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Solution strategy based on Gaussian mixture models and dispersion reduction for the capacitated centered clustering problem.

ABSTRACT: The Capacitated Centered Clustering Problem (CCCP)-a multi-facility location model-is very important within the logistics and supply chain management fields due to its impact on industrial transportation and distribution. However, solving the CCCP is a challenging task due to its computational complexity. In this work, a strategy based on Gaussian mixture models (GMMs) and dispersion reduction is presented to obtain the most likely locations of facilities for sets of client points considering their distribution patterns. Experiments performed on large CCCP instances, and considering updated best-known solutions, led to estimate the performance of the GMMs approach, termed as Dispersion Reduction GMMs, with a mean error gap smaller than 2.6%. This result is more competitive when compared to Variable Neighborhood Search, Simulated Annealing, Genetic Algorithm and CKMeans and faster to achieve when compared to the best-known solutions obtained by Tabu-Search and Clustering Search.

SUBMITTER: Caballero-Morales SO

PROVIDER: S-EPMC7959615 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:The investigation of genetic clusters in natural populations is an ubiquitous problem in a range of fields relying on the analysis of genetic data, such as molecular ecology, conservation biology and microbiology. Typically, genetic clusters are defined as distinct panmictic populations, or parental groups in the context of hybridisation. Two types of methods have been developed for identifying such clusters: model-based methods, which are usually computer-intensive but yield results which can be interpreted in the light of an explicit population genetic model, and geometric approaches, which are less interpretable but remarkably faster.Here, we introduce snapclust, a fast maximum-likelihood solution to the genetic clustering problem, which allies the advantages of both model-based and geometric approaches. Our method relies on maximising the likelihood of a fixed number of panmictic populations, using a combination of geometric approach and fast likelihood optimisation, using the Expectation-Maximisation (EM) algorithm. It can be used for assigning genotypes to populations and optionally identify various types of hybrids between two parental populations. Several goodness-of-fit statistics can also be used to guide the choice of the retained number of clusters.Using extensive simulations, we show that snapclust performs comparably to current gold standards for genetic clustering as well as hybrid detection, with some advantages for identifying hybrids after several backcrosses, while being orders of magnitude faster than other model-based methods. We also illustrate how snapclust can be used for identifying the optimal number of clusters, and subsequently assign individuals to various hybrid classes simulated from an empirical microsatellite dataset. snapclust is implemented in the package adegenet for the free software R, and is therefore easily integrated into existing pipelines for genetic data analysis. It can be applied to any kind of co-dominant markers, and can easily be extended to more complex models including, for instance, varying ploidy levels. Given its flexibility and computer-efficiency, it provides a useful complement to the existing toolbox for the study of genetic diversity in natural populations.

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Solution strategy based on Gaussian mixture models and dispersion reduction for the capacitated centered clustering problem.

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