On Statistical Analysis of MOEAs with Multiple Performance Indicators
This addresses a methodological gap for researchers in evolutionary computation by improving the statistical analysis of MOEA performance comparisons, though it is incremental as it builds on existing indicators and methods.
The paper tackles the problem of assessing Multi-Objective Evolutionary Algorithms (MOEAs) by proposing a multivariate statistical test and post-hoc procedure to analyze multiple performance indicators jointly, rather than independently, and demonstrates its effectiveness through experimentation on four algorithms, 16 problems, and 6 objective numbers.
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.