  Minimum sum-of-squares clustering (MSSC) is a widely used clustering model,
of which the popular K-means algorithm constitutes a local minimizer. It is
well known that the solutions of K-means can be arbitrarily distant from the
true MSSC global optimum, and dozens of alternative heuristics have been
proposed for this problem. However, no other algorithm has been predominantly
adopted in the literature. This may be related to differences of computational
effort, or to the assumption that a near-optimal solution of the MSSC has only
a marginal impact on clustering validity. In this article, we dispute this
belief. We introduce an efficient population-based metaheuristic that uses
K-means as a local search in combination with problem-tailored crossover,
mutation, and diversification operators. This algorithm can be interpreted as a
multi-start K-means, in which the initial center positions are carefully
sampled based on the search history. The approach is scalable and accurate,
outperforming all recent state-of-the-art algorithms for MSSC in terms of
solution quality, measured by the depth of local minima. This enhanced accuracy
leads to clusters which are significantly closer to the ground truth than those
of other algorithms, for overlapping Gaussian-mixture datasets with a large
number of features. Therefore, improved global optimization methods appear to
be essential to better exploit the MSSC model in high dimension.
