A Lagrangean Heuristic Based Branch-and-Bound Method for the Capacitated Network Design Problem

Holmberg, Kaj; Yuan, Di

doi:10.1007/978-3-642-60744-8_15

Cited by 24 publications

(39 citation statements)

References 6 publications

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“…The cumulative distribution of the performance profiles confirm this result. The heuristical variable fixing in NDBC were first presented in [HY00] and were adapted in our project to be used with a bundle method solver. It was stopped in these experiments after 600 seconds for each instance.…”

Section: Methodsmentioning

confidence: 99%

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Relax-and-Cut for Capacitated Network Design

Kliewer

Timajev

2005

Algorithms – ESA 2005

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Abstract. We present an evaluation of a Lagrangean-based branch-andbound algorithm with additional valid inequalities for the capacitated network design problem. The focus is on two types of valid inequalities, the cover inequalities and local cuts. We show how these inequalities can be considered in a Lagrangean relaxation without destroying the computationally simple structure of the subproblems. We present an extensive computational study on a large set of benchmark data. The results show that the presented algorithm outperforms many other exact and heuristical solvers in terms of running time and solution quality.

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Section: Methodsmentioning

confidence: 99%

“…Several heuristic approaches for this problem formulation are presented in [CGF00], [GCG03], [GCG04], [CGH04]. In [HY00], a Lagrangianrelaxation based branch-and-bound algorithm is presented. In [SKK02a] we have presented Lagrangian cardinality cuts and coupled variable fixing algorithms in a similar algorithmic approach.…”

Section: Related Workmentioning

confidence: 99%

Relax-and-Cut for Capacitated Network Design

Kliewer

Timajev

2005

Algorithms – ESA 2005

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“…However, results from other papers also suggest that one should not ignore the second type of relaxation. For instance, Holmberg and Yuan [18] show that the second relaxation provides valuable information for a branchand-bound procedure. Crainic et al [6] have also shown that, using an adequate "tuning" of the subgradient optimization procedure, the second relaxation is a viable alternative to the network flow based relaxation.…”

Section: Lagrangean Relaxationsmentioning

confidence: 99%

Models and heuristics for a minimum arborescence problem

et al. 2007

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The Minimum Arborescence problem (MAP) consists of finding a minimum cost arborescence in a directed graph. This problem is NP-Hard and is a generalization of two well-known problems: the Minimum Spanning Arborescence Problem (MSAP) and the Directed Node Weighted Steiner Tree Problem (DNWSTP). We start the model presentation in this paper by describing four models for the MSAP (including two new ones, using so called "connectivity" constraints which forbid disconnected components) and we then describe the changes induced on the polyhedral structure of the problem by the removal of the spanning property. Only two (the two new ones) of the four models for the MSAP remain valid when the spanning property is removed. We also describe a multicommodity flow reformulation for the MAP that differs from well-known multicommodity flow reformulations in the sense that the flow conservation constraints at source and destination are replaced by inequalities. We show that the linear programming relaxation of this formulation is equivalent to the linear programming relaxation of the best of the two previous valid formulations and we also propose two Lagrangean relaxations based on the multicommodity flow reformulation. From the upper bound perspective, we describe a constructive heuristic as well as a local search procedure involving the concept of key path developed earlier for the Steiner Tree Problem. Numerical experiments taken from instances with up

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“…For example, it may be of interest to use ring structures, tree structures, or some other type of particular structure. Such requirements may be included in the model, e.g., (Gavish, 1982;Holmberg and Yuan, 2000). 11.5.2.6 Routing constraints.…”

Section: Network Loading Problem Network Loading Problemmentioning

confidence: 99%

“…The question is how to send a set of commodities through a network at minimal cost subject to capacity constraints on the arcs. Mathematically, the problem may be formulated as See, e.g., Balakrishnan et al (1991); Barahona (1996); Bienstock et al (1998);Holmberg and Yuan (1998);Gunluk (1999); Holmberg and Yuan (2000).…”

Section: Important Problem Classesmentioning

confidence: 99%

Telecommunications Network Design

Forsgren

Prytz

Handbook of Optimization in Telecommunications

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Abstract:Telecommunications networks are fundamental in any telecommunications system. The network has to meet a number of criteria for the performance to be satisfactory. Hence, when designing the network, one may pose a number of optimization problems whose solutions give networks that are, in some sense, optimally designed. As the networks have become increasingly complex, the aid of optimization techniques has also become increasingly important. This is a vast area, and this chapter considers an overview of the issues that arise as well as a number of specific optimization models and problems. Often the problems may be formulated as mixed-integer linear programs. Due to problem size and problem structure, in many cases specially tailored solution techniques need to be used in order to solve, or approximately solve, the problems.

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A Lagrangean Heuristic Based Branch-and-Bound Method for the Capacitated Network Design Problem

Cited by 24 publications

References 6 publications

Relax-and-Cut for Capacitated Network Design

Relax-and-Cut for Capacitated Network Design

Models and heuristics for a minimum arborescence problem

Telecommunications Network Design

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