Solving the planar p-median problem by variable neighborhood and concentric searches

Drezner, Zvi; Brimberg, Jack; Mladenović, Nenad; Salhi, Saı̈d

doi:10.1007/s10898-014-0183-1

Cited by 13 publications

(5 citation statements)

References 29 publications

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“…Many authors have considered various approaches to solving p-median problems [4,16]. Fo continuous problems, Brimberg, Drezner, Mladenovic [17,18] presented various local search algorithms, including Variable Neighborhood Search (VNS) algorithms. Reducing the amount of data [19] by randomly (or deterministically) selecting only a part of the original data set and using a result obtained with these sample data as an initial solution for the complete data [14] is also rather efficient.…”

Section: Known Approachesmentioning

confidence: 99%

“…Local search algorithms and algorithmic combinations of the randomized and local search algorithms are investigated in many works. VNS algorithms [17] or agglomerative algorithms, as well as their combinations [21], often perform well. There are also widely presented initialization, including random filling and point distribution estimation [22].…”

Section: Known Approachesmentioning

confidence: 99%

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Hybrid algorithms with alternative embedded local search schemes for the p-median problem

Rezova,

Kazakovtsev,

Rozhnov

et al. 2023

IJITS JOURNAL

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Progress in the development of location theory and clustering methods is mainly aimed at improving the performance of algorithms. We study the continuous p-median problem with the Euclidean metric. Various algorithmic combinations of the ALA procedure embedded into more sophisticated algorithmic combinations are used. Two repeated steps of the ALA algorithm solve the simplest discrete optimization problem, and then a series of central point search problems (Weber problem) for each cluster. A parallel implementation of the ALA algorithm is used. The paper studies the issue of choosing from two strategies: solve the Weber problem until accuracy ε is achieved at each iteration, or perform only one iteration of the Weiszfeld algorithm at each ALA iteration.

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Section: Known Approachesmentioning

confidence: 99%

Section: Known Approachesmentioning

confidence: 99%

Hybrid algorithms with alternative embedded local search schemes for the p-median problem

Rezova,

Kazakovtsev,

Rozhnov

et al. 2023

IJITS JOURNAL

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“…In [14], Drezner et al proposed four heuristic procedures to solve p-median problem: two versions of variable neighborhood search, a genetic algorithm, and a combination of both. In [15], Drezner et al proposed two new approaches to solve the p-median problem; the fust is a variable neighborhood search and the second one is a concentric search. All these researches conducted an extensive empirical experiment on four well-known datasets.…”

Section: The P-median Loca Non Problemmentioning

confidence: 99%

Particle Swarm Optimization algorithm for the continuous p-median location problems

Rabie

El-Khodary

Tharwat

2014

2014 10th International Computer Engineering Conference (ICENCO)

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A Particle Swarm Optimization (PSO) algorithm is proposed for the solution of large-scale continuous p-median location problems in plane. A PSO algorithm previously developed for the solution of the continuous p-center has been extended to solve the p-median location problem. The p-median location problem seeks to locate p facilities in plane so that the sum of Euclidean distances from p medians to a set of n demand points is minimized. The p-median problem is proven to be NP hard.In this paper, we introduce a new PSO algorithm for large scale p-median location problems. Computational results show that the proposed PSO algorithm is able to find good feasible solutions for instances from TSP library with demand points up to 9,976 and medians (P) up to 75. Our proposed PSO algorithm outperformed one of the most recent aggregation methods, which has been developed to solve large-scale p-median.

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“…In [18][19][20], the authors reviewed various heuristic solution techniques for k-means and p-median problems. In [21][22][23], the authors presented local search approaches including the Variable Neighborhood Search (VNS) and concentric search. In [22], Drezner et al proposed heuristic procedures including the genetic algorithm (GA), for rather small datasets.…”

Section: Introductionmentioning

confidence: 99%

“…Local search algorithms and their randomized versions are widely presented. For instance, Variable Neighborhood Search (VNS) algorithms [23,31,32] or agglomerative algorithms [33,34] sometimes show good results. A large number of articles are devoted to the initialization procedures for local search algorithms, such as random seeding and estimating the distribution of the data vectors [30].…”

Section: Introductionmentioning

confidence: 99%

K-Means Genetic Algorithms with Greedy Genetic Operators

Kazakovtsev

Rozhnov

Shkaberina

et al. 2020

Mathematical Problems in Engineering

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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.

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Solving the planar p-median problem by variable neighborhood and concentric searches

Cited by 13 publications

References 29 publications

Hybrid algorithms with alternative embedded local search schemes for the p-median problem

Hybrid algorithms with alternative embedded local search schemes for the p-median problem

Particle Swarm Optimization algorithm for the continuous p-median location problems

K-Means Genetic Algorithms with Greedy Genetic Operators

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