Local cuts revisited

Buchheim, Christoph; Liers, Frauke; Oswald, Marcus

doi:10.1016/j.orl.2008.01.004

Cited by 18 publications

(32 citation statements)

References 2 publications

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“…In [7], the separation of target cuts was introduced as a variant of the local cuts by Applegate et al [5]. No predescribed structure is imposed on the generated cutting planes.…”

Section: Primal Heuristicsmentioning

confidence: 99%

“…Furthermore, it is proven in [7] that an optimum solution of (3) defines a facet of P . In case (3) is unbounded, then a ⊤ (x − q) = 0 is a valid equation for P and violated by x * , where a is an unbounded ray.…”

Section: Primal Heuristicsmentioning

confidence: 99%

“…In our implementation, target cuts are generated by delayed column generation [7]. Starting from a small subset of feasible points in P , the remaining points of P are generated only if necessary.…”

Section: Cut Generationmentioning

confidence: 99%

“…While for binary problems it might be a feasible approach to completely enumerate all integer points in P at once, at least in small dimensions, this is practically not possible any more in the presence of general integer variables, since the number of these point could become much larger. As described in [7], the delayed column generation procedure can be applied even if the set of initial points is lowdimensional. However, to avoid dealing with numerical problems and to speed up the cut generation process significantly, we always start from a full-dimensional polyhedron P 0 , which is computed as sketched in the following.…”

Section: Cut Generationmentioning

confidence: 99%

“…In this work, we provide a branch-and-cut algorithm, based on the natural flow formulation strengthened by generating local cuts, revisited according to [7]. We test our algorithm on a wide set of realistic instances, and show that in this application local cuts significantly improve the computational time to find an optimal integral solution.…”

Section: Introductionmentioning

confidence: 99%

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An Exact Algorithm for Robust Network Design

Buchheim

Liers

Sanità

2011

Lecture Notes in Computer Science

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Abstract. Modern life heavily relies on communication networks that operate efficiently. A crucial issue for the design of communication networks is robustness with respect to traffic fluctuations, since they often lead to congestion and traffic bottlenecks. In this paper, we address an NP-hard single commodity robust network design problem, where the traffic demands change over time. For k different times of the day, we are given for each node the amount of single-commodity flow it wants to send or to receive. The task is to determine the minimum-cost edge capacities such that the flow can be routed integrally through the net at all times. We present an exact branch-and-cut algorithm, based on a decomposition into biconnected network components, a clever primal heuristic for generating feasible solutions from the linear-programming relaxation, and a general cutting-plane separation routine that is based on projection and lifting. By presenting extensive experimental results on realistic instances from the literature, we show that a suitable combination of these algorithmic components can solve most of these instances to optimality. Furthermore, cutting-plane separation considerably improves the algorithmic performance.

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“…In [7], the separation of target cuts was introduced as a variant of the local cuts by Applegate et al [5]. No predescribed structure is imposed on the generated cutting planes.…”

Section: Primal Heuristicsmentioning

confidence: 99%

Section: Primal Heuristicsmentioning

confidence: 99%

Section: Cut Generationmentioning

confidence: 99%

Section: Cut Generationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An Exact Algorithm for Robust Network Design

Buchheim

Liers

Sanità

2011

Lecture Notes in Computer Science

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Robust Network Design

Koster

Schmidt

2020

Network Design With Applications to Transportation and Logistics

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Engineering Branch-and-Cut Algorithms for the Equicut Problem

Anjos

Liers

Pardella

et al. 2013

Discrete Geometry and Optimization

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A minimum equicut of an edge-weighted graph is a partition of the nodes of the graph into two sets of equal size such that the sum of the weights of edges joining nodes in different partitions is minimum. We compare basic linear and semidefinite relaxations for the equicut problem, and find that linear bounds are competitive with the corresponding semidefinite ones but can be computed much faster. Motivated by an application of equicut in theoretical physics, we revisit an approach by Brunetta et al. and present an enhanced branch-and-cut algorithm. Our computational results suggest that the proposed branch-andcut algorithm has a better performance than the algorithm of Brunetta et al.. Further, it is able to solve to optimality in reasonable time several instances with more than 200 nodes from the physics application.

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Local cuts revisited

Cited by 18 publications

References 2 publications

An Exact Algorithm for Robust Network Design

An Exact Algorithm for Robust Network Design

Robust Network Design

Engineering Branch-and-Cut Algorithms for the Equicut Problem

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