Robust branch-cut-and-price for the Capacitated Minimum Spanning Tree problem over a large extended formulation

Uchôa, Eduardo; Fukasawa, Ricardo; Lysgaard, Jens; Pessoa, Artur Alves; Aragão, Marcus Poggi de; Andrade, Diogo V.

doi:10.1007/s10107-006-0043-y

Cited by 48 publications

(39 citation statements)

References 37 publications

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“…The experiments use some complete graph instances on 21, 41, 61, 81, 101, 121 and 161 nodes that have been used in previous papers for the HMSTP (see, for instance, [8]) and for other constrained spanning trees, namely the capacitated minimum spanning tree problem (see, for instance [36]). For each size, we have considered one random cost instance, denoted by TR, and two Euclidean cost instances.…”

Section: Computational Results For the Hmstpmentioning

confidence: 99%

Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs

2009

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The Hop-Constrained Minimum Spanning Tree Problem (HMSTP) is a NP-hard problem arising in the design of centralized telecommunication networks with quality of service constraints. We show that the HMSTP is equivalent to a Steiner Tree Problem (STP) in an adequate layered graph. We prove that the directed cut formulation for the STP defined in the layered graph, dominates (in terms of the linear programming relaxation) the best previously known formulations for the HMSTP. We then show how cuts in the extended layered graph space can be projected into new families of cuts in the original design space. We also adapt the proposed approach for the Diameter-Constrained Minimum Spanning Tree Problem (DMSTP). For situations when the diameter is odd we propose a new transformation into a single center problem that is quite effective. Computational results with a branch-and-cut algorithm show that the proposed method is significantly better than previously known methods on both problems.

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Section: Computational Results For the Hmstpmentioning

confidence: 99%

Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs

2009

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“…In [16], it is shown that (11) also dominates root cut-sets inequalities. An even stronger inequality can be obtained by considering that some arcs leaving S with a sufficiently large demand index may receive a negative coefficient: (12) where d is the smallest integer such that…”

Section: Definitionmentioning

confidence: 97%

A robust branch‐cut‐and‐price algorithm for the heterogeneous fleet vehicle routing problem

2009

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This article presents a robust branch-cut-and-price algorithm for the heterogeneous fleet vehicle routing problem (HFVRP), vehicles may have distinct capacities and costs. The columns in the formulation are associated to q-routes, a relaxation of capacitated elementary routes that makes the pricing problem solvable in pseudopolynomial time. Powerful new families of cuts are also proposed, which are expressed over a very large set of variables. Those cuts do not increase the complexity of the pricing subproblem. Experiments are reported where instances with up to 75 vertices were solved to optimality, a major improvement with respect to previous algorithms.

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“…For cut-and-price, recent papers include Fukasawa et al [41] on vehicle routing and Ochoa et al [86] on capacitated spanning trees. In the latter paper use was also made of the capacityindexed variables from subsection 5.3.…”

Section: Hybrid Algorithms and Stronger Dual Boundsmentioning

confidence: 99%

Reformulation and Decomposition of Integer Programs

Vanderbeck

Wolsey

2009

50 Years of Integer Programming 1958-2008

110

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In this survey we examine ways to reformulate integer and mixed integer programs. Typically, but not exclusively, one reformulates so as to obtain stronger linear programming relaxations, and hence better bounds for use in a branch-and-bound based algorithm. First we cover in detail reformulations based on decomposition, such as Lagrangean relaxation, Dantzig-Wolfe column generation and the resulting branch-and-price algorithms. This is followed by an examination of Benders' type algorithms based on pro jection. Finally we discuss in detail extended formulations involving additional variables that are based on problem structure. These can often be used to provide strengthened a priori formulations. Reformulations obtained by adding cutting planes in the original variables are not treated here.

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Robust branch-cut-and-price for the Capacitated Minimum Spanning Tree problem over a large extended formulation

Cited by 48 publications

References 37 publications

Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs

Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs

A robust branch‐cut‐and‐price algorithm for the heterogeneous fleet vehicle routing problem

Reformulation and Decomposition of Integer Programs

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