A Simple Statistical Test Against Origin-Biased Metaheuristics

One of the strong points of evolutionary algorithms and other similar metaheuristics is their robustness, which means that their performance is consistent across large varieties of problem settings. In particular, such algorithms avoid preferring one solution to another unless the optimized function gives enough reasons for doing that. This property is formally captured as invariance with regards to certain transformations of the search space and the problem definition, such as translation or rotation. The lack of some basic invariance properties in some recently proposed “nature-inspired” algorithms, together with the deliberate misuse of commonly used benchmark functions, can present them as excellent optimizers, which they are not. One particular class of such algorithms, origin-biased metaheuristics, are good at finding an optimum at the origin and are much worse for any other purpose. This paper presents a statistical testing procedure which can help to reveal such algorithms and to illustrate the negative aspects of their behavior. A case study involving 15 different algorithms shows that this test successfully detects most origin-biased algorithms.