Tree polytope on 2-trees

Margot, François; Prodon, Alain; Liebling, Th. M.

doi:10.1007/bf01582065

Cited by 26 publications

(28 citation statements)

References 9 publications

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“…This model with T = ∅ was used by Lucena and Resende [35]. Margot et al [36] have proved that the x i j variables need not be declared as integer. 2.…”

Section: Network Location Modelsmentioning

confidence: 99%

Planning rapid transit networks

Laporte

Mesa

Ortega

et al. 2011

Socio-Economic Planning Sciences

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Rapid transit construction projects are major endeavours that require long-term planning by several players, including politicians, urban planners, engineers, management consultants, and citizen groups. Traditionally, operations research methods have not played a major role at the planning level but several tools developed in recent years can assist the decision process and help produce tentative network designs that can be submitted to the planners for further evaluation. This article reviews some indices for the quality of a rapid transit network, as well as mathematical models and heuristics that can be used to design networks.

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“…This model with T = ∅ was used by Lucena and Resende [35]. Margot et al [36] have proved that the x i j variables need not be declared as integer. 2.…”

Section: Network Location Modelsmentioning

confidence: 99%

Planning rapid transit networks

Laporte

Mesa

Ortega

et al. 2011

Socio-Economic Planning Sciences

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show abstract

“…To fight against this symmetry, we have added some symmetry breaking constraints (11), which force a connection between the root and the node of the communication network in the solution with smallest index.…”

Section: Definitions and Formulationmentioning

confidence: 99%

“…Prize-Collecting Steiner's Problem, and we don't know any alternate way to model them directly in a Mixed Integer Program. These Steiner's problems are NP-hard, except on special graphs [e.g., 11], but polyhedral approaches like those described by [5][6][7][8] may help to find optimal or good approximate solutions.…”

mentioning

confidence: 99%

Locating leak detecting sensors in a water distribution network by solving prize-collecting Steiner arborescence problems

2010

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We consider the problem of optimizing a novel acoustic leakage detection system for urban water distribution networks. The system is composed of a number of detectors and transponders to be placed in a choice of hydrants such as to provide a desired coverage under given budget restrictions. The problem is modeled as a particular Prize-Collecting Steiner Arborescence Problem. We present a branchand-cut-and-bound approach taking advantage of the special structure at hand which performs well when compared to other approaches. Furthermore, using a suitable stopping criterion, we obtain approximations of provably excellent quality (in most cases actually optimal solutions). The test bed includes the real water distribution network from the Lausanne region, as well as carefully randomly generated realistic instances.

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“…The class of valid inequalities (74) were independently introduced by Goemans [58], Lucena [59] and Margot, Prodon, and Liebling [60], for another extended formulation of STP. The inequalities (75) were introduced in [58,60].…”

Section: X(e(s)) + X(e(s \ {V} | {0})) ≤ |S| − 1 ∀S ⊆ V S ∩mentioning

confidence: 99%

“…The inequalities (75) were introduced in [58,60]. The separation problem for inequalities (74) and (75) The MSTP can be solved in O(|E| log |V |) time using Prim's algorithm [62].…”

Section: X(e(s)) + X(e(s \ {V} | {0})) ≤ |S| − 1 ∀S ⊆ V S ∩mentioning

confidence: 99%

Decomposition in Integer Linear Programming

Galati¹,

Ralphs²

2005

Integer Programming

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Both cutting plane methods and traditional decomposition methods are procedures that compute a bound on the optimal value of an integer linear program (ILP) by constructing an approximation to the convex hull of feasible solutions. This approximation is obtained by intersecting the polyhedron associated with the continuous relaxation, which has an explicit representation, with an implicitly defined polyhedron having a description of exponential size. In this paper, we first review these classical procedures and then introduce a new class of bounding methods called integrated decomposition methods, in which the bound yielded by traditional approaches is potentially improved by introducing a second implicitly defined polyhedron. We also discuss the concept of structured separation, which is related to the well-known template paradigm for dynamically generating valid inequalities and is central to our algorithmic framework. Finally, we briefly introduce a software framework for implementing the methods discussed in the paper and illustrate the concepts through the presentation of applications.

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Tree polytope on 2-trees

Cited by 26 publications

References 9 publications

Planning rapid transit networks

Planning rapid transit networks

Locating leak detecting sensors in a water distribution network by solving prize-collecting Steiner arborescence problems

Decomposition in Integer Linear Programming

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