• DOI:10.1109/TEVC.2022.3144134
• Corpus ID: 238583811

Recombinator-k-Means: An Evolutionary Algorithm That Exploits k-Means++ for Recombination

@article{Baldassi2019RecombinatorkMeansAE,
  title={Recombinator-k-Means: An Evolutionary Algorithm That Exploits k-Means++ for Recombination},
  author={Carlo Baldassi},
  journal={IEEE Transactions on Evolutionary Computation},
  year={2019},
  volume={26},
  pages={991-1003}
}

• Carlo Baldassi
• Published 1 May 2019
• Computer Science
• IEEE Transactions on Evolutionary Computation

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