Single-commodity robust network design problem: Complexity, instances and heuristic solutions

Álvarez-Miranda, Eduardo; Cacchiani, Valentina; Lodi, Andrea; Parriani, Tiziano; Schmidt, Daniel R.

doi:10.1016/j.ejor.2014.04.023

Cited by 8 publications

(12 citation statements)

References 26 publications

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“…Finally, we use the large neighborhood search heuristic introduced in [3,4], but only at the root node, in the finite case and with a time limit of 120 CPU seconds.…”

Section: Computational Resultsmentioning

confidence: 99%

“…• JMP: The instances are generated according to the method in [27] with zero-one balances as proposed in [4].…”

Section: Experiments With Finite Uncertainty Setsmentioning

confidence: 99%

“…The model allows to compute a different routing for each b ∈ D. We call this way of routing a dynamic routing, as opposed to static routing schemes that route all scenarios on the same fixed set of paths. As a consequence, one set of arc-flow variables is needed for each b ∈ D. In a previous joint work [4] with Álvarez-Miranda and Parriani, the authors of this article present a linear programming based heuristic for this model. Here, however, we are interested in solving the problem with an exact algorithm and show a different integer programming formulation whose size does not depend on |D|.…”

Section: Introductionmentioning

confidence: 99%

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Single-commodity robust network design with finite and Hose demand sets

et al. 2016

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We study a single-commodity Robust Network Design problem (sRND) defined on an undirected graph. Our goal is to determine minimum cost capacities such that any traffic demand from a given uncertainty set can be satisfied by a feasible single-commodity flow. We consider two ways of representing the uncertainty set, either as a finite list of scenarios or as a polytope. We propose a branch-andcut algorithm to derive optimal solutions to sRND, built on a capacity-based integer linear programming formulation. It is strenghtened with valid inequalities derived as {0, 1 2 }-Chvátal-Gomory cuts. Since the formulation contains exponentially many constraints, we provide practical separation algorithms. Extensive computational experiments show that our approach is effective, in comparison to existing approaches from the literature as well as to solving a flow based formulation by a general purpose solver. * We thank the Ateneo Italo-Tedesco VIGONI programme 2011-2012 for its financial support.

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“…Finally, we use the large neighborhood search heuristic introduced in [3,4], but only at the root node, in the finite case and with a time limit of 120 CPU seconds.…”

Section: Computational Resultsmentioning

confidence: 99%

“…• JMP: The instances are generated according to the method in [27] with zero-one balances as proposed in [4].…”

Section: Experiments With Finite Uncertainty Setsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Single-commodity robust network design with finite and Hose demand sets

et al. 2016

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“…Under arc capacity uncertainty, Minoux show that the related RND is NP‐hard in general. Álvarez‐Miranda et al discuss the complexity and heuristic results for single‐commodity RND variants; Cacchiani et al focus on the derivation of optimal solutions to the single‐commodity RND by using the branch‐and‐cut algorithm. They consider uncertainty sets of the hose demand modeled as a finite set of scenarios or as a polytope.…”

Section: Introductionmentioning

confidence: 99%

“…Cutting-plane algorithm for solving the RND problem in Eq. (3) Input: An instance of problem(3). Output: An ε-optimal solution to problem (3), or no feasible solution exits.Step 0: Setx ij = 1, ∀(i, j) ∈ A.…”

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confidence: 99%

Single‐commodity stochastic network design under demand and topological uncertainties with insufficient data

Shen¹,

You²,

Ma³

2017

Naval Research Logistics

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Stochastic network design is fundamental to transportation and logistic problems in practice, yet faces new modeling and computational challenges resulted from heterogeneous sources of uncertainties and their unknown distributions given limited data. In this article, we design arcs in a network to optimize the cost of single‐commodity flows under random demand and arc disruptions. We minimize the network design cost plus cost associated with network performance under uncertainty evaluated by two schemes. The first scheme restricts demand and arc capacities in budgeted uncertainty sets and minimizes the worst‐case cost of supply generation and network flows for any possible realizations. The second scheme generates a finite set of samples from statistical information (e.g., moments) of data and minimizes the expected cost of supplies and flows, for which we bound the worst‐case cost using budgeted uncertainty sets. We develop cutting‐plane algorithms for solving the mixed‐integer nonlinear programming reformulations of the problem under the two schemes. We compare the computational efficacy of different approaches and analyze the results by testing diverse instances of random and real‐world networks. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 154–173, 2017

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On the robustness of potential-based flow networks

et al. 2022

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Potential-based flows provide a simple yet realistic mathematical model of transport in many real-world infrastructure networks such as, e.g., gas or water networks, where the flow along each edge depends on the difference of the potentials at its end nodes. We call a network topology robust if the maximal node potential needed to satisfy a set of demands never increases when demands are decreased. This notion of robustness is motivated by infrastructure networks where users first make reservations for certain demands that may be larger than the actual flows sent later on. In these networks, node potentials correspond to physical quantities such as pressures or hydraulic heads and must be guaranteed to lie within a fixed range, even if the actual amounts are smaller than the previously reserved demands. Our main results are a precise characterization of robust network topologies for the case of point-to-point demands via forbidden node-labeled graph minors, as well as an efficient algorithm for testing robustness.

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Single-commodity robust network design problem: Complexity, instances and heuristic solutions

Cited by 8 publications

References 26 publications

Single-commodity robust network design with finite and Hose demand sets

Single-commodity robust network design with finite and Hose demand sets

Single‐commodity stochastic network design under demand and topological uncertainties with insufficient data

On the robustness of potential-based flow networks

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