Recombinator-<i>k</i>-Means: An Evolutionary Algorithm That Exploits <i>k</i>-Means++ for Recombination

We introduce an evolutionary algorithm called recombinator-$k$-means for optimizing the highly non-convex kmeans problem. Its defining feature is that its crossover step involves all members of current generation, stochastically recombining them with a repurposed variant $k$-means++ seeding algorithm. The recombination also uses reweighting mechanism realizes progressively sharper stochastic selection policy and ensures population eventually coalesces into single solution. compare this scheme state-of-the-art alternative, more standard genetic deterministic pairwise-nearest-neighbor elitist policy, which we provide augmented efficient implementation. Extensive tests on large challenging datasets (both synthetic real-word) show fixed sizes generally superior in terms optimization objective, at cost expensive step. When adjusting two algorithms to match their running times, find short times (augmented) method always superior, while longer will it and, most difficult examples, take over. conclude reweighted whole-population costly, but better escaping local minima. Moreover, algorithmically simpler general (it could be applied even $k$-medians or $k$-medoids, example). Our implementations are publicly available \href{https://github.com/carlobaldassi/RecombinatorKMeans.jl}{https://github.com/carlobaldassi/RecombinatorKMeans.jl}.