A Standardized Benchmark Set of Clustering Problem Instances for Comparing Black-Box Optimizers

One key challenge in optimization is the selection of a suitable set of benchmark problems. A common goal is to find functions which are representative of a class of real-world optimization problems in order to ensure findings on the benchmarks will translate to relevant problem domains. While some problem characteristics are well-covered by popular benchmarking suites, others are often overlooked. One example of such a problem characteristic is permutation invariance, where the search space consists of a set of symmetrical search regions. This type of problem occurs e.g. when a set of solutions has to be found, but the ordering within this set does not matter. The data clustering problem, often seen in machine learning contexts, is a clear example of such an optimization landscape, and has thus been proposed as a base from which optimization benchmarks can be created. In addition to the symmetry aspect, these clustering problems also contain potential regions of neutrality, which can provide an additional challenge to optimization algorithms. In this paper, we present a standardized benchmark suite for the evaluation of continuous black-box optimization algorithms, based on data clustering problems. To gain insight into the diversity of the benchmark set, both internally and in comparison to existing suites, we perform a benchmarking study of a set of modular CMA-ES configurations, as well as an analysis using exploratory landscape analysis. Our benchmark set is open-source and integrated with the IOHprofiler benchmarking framework to encourage its use in future research.