A tree search algorithm for the p-median problem

Christofides, Nicos; Beasley, John E.

doi:10.1016/0377-2217(82)90160-6

Cited by 102 publications

(38 citation statements)

References 13 publications

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“…Kariv and Hakimi [21] proved that the PMP is N P-hard. Optimization algorithms based on Lagrangean relaxation have been proposed by Narula et al [33], Cornuéjols et al [11], Christofides and Beasley [9] and Beasley [4]; approaches based on dual formulations are illustrated in Galvao [15] and Hanjoul and Peeters [18]. Among the most recent contributions we cite the branch-and-cut-and-price algorithm by Avella et al [2], the branch-and-price algorithm by Senne et al [41] and the semi-Lagrangean relaxation algorithm by Beltran et al [5].…”

Section: Cardinality Constraintsmentioning

confidence: 99%

A computational evaluation of a general branch-and-price framework for capacitated network location problems

2008

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The purpose of this paper is to illustrate a general framework for network location problems, based on column generation and branch-andprice. In particular we consider capacitated network location problems with single-source constraints. We consider several different network location models, by combining cardinality constraints, fixed set-up costs, concentrator restrictions and regional constraints. Our general branchand-price-based approach can be seen as a natural counterpart of the branch-and-cut-based commercial ILP solvers, with the advantage of exploiting the tightness of the lower bound provided by the set partitioning reformulation of network location problems. Branch-and-price and branch-and-cut are compared through an extensive set of experimental tests.

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Section: Cardinality Constraintsmentioning

confidence: 99%

A computational evaluation of a general branch-and-price framework for capacitated network location problems

2008

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“…A number of non-genetic algorithms have been developed to address the location allocation / p-median problem -see for example Teitz andBart (1968), Christofides andBeasley (1982), or Reese (2006) for a comprehensive overview. However, in practice these methods proved prone to finding 'local' optima (where the algorithm failed to converge on the global optimum arrangement) or to require very long running times.…”

Section: Algorithm Developmentmentioning

confidence: 99%

A modified grouping genetic algorithm to select ambulance site locations

Comber

Sasaki

Sano

et al. 2011

International Journal of Geographical Information Science

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This paper describes the development and application of a modified Grouping Genetic Algorithm (GGA) used to identify sets of optimal ambulance locations. The GGA was modified to consider a special case with only two groups, and the reproduction and mutation schemes were modified to operate more efficiently. It was applied to a case study locating ambulances from a fixed set of alternative locations. The sites were evaluated using data of emergency medical services (EMS) calls summarised over census areas and weighted by network distance. Census areas serviced by the same selected location defined ambulance catchments. The results indicated alternative sites for ambulances to be located, with average EMS response times improved by 1 minute 14 seconds and showed the impacts of having different numbers of ambulances in current locations and in new locations. The algorithmic developments associated with the modified GGA and the advantages of using census areas as spatial units to summarise data are discussed.

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“…The technique of determining a solution with a prespecified number of established facilities (i. e. solving a "/?-median" problem) by varying the fixed costs of UFLPs has been proposed several times in literature [3,6,11,15,17]. To obtain a certain p value, two papers [11,17] independently suggested a scheme for updating y.…”

Section: Solution Approachmentioning

confidence: 99%

“…• If this région does not contain values of co, we will fmd oe(#(y)), a?^q(y)èb, cm t^e line Connecting oe(a) and G) (6). Such a resuit proves that no further co(/>), a<p<b, can be determined by solving an UFLP.…”

Section: Solution Approachmentioning

confidence: 99%

Discrete facility location with nonlinear facility costs

Körkel¹

1991

RAIRO-Oper. Res.

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A tree search algorithm for the p-median problem

Cited by 102 publications

References 13 publications

A computational evaluation of a general branch-and-price framework for capacitated network location problems

A computational evaluation of a general branch-and-price framework for capacitated network location problems

A modified grouping genetic algorithm to select ambulance site locations

Discrete facility location with nonlinear facility costs

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