BBOB Instance Analysis: Landscape Properties and Algorithm Performance Across Problem Instances

Fu Xing Long, Diederick Vermetten, Bas van Stein, Anna V. Kononova

Abstract: Benchmarking is a key aspect of research into optimization algorithms, and as such the way in which the most popular benchmark suites are designed implicitly guides some parts of algorithm design. One of these suites is the black-box optimization benchmarking (BBOB) suite of 24 single-objective noiseless functions, which has been a standard for over a decade. Within this problem suite, different instances of a single problem can be created, which is beneficial for testing the stability and invariance of algorithms under transformations. In this paper, we investigate the BBOB instance creation protocol by considering a set of 500 instances for each BBOB problem. Using exploratory landscape analysis, we show that the distribution of landscape features across BBOB instances is highly diverse for a large set of problems. In addition, by running a set of eight algorithms across these 500 instances, we demonstrate that statistically significant differences in performances can be observed, e.g., in CMA-ES, even though it is expected to be invariant to the translations used to create these instances. We argue that, while the transformations applied in BBOB instances do indeed seem to preserve the high-level properties of the functions, their difference in practice should not be overlooked, particularly when treating the problems as box-constrained instead of unconstrained.