - 对性能指标的联合经验分布进行测试以检测数据中的电位差异，然后进行事后过程，以利用线性判别分析来确定算法之间的优势。在四种算法，16个问题和6个不同数量的目标上进行的实验支持了该绩效分析的有效性。
Assessing the empirical performance of Multi-Objective Evolutionary Algorithms (MOEAs) is vital when we extensively test a set of MOEAs and aim to determine a proper ranking thereof. Multiple performance indicators, e.g., the generational distance and the hypervolume, are frequently applied when reporting the experimental data, where typically the data on each indicator is analyzed independently from other indicators. Such a treatment brings conceptual difficulties in aggregating the result on all performance indicators, and it might fail to discover significant differences among algorithms if the marginal distributions of the performance indicator overlap. Therefore, in this paper, we propose to conduct a multivariate $\mathcal{E}$-test on the joint empirical distribution of performance indicators to detect the potential difference in the data, followed by a post-hoc procedure that utilizes the linear discriminative analysis to determine the superiority between algorithms. This performance analysis's effectiveness is supported by an experimentation conducted on four algorithms, 16 problems, and 6 different numbers of objectives.
