Modeling and solving the rooted distance-constrained minimum spanning tree problem

Gouveia, Luís; Paias, Ana; Sharma, Dushyant

doi:10.1016/j.cor.2006.03.022

Cited by 41 publications

(37 citation statements)

References 8 publications

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“…Let H be the pre-defined maximum number of arcs in any path connecting the source vertex to any other vertex. Several formulations have been provided by Gouveia and his co-authors, see (Gouveia and Requejo, 2001;Gouveia et al, 2008) and the references therein.…”

Section: Problem Descriptionmentioning

confidence: 99%

A Multi-Population Genetic Algorithm for Tree-Shaped Network Design Problems

Fontes

Gonçalves

2009

Proceedings of the International Joint Conference on Computational Intelligence

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Abstract:In this work we propose a multi-population genetic algorithm for tree-shaped network design problems using random keys. Recent literature on finding optimal spanning trees suggests the use of genetic algorithms. Furthermore, random keys encoding has been proved efficient at dealing with problems where the relative order of tasks is important. Here we propose to use random keys for encoding trees. The topology of these trees is restricted, since no path from the root vertex to any other vertex may have more than a pre-defined number of arcs. In addition, the problems under consideration also exhibit the characteristic of flows. Therefore, we want to find a minimum cost tree satisfying all demand vertices and the pre-defined number of arcs. The contributions of this paper are twofold: on one hand we address a new problem, which is an extension of the well known NP-hard hop-constrained MST problem since we also consider determining arc flows such that vertices requirements are met at minimum cost and the cost functions considered include a fixed cost component and a nonlinear flow routing component; on the other hand, we propose a new genetic algorithm to efficiently find solutions to this problem.

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Section: Problem Descriptionmentioning

confidence: 99%

A Multi-Population Genetic Algorithm for Tree-Shaped Network Design Problems

Fontes

Gonçalves

2009

Proceedings of the International Joint Conference on Computational Intelligence

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“…11 Different formulation of the DCMST has been found in the literature. 8,11,12 These formulations implicitly use a property of feasible diameter constrained spanning tree, pointed out by Handler. 13 He pointed out that, when D is even, a central vertex i ∈ V must exist in a feasible tree T , such that no other vertex of T is more than D/2 edges away from i and when D is odd, a central edge e = (i, j) ∈ E must exist in T , such that no vertex of T is more than (D − 1)/2 edges away from the closest extremity of (i, j).…”

Section: Introductionmentioning

confidence: 99%

“…7 Gouvieta and Magnanti 8 have modeled the problem as a network design to set up communication between every pair of vertices, meeting or surpassing a given quality requirement. This problem has also been applied to data compression by Bookstien and Klien, 9 and distributed mutual exclusion in parallel computing by Raymond, 10 and Deo and Abdalla.…”

Section: Introductionmentioning

confidence: 99%

Diameter Constrained Fuzzy Minimum Spanning Tree Problem

Nayeem

Pal

2013

IJCIS

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In this paper, we have studied the constrained version of the fuzzy minimum spanning tree problem. Costs of all the edges are considered as fuzzy numbers. Using the m λ measure, a generalization of credibility measure, the problem is formulated as chance-constrained programming problem and dependent-chance programming problem according to different decision criteria. Then the crisp equivalents are derived when the fuzzy costs are characterized by trapezoidal fuzzy numbers. Furthermore, a fuzzy simulation based hybrid genetic algorithm is designed to solve the proposed models using Prüfer like code representation of labeled trees.

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“…Computational results with a branch-and-cut algorithm show that the proposed method is significantly better than previously known methods. Gouveia et al (2008) study a distance-constrained version of the HMST problem where edges have different transmission delays and the bound p on the number of hops is replaced by a bound on the sum of edge delays along any path from the root node. The authors present a column generation scheme, a Lagrangian relaxation procedure combined with subgradient optimization, and a shortest path (compact) reformulation which views the underlying subproblem as defined on an extended layered graph.…”

Section: Introductionmentioning

confidence: 99%

New formulations of the Hop-Constrained Minimum Spanning Tree problem via Miller–Tucker–Zemlin constraints

Akgün

Tansel

2011

European Journal of Operational Research

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a b s t r a c tGiven an undirected network with positive edge costs and a natural number p, the Hop-Constrained Minimum Spanning Tree problem (HMST) is the problem of finding a spanning tree with minimum total cost such that each path starting from a specified root node has no more than p hops (edges). In this paper, we develop new formulations for HMST. The formulations are based on Miller-Tucker-Zemlin (MTZ) subtour elimination constraints, MTZ-based liftings in the literature offered for HMST, and a new set of topologyenforcing constraints. We also compare the proposed models with the MTZ-based models in the literature with respect to linear programming relaxation bounds and solution times. The results indicate that the new models give considerably better bounds and solution times than their counterparts in the literature and that the new set of constraints is competitive with liftings to MTZ constraints, some of which are based on well-known, strong liftings of Desrochers and Laporte (1991).

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Modeling and solving the rooted distance-constrained minimum spanning tree problem

Cited by 41 publications

References 8 publications

A Multi-Population Genetic Algorithm for Tree-Shaped Network Design Problems

A Multi-Population Genetic Algorithm for Tree-Shaped Network Design Problems

Diameter Constrained Fuzzy Minimum Spanning Tree Problem

New formulations of the Hop-Constrained Minimum Spanning Tree problem via Miller–Tucker–Zemlin constraints

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