New heuristic algorithms for solving the planar p-median problem

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

doi:10.1016/j.cor.2014.05.010

Cited by 57 publications

(48 citation statements)

References 37 publications

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“…The best results to date were obtained by [14]. For recent reviews of solution approaches to the continuous p-median problem the reader is referred to [4,6,13,14].…”

Section: Introductionmentioning

confidence: 98%

“…As an example we use one of the most powerful metaheuristic recently developed in [13,14] known as the COMB heuristic which is readily available to us but any other metaheuristic could also be used for this Table 1: Sensitivity Analysis on the Values of α and θ(ρ = 1 + θ) in FIMP using average results over all values of p θ using (6) ρ = 1 + θ using (7) θ using (6) ρ = 1 + θ using (7) purpose. COMB is a hybrid of a Genetic Algorithm (GA) which is supplemented by an effective variable neighbourhood search (VNS) as a post-optimizer.…”

Section: Hybridization Of Fimp With a Powerful Metaheuristicmentioning

confidence: 99%

“…Further gains may be obtained by using new local searches (e.g., [13]) or variable neighborhood descent within a general variable neighborhood search [23]. The best results to date were obtained by [14]. For recent reviews of solution approaches to the continuous p-median problem the reader is referred to [4,6,13,14].…”

Section: Introductionmentioning

confidence: 99%

“…For more details on this algorithm and other powerful metaheuristics for the p-median problem on the plane, see [13,14].…”

Section: Introductionmentioning

confidence: 99%

“…The leading heuristics to date for solving this problem are based on variable neighborhood search (e.g. see [7,14]). For larger scale problem instances, decomposition strategies are successfully applied [5,30].…”

Section: Introductionmentioning

confidence: 99%

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Incorporating neighborhood reduction for the solution of the planar p-median problem

Drezner

Salhi

2015

Ann Oper Res

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Two efficient neighborhood reduction schemes are proposed for the solution of the p-Median problem on the plane. Their integration into a local search significantly reduces the run time with an insignificant deterioration in the quality of the solution. For completeness this fast local search is also embedded into one of the most powerful metaheuristic algorithms recently developed for this continuous location problem. Excellent results for instances with up to 1060 demand points with various values of p are reported. Eight new best known solutions for ten instances of a large problem with 3,038 demand points and up to 500 facilities are also found.

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“…The best results to date were obtained by [14]. For recent reviews of solution approaches to the continuous p-median problem the reader is referred to [4,6,13,14].…”

Section: Introductionmentioning

confidence: 98%

Section: Hybridization Of Fimp With a Powerful Metaheuristicmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…For more details on this algorithm and other powerful metaheuristics for the p-median problem on the plane, see [13,14].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Incorporating neighborhood reduction for the solution of the planar p-median problem

Drezner

Salhi

2015

Ann Oper Res

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Mixed planar and network single‐facility location problems

2016

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We consider the problem of optimally locating a single facility anywhere in a network to serve both on-network and off-network demands. Off-network demands occur in a Euclidean plane, while on-network demands are restricted to a network embedded in the plane. On-network demand points are serviced using shortest-path distances through links of the network (e.g., on-road travel), whereas demand points located in the plane are serviced using more expensive Euclidean distances. Our base objective minimizes the total weighted distance to all demand points. We develop several extensions to our base model, including: (i) a threshold distance model where if network distance exceeds a given threshold, then service is always provided using Euclidean distance, and (ii) a minimax model that minimizes worst-case distance. We solve our formulations using the "Big Segment Small Segment" global optimization method, in conjunction with bounds tailored for each problem class. Computational experiments demonstrate the effectiveness of our solution procedures. Solution times are very fast (often under one second), making our approach a good candidate for embedding within existing heuristics that solve multi-facility problems by solving a sequence of single-facility problems.

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Studying Solutions of the p-Median Problem for the Location of Public Bike Stations

Cintrano

Chicano

Stützle

et al. 2018

Advances in Artificial Intelligence

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The use of bicycles as a means of transport is becoming more and more popular today, especially in urban areas, to avoid the disadvantages of individual car traffic. In fact, city managers react to this trend and actively promote the use of bicycles by providing a network of bicycles for public use and stations where they can be stored. Establishing such a network involves the task of finding best locations for stations, which is, however, not a trivial task. In this work, we examine models to determine the best location of bike stations so that citizens will travel the shortest distance possible to one of them. Based on real data from the city of Malaga, we formulate our problem as a p-median problem and solve it with a variable neighborhood search algorithm that was automatically configured with irace. We compare the locations proposed by the algorithm with the real ones used currently by the city council. We also study where new locations should be placed if the network grows.

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New heuristic algorithms for solving the planar p-median problem

Abstract: The version in the Kent Academic Repository may differ from the final published version. Users are advised to check http://kar.kent.ac.uk for the status of the paper. Users should always cite the published version of record.

Cited by 57 publications

References 37 publications

Incorporating neighborhood reduction for the solution of the planar p-median problem

Incorporating neighborhood reduction for the solution of the planar p-median problem

Mixed planar and network single‐facility location problems

Studying Solutions of the p-Median Problem for the Location of Public Bike Stations

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