A column generation approach for SONET ring assignment

This paper describes the ring spur assignment problem (RSAP), a new problem arising in the design of next generation networks. The RSAP complements the sonet ring assignment problem (SRAP). We describe the RSAP, positioning it in relation to problems previously addressed in the literature. We decompose the problem into two IP problems and describe a branch-and-cut decomposition heuristic algorithm suitable for solving problem instances in a reasonable time. We present promising computational results.

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“…Another formulation of SRAP as a set‐partitioning model with additional knapsack constraints is given in Macambira et al. .…”

Section: Background Materialsmentioning

confidence: 99%

A decomposition algorithm for the ring spur assignment problem

Carroll

McGarraghy

2012

Int Trans Operational Res

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“…The GPCC problem has applications in the field of telecommunication network optimization, in particular it turns out to be a relevant model for optimum design of optical networks (see e.g. references [1,7,10]). In this application, the node set V corresponds to geographical sites and t (u,v) to the traffic demands between locations u and v. For various technological reasons, network operators often want to partition the node set V into clusters on which a certain network topology is imposed.…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of the present paper is to investigate and compare several 0-1 integer linear programming models for GPCC which can be qualified as compact, i.e. featuring a polynomial number of variables and constraints (by contrast, the model underlying the column generation approach in [10] which is a large scale set partitioning model with exponentially many columns, is essentialy noncompact). Note that two main compact 0-1 models for graph partitioning, namely Node-Cluster models and Node-Node models, have been investigated in the litterature where binary variables represent respectively relations of membership between nodes and clusters (case of the Node-Cluster model) and relations between nodes belonging to a same cluster (case of the Node-Node model).…”

Section: Introductionmentioning

confidence: 99%

Improved linearized models for graph partitioning problem under capacity constraints

Nguyễn

Minoux

2016

Optimization Methods and Software

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We investigate a variant of the Graph Partitioning Problem with capacity constraints imposed on the clusters, giving rise to quadratic constraints in 0-1 formulations. Several compact linearized models of the problem are proposed and analyzed: a) a model featuring O(n 3) binary variables which results from the application of the standard Fortet linearization technique; b) a more compact model featuring only O(n 2) binary variables, obtained by linearization after reformulation of the quadratic constraints as bilinear constraints; c) a strengthened version of the latter model, still featuring O(n 2) variables. Computational experiments comparing the relative strength and efficiency of the various models on a series of test instances involving complete graphs with up to 50 nodes are reported and discussed.

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“…Several techniques have been proposed to effectively solve integer linear programs that are plagued with symmetry. First, the problem may be reformulated, as possible, in a fashion that breaks the original symmetry (Fourer, 2000;Ghoniem and Sherali, 2010a); this often results in models that possess a very large number of columns and lend themselves to column generation approaches (Barnhart et al, 1998;Macambira and Maculan, 2006). A second approach that has gained popularity consists in enforcing tailored hierarchical constraints (Sherali and Smith, 2001), which ranks and imparts specific identities to indistinguishable model entities, thereby breaking symmetry and significantly enhancing algorithmic performance and problem solvability by reducing the search domain.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, Sherali and Smith (2001) successfully employed this approach to a telecommunications network design problem (also see Macambira and Maculan (2006)), a noise pollution problem, and a machine procurement and operation problem. In addition, various symmetry-enhanced formulations for facility layout problems have been discussed by Sherali et al (2003), Meller et al (2007), and Konak et al (2006).…”

Section: Introductionmentioning

confidence: 99%

Defeating symmetry in combinatorial optimization via objective perturbations and hierarchical constraints

Ghoniem¹,

Sherali

2011

IIE Transactions

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This article introduces the concept of defeating symmetry in combinatorial optimization via objective perturbations based on, and combined with, symmetry-defeating constraints. Under this novel reformulation, the original objective function is suitably perturbed using a weighted sum of expressions derived from hierarchical symmetry-defeating constraints in a manner that preserves optimality and judiciously guides and curtails the branch-and-bound enumeration process. Computational results are presented for a noise dosage problem, a doubles tennis scheduling problem, and a wagon load-balancing problem to demonstrate the efficacy of using this strategy in concert with traditional hierarchical symmetry-defeating constraints. The proposed methodology is shown to significantly outperform the use of hierarchical constraints or objective perturbations in isolation, as well as the automatic symmetry-defeating feature that is enabled by CPLEX, version 11.2.

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A column generation approach for SONET ring assignment

Cited by 10 publications

References 13 publications

A decomposition algorithm for the ring spur assignment problem

A decomposition algorithm for the ring spur assignment problem

Improved linearized models for graph partitioning problem under capacity constraints

Defeating symmetry in combinatorial optimization via objective perturbations and hierarchical constraints

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