Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem

Consoli, Sergio; Darby‐Dowman, Ken; Mladenović, Nenad; Moreno-Pérez, José A.

doi:10.1016/j.ejor.2008.03.014

“…propose a VNS approach which uses three different neighbourhood types to solve the generalized minimum spanning tree problem. Finally, a VNS is used to solve the minimum labelling spanning tree problem by Consoli et al (2008).…”

Section: Graph Problemsmentioning

confidence: 99%

Variable neighbourhood search: methods and applications

Hansen

¹

,

Mladenović

²

,

Moreno-Pérez

³

2008

4OR

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Variable neighbourhood search (VNS) is a metaheuristic, or a framework for building heuristics, based upon systematic changes of neighbourhoods both in descent phase, to find a local minimum, and in perturbation phase to emerge from the corresponding valley. It was first proposed in 1997 and has since then rapidly developed both in its methods and its applications. In the present paper, these two aspects are thoroughly reviewed and an extensive bibliography is provided. Moreover, one section is devoted to newcomers. It consists of steps for developing a heuristic for any particular problem. Those steps are common to the implementation of other metaheuristics.

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“…A VNS is used in Martins and de Souza (2009) to solve the minimum spanning tree problem with minimum degree constraints in all nodes except the leaves. Finally, VNS is used to solve the minimum labelling spanning tree problem in Consoli et al (2009aConsoli et al ( , 2009b.…”

Section: Graph Problemsmentioning

confidence: 99%

Variable neighbourhood search: methods and applications

Hansen

¹

,

Mladenović

²

,

Moreno-Pérez

³

2009

View full text Add to dashboard Cite

Variable neighbourhood search (VNS) is a metaheuristic, or a framework for building heuristics, based upon systematic changes of neighbourhoods both in descent phase, to find a local minimum, and in perturbation phase to emerge from the corresponding valley. It was first proposed in 1997 and has since then rapidly developed both in its methods and its applications. In the present paper, these two aspects are thoroughly reviewed and an extensive bibliography is provided. Moreover, one section is devoted to newcomers. It consists of steps for developing a heuristic for any particular problem. Those steps are common to the implementation of other metaheuristics.

show abstract

“…The minimum labelling spanning tree (MLST) problem is used where, given a graph with coloured edges, one seeks a spanning tree with the least number of colours (Chang and Leu 1997;Krumke and Wirth 1998). Several heuristics have been proposed in (Cerulli et al 2005;Xiong et al 2006;Consoli et al 2008).…”

Section: The Minimum Labelling Steiner Tree Problemmentioning

confidence: 99%

Discrete Particle Swarm Optimization for the minimum labelling Steiner tree problem

Consoli

¹

,

Moreno-Pérez

²

,

Darby‐Dowman

³

et al. 2009

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Particle Swarm Optimization is an evolutionary method inspired by the social behaviour of individuals inside swarms in nature. Solutions of the problem are modelled as members of the swarm which fly in the solution space. The evolution is obtained from the continuous movement of the particles that constitute the swarm submitted to the effect of the inertia and the attraction of the members who lead the swarm. This work focuses on a recent Discrete Particle Swarm Optimization for combinatorial optimization, called Jumping Particle Swarm Optimization. Its effectiveness is illustrated on the minimum labelling Steiner tree problem: given an undirected labelled connected graph, the aim is to find a spanning tree covering a given subset of nodes, whose edges have the smallest number of distinct labels.

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Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem

Cited by 34 publications

References 17 publications

Variable neighbourhood search: methods and applications

Variable neighbourhood search: methods and applications

Variable neighbourhood search: methods and applications

Discrete Particle Swarm Optimization for the minimum labelling Steiner tree problem

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