Towards improved benchmarking of black-box optimization algorithms using clustering problems

The field of Metaheuristics has produced a large number of algorithms for continuous, black-box optimization. In contrast, there are few standard benchmark problem sets, limiting our ability to gain insight into the empirical performance of these algorithms. Clustering problems have been used many times in the literature to evaluate optimization algorithms. However, much of this work has occurred independently on different problem instances and the various experimental methodologies used have produced results which are frequently incomparable and provide little knowledge regarding the difficulty of the problems used, or any platform for comparing and evaluating the performance of algorithms. This paper discusses sum of squares clustering problems from the optimization viewpoint. Properties of the fitness landscape are analysed and it is proposed that these problems are highly suitable for algorithm benchmarking. A set of 27 problem instances (from 4-D to 40-D), based on three well-known datasets, is specified. Baseline experimental results are presented for the Covariance Matrix Adaptation-Evolution Strategy and several other standard algorithms. A web-repository has also been created for this problem set to facilitate future use for algorithm evaluation and comparison.