Abstract
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 resevanje problema lokacije k-medoidov in grozdenja.
Highlights
The rapid development of artificial intelligence systems using, inter alia, methods of automatic data grouping and methods of location theory, as well as increasing requirements for economic efficiency in all branches, creates a request for the creation of new algorithms with higher requirements for accuracy of the result.The attempts to discover a universal and, at the same time, exact method for solving most popular location and clustering problems (k-means, k-medoids, etc.), which guarantees the global optimum of the objective function, in the case of a large amount of input data has been recognized as unpromising
We propose the use of local search algorithms that contain greedy agglomerative heuristic procedures, as well as the well-known PAM algorithm, using an idea of the Variable Neighborhood Search (VNS) [20]
A popular idea in solving continuous clustering problems is the use of genetic algorithms (GA) and other evolutionary approaches to improve the results of local search [29,30,31]
Summary
The rapid development of artificial intelligence systems using, inter alia, methods of automatic data grouping (clustering) and methods of location theory, as well as increasing requirements for economic efficiency in all branches, creates a request for the creation of new algorithms with higher requirements for accuracy of the result. The attempts to discover a universal and, at the same time, exact method for solving most popular location and clustering problems (k-means, k-medoids, etc.), which guarantees the global optimum of the objective function, in the case of a large amount of input data has been recognized as unpromising. Vectors A1,...,AN are data vectors in a d-dimensional space, Ai=(ai,1,...,ai,d), Ai ∈ Rd Ai Rd. In the k-medoids model and problem, cluster centers Xj=(xj,1,...,xj,k) called medoids, are searched among the known points Ai, and this is a discrete optimization problem. We propose the use of local search algorithms that contain greedy agglomerative heuristic procedures, as well as the well-known PAM algorithm, using an idea of the Variable Neighborhood Search (VNS) [20]. It is shown that new VNS algorithms have advantages over the standard PAM algorithm and are competitive in comparison with the known genetic algorithms of the Greedy Heuristics Method for the considered problem [21]
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