The continuous p-median problem (CPMP) is one of the most popular and widely used models in location theory that minimizes the sum of distances from known demand points to the sought points called centers or medians. This NP-hard location problem is also useful for clustering (automatic grouping). In this case, sought points are considered as cluster centers. Unlike similar k-means model, p-median clustering is less sensitive to noisy data and appearance of the outliers (separately located demand points that do not belong to any cluster). Local search algorithms including Variable Neighborhood Search as well as evolutionary algorithms demonstrate rather precise results. Various algorithms based on the use of greedy agglomerative procedures are capable of obtaining very accurate results that are difficult to improve on with other methods. The computational complexity of such procedures limits their use for large problems, although computations on massively parallel systems significantly expand their capabilities. In addition, the efficiency of agglomerative procedures is highly dependent on the setting of their parameters. For the majority of practically important p-median problems, one can choose a very efficient algorithm based on the agglomerative procedures. However, the parameters of such algorithms, which ensure their high efficiency, are difficult to predict. We introduce the concept of the AGGL_r neighborhood based on the application of the agglomerative procedure, and investigate the search efficiency in such a neighborhood depending on its parameter r. Using the similarities between local search algorithms and (1 + 1)-evolutionary algorithms, as well as the ability of the latter to adapt their search parameters, we propose a new algorithm based on a greedy agglomerative procedure with the automatically tuned parameter r. Our new algorithm does not require preliminary tuning of the parameter r of the agglomerative procedure, adjusting this parameter online, thus representing a more versatile computational tool. The advantages of the new algorithm are shown experimentally on problems with a data volume of up to 2,000,000 demand points.

Basic concepts of the “Regional Management Center” of the Krasnoyarsk Territory organization, aimed at continuation of the digital transformation of the activities of the executive authorities and local self-government bodies of the Territory with digital technologies and platform solutions application in the spheres of public administration and public service provision, ensuring qualitative improvement of indicators of socio-economic development of the region, are proposed.

Authors provide a comparative analysis of the results of applying various automatic grouping (clustering) algorithms to a problem of separating homogeneous batches of electrical radio products from a mixed batch. Authors consider opportunities of optimizing the algorithm parameters as well as compilation of ensembles of clustering algorithms. The obtained results demonstrate that the homogeneity analysis of batches of the electronic components installed in real space systems is an actual problem, especially in the case of A high level of integration. Authors substantiate the necessity of centralized acquisition of spacecraft equipment on the principle of equal reliability by creating special production batches manufactured for space industry.

Progress in location theory methods and clustering algorithms is mainly targeted at improving the performance of the algorithms. The most popular clustering models are based on solving the p-median and similar location problems (k-means, k-medoids). In such problems, the algorithm must find several points called cluster centers, centroids, medoids, depending on the specific problem which minimize some function of distances from known objects to the centers. In the the k-medoids problem, the centers (medoids) of the cluster must coincide with one of the clustered objects. The problem is NP-hard, and the efforts of researchers are focused on the development of compromise heuristic algorithms that provide a fairly quick solution with minimal error. In this paper, we propose new algorithms of the Greedy Heuristic Method which use the idea of the Variable Neighborhood Search (VNS) algorithms for solving the k-medoids problem (which is also called the discrete p-median problem). In addition to the known PAM (Partition Around Medoids) algorithm, neighborhoods of a known solution are formed by applying greedy agglomerative heuristic procedures. According to the results of computational experiments, the new search algorithms (Greedy PAM-VNS) give more accurate and stable results (lower average value of the objective function and its standard deviation, smaller spread) in comparison with known algorithms on various data sets.Povzetek: Avtorji predlagajo nove algoritme za reševanje problema lokacije k-medoidov in grozdenja.

The k-means problem is one of the most popular models of cluster analysis. The problem is NP-hard, and modern literature offers many competing heuristic approaches. Sometimes practical problems require obtaining such a result (albeit notExact), within the framework of the k-means model, which would be difficult to improve by known methods without a significant increase in the computation time or computational resources. In such cases, genetic algorithms with greedy agglomerative heuristic crossover operator might be a good choice. However, their computational complexity makes it difficult to use them for large-scale problems. The crossover operator which includes the k-means procedure, taking the absolute majority of the computation time, is essential for such algorithms, and other genetic operators such as mutation are usually eliminated or simplified. The importance of maintaining the population diversity, in particular, with the use of a mutation operator, is more significant with an increase in the data volume and available computing resources such as graphical processing units (GPUs). In this article, we propose a new greedy heuristic mutation operator for such algorithms and investigate the influence of new and well-known mutation operators on the objective function value achieved by the genetic algorithms for large-scale k-means problems. Our computational experiments demonstrate the ability of the new mutation operator, as well as the mechanism for organizing subpopulations, to improve the result of the algorithm.

We propose new algorithms of Greedy Heuristic Method for solving the classical problem of cluster analysis, k-Means, which allows us to obtain results with better objective function values in comparison with known algorithms such as k-Means and j-Means. Their comparative efficiency is proved by experiment on various data sets including multidimensional data of non-destructive rejection tests of electronic components for the space industry.