On Statistical Analysis of MOEAs with Multiple Performance Indicators

TL;DR

This paper introduces a multivariate statistical testing approach for evaluating MOEAs using multiple performance indicators simultaneously, improving the detection of significant differences among algorithms.

Contribution

It proposes a multivariate $ ext{E}$-test combined with linear discriminative analysis for more comprehensive performance evaluation of MOEAs.

Findings

The method effectively detects differences in algorithm performance.

It provides a more integrated analysis of multiple indicators.

Experimental results validate the approach across various algorithms and problems.

Abstract

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.