Bayesian performance analysis for black-box optimization benchmarking

The most commonly used statistics in Evolutionary Computation (EC) are of the Wilcoxon-Mann-Whitney-test type, in its either paired or non-paired version. However, using such statistics for drawing performance comparisons has several known drawbacks. At the same time, Bayesian inference for performance analysis is an emerging statistical tool, which has the potential to become a promising complement to the statistical perspectives offered by the aforementioned p-value type test. This work exhibits the practical use of Bayesian inference in a typical EC setting, where several algorithms are to be compared with respect to various performance indicators. Explicitly we examine performance data of 11 evolutionary algorithms (EAs) over a set of 23 discrete optimization problems in several dimensions. Using this data, and following a brief introduction to the relevant Bayesian inference practice, we demonstrate how to draw the algorithms' probabilities of winning. Apart from fixed-target and fixed-budget results for the individual problems, we also provide an illustrative example per groups of problems. We elaborate on the computational steps, explain the associated uncertainties, and articulate considerations such as the prior distribution and the sample sizing. We also present as a reference the classical p-value tests.