Genetic Algorithms with the Crossover-Like Mutation Operator for the k-Means Problem

Kazakovtsev, Lev; Shkaberina, Guzel; Rozhnov, Ivan; Li, Rui; Kazakovtsev, Vladimir

doi:10.1007/978-3-030-58657-7_28

Cited by 4 publications

(3 citation statements)

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“…Greedy agglomerative procedures are widely used as crossover operators in genetic algorithms [46,88,90,110]. In this case, most often, the "parent" solutions are merged completely to obtain an intermediate solution with an excessive number of centers or centroids [46,88], which corresponds to the search in the GREEDY k neighborhood (one of the crossed "parent" solutions acts as the parameter S 2 ), although, other versions of the greedy agglomerative crossover operator are also possible [90,110]. Such algorithms successfully compete with the advanced local search algorithms discussed in this article.…”

Section: Discussionmentioning

confidence: 99%

“…Greedy agglomerative procedures can be used as independent algorithms, as well as being embedded into genetic operators [110] or VNS algorithms [79]. The basic greedy agglomerative procedure for the k-means problem can be described as follows (see Algorithm 2).…”

Section: Agglomerative Approach and Greedyr Neyborhoodsmentioning

confidence: 99%

“…In [79,90,110], the authors embed the BasicGreedy() procedure into three algorithms which differ in r value only. All of these algorithms can be described as follows (see Algorithm 3):…”

Section: Agglomerative Approach and Greedy R Neyborhoodsmentioning

confidence: 99%

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Self-Adjusting Variable Neighborhood Search Algorithm for Near-Optimal k-Means Clustering

Kazakovtsev¹,

Rozhnov²,

Popov³

et al. 2020

Computation

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The k-means problem is one of the most popular models in cluster analysis that minimizes the sum of the squared distances from clustered objects to the sought cluster centers (centroids). The simplicity of its algorithmic implementation encourages researchers to apply it in a variety of engineering and scientific branches. Nevertheless, the problem is proven to be NP-hard which makes exact algorithms inapplicable for large scale problems, and the simplest and most popular algorithms result in very poor values of the squared distances sum. If a problem must be solved within a limited time with the maximum accuracy, which would be difficult to improve using known methods without increasing computational costs, the variable neighborhood search (VNS) algorithms, which search in randomized neighborhoods formed by the application of greedy agglomerative procedures, are competitive. In this article, we investigate the influence of the most important parameter of such neighborhoods on the computational efficiency and propose a new VNS-based algorithm (solver), implemented on the graphics processing unit (GPU), which adjusts this parameter. Benchmarking on data sets composed of up to millions of objects demonstrates the advantage of the new algorithm in comparison with known local search algorithms, within a fixed time, allowing for online computation.

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