多绩效指标MOEA的统计分析
On Statistical Analysis of MOEAs with Multiple Performance Indicators
摘要：
当我们广泛地测试一组多目标进化算法并旨在确定其适当的排名时，评估多目标进化算法（MOEAs）的经验性能是至关重要的。多个性能指标，例如，在报告实验数据时，经常采用代间距离和超体积，通常对每一指标的数据进行独立于其他指标的分析。这种处理方法在汇总所有性能指标的结果时带来了概念上的困难，并且如果性能指标的边缘分布重叠，则可能无法发现算法之间的显著差异。因此，在本文中，我们建议进行多变量$\mathcal{E}$ -测试的联合经验分布的性能指标，以检测潜在的差异的数据，随后由事后程序，利用线性判别分析，以确定算法之间的优越性。这种性能分析的有效性是由四个算法，16个问题，和6个不同数量的目标进行的实验支持。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
