Large neighborhood local search for the p-median problem

Kochetov, Yury; Levanova, Tatyana; Алексеева, Е. А.; Loresh, Maxim

doi:10.2298/yjor0501053k

Cited by 38 publications

(13 citation statements)

References 9 publications

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“…The interchange neighborhood appears to be a better choice than the alternate, or drop/add. The variable depth neighborhood structure LK(k) (Kochetov and Alekseeva, 2005) seems to be a better choice than the 1-interchange. (ii) The implementation of 1-interchange local search is the second very important issue.…”

Section: Discussionmentioning

confidence: 99%

The p-median problem: A survey of metaheuristic approaches

Mladenović

Brimberg

Hansen

et al. 2007

European Journal of Operational Research

361

182

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Abstract. The p-median problem, like most location problems, is classified as N P -hard, and so, heuristic methods are usually used for solving it. The pmedian problem is a basic discrete location problem with real application that have been widely used to test heuristics. Metaheuristics are frameworks for building heuristics. In this survey, we examine the p-median, with the aim of providing an overview on advances in solving it using recent procedures based on metaheuristic rules.

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Section: Discussionmentioning

confidence: 99%

The p-median problem: A survey of metaheuristic approaches

Mladenović

Brimberg

Hansen

et al. 2007

European Journal of Operational Research

361

182

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“…As for more general k-median problem, its NPhardness was proved [8], and approximation algorithms have been proposed [1], [9], [12].…”

Section: Copyright Cmentioning

confidence: 99%

An Efficient Approximate Algorithm for the 1-Median Problem on a Graph

Tabata

Nakamura

Kudo

2017

IEICE Trans. Inf. & Syst.

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SUMMARYWe propose a heuristic approximation algorithm for the 1-median problem. The 1-median problem is the problem of finding a vertex with the highest closeness centrality. Starting from a randomly selected vertex, our algorithm repeats to find a vertex with higher closeness centrality by approximately calculating closeness centrality of each vertex using simpler spanning subgraphs, which are called k-neighbor dense shortest path graphs with shortcuts. According to our experimental results using real networks with more than 10,000 vertices, our algorithm is more than 100 times faster than the exhaustive search and more than 20 times faster than the state-of-the-art approximation algorithm using annotated information to the vertices while the solutions output by our algorithm have higher approximation ratio.

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“…First, it is a classic NP-hard problem (Kariv and Hakimi, 1979) from the location theory with wide applications ranging from industry to data mining. Second, for the p-median problem, there exist various metaheuristics from which the LLHs can be extracted, such as VNS (Hansen and Mladenović, 1997), ACO (Kochetov et al, 2005), and GA (Correa et al, 2001). In addition, there are several parameterized LLHs for the p-median problem, which makes it suitable as the test problem.…”

Section: Preliminariesmentioning

confidence: 99%

“…Traversing an LK(k) neighborhood involves k swaps, which is k times that of interchange. From the implementation aspect, since the interchange neighborhood is a subset of an LK(k) neighborhood (Kochetov et al, 2005), LK(k) can benefit from the trade-off as in Resende and Werneck (2003). Thus, an implementation based on Resende and Werneck (2003) is adopted.…”

Section: Lk(k)mentioning

confidence: 99%

Hyper-Heuristics with Low Level Parameter Adaptation

Zhang

Jiang

Xuan

et al. 2012

Evolutionary Computation

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Recent years have witnessed the great success of hyper-heuristics applying to numerous real-world applications. Hyper-heuristics raise the generality of search methodologies by manipulating a set of low level heuristics (LLHs) to solve problems, and aim to automate the algorithm design process. However, those LLHs are usually parameterized, which may contradict the domain independent motivation of hyper-heuristics. In this paper, we show how to automatically maintain low level parameters (LLPs) using a hyper-heuristic with LLP adaptation (AD-HH), and exemplify the feasibility of AD-HH by adaptively maintaining the LLPs for two hyper-heuristic models. Furthermore, aiming at tackling the search space expansion due to the LLP adaptation, we apply a heuristic space reduction (SAR) mechanism to improve the AD-HH framework. The integration of the LLP adaptation and the SAR mechanism is able to explore the heuristic space more effectively and efficiently. To evaluate the performance of the proposed algorithms, we choose the p-median problem as a case study. The empirical results show that with the adaptation of the LLPs and the SAR mechanism, the proposed algorithms are able to achieve competitive results over the three heterogeneous classes of benchmark instances.

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Large neighborhood local search for the p-median problem

Cited by 38 publications

References 9 publications

The p-median problem: A survey of metaheuristic approaches

The p-median problem: A survey of metaheuristic approaches

An Efficient Approximate Algorithm for the 1-Median Problem on a Graph

Hyper-Heuristics with Low Level Parameter Adaptation

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