Models and Algorithms for Robust Network Design with Several Traffic Scenarios

Álvarez-Miranda, Eduardo; Cacchiani, Valentina; Dorneth, Tim; Jünger, Michael; Liers, Frauke; Lodi, Andrea; Parriani, Tiziano; Schmidt, Daniel R.

doi:10.1007/978-3-642-32147-4_24

Cited by 6 publications

(15 citation statements)

References 25 publications

(29 reference statements)

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“…They gave an exact branch-and-cut algorithm that solves a flowmodel MIP through sophisticated general-purpose cutting planes. Lately, Álvarez-Miranda et al [2] introduced a capacity-based MIP-model, and discussed a preliminary set of results of the biennial "Vigoni 2011-2012" between the universities of Köln and Bologna.…”

Section: Related Literaturementioning

confidence: 99%

“…Motivated by the computational investigations in [9,2], in the following, we analyze some special cases:…”

Section: Complexitymentioning

confidence: 99%

“…According to the results that we present in the following subsections, we are able to get a better understanding of empirical results in [9,2], and we propose a family of randomly generated instances that are challenging for the natural flow formulation already for |V | = 50 and K = 10.…”

Section: Complexitymentioning

confidence: 99%

“…Contribution of the paper. Preliminary computational investigations have been performed on classical graphs from the literature with random balances [9] and on special hypercubes with {−1, 0, 1} balances [2]. The results in both papers have shown that the former instances are surprisingly easy for a general-purpose Mixed-Integer Programming (MIP) solver on the natural flow-formulation (1)- (5), while the latter instances are structurally difficult.…”

Section: Introductionmentioning

confidence: 99%

“…2 A preliminary version of the heuristic approaches described here was introduced in [2] where the first phase of the investigation on RND, which was the topic of the "Vigoni 2011-2012" project between the University of Köln and the University of Bologna, was summarized.…”

Section: Introductionmentioning

confidence: 99%

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

Álvarez-Miranda

Cacchiani

Lodi

et al. 2014

European Journal of Operational Research

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We study a single-commodity Robust Network Design problem (RND) in which an undirected graph with edge costs is given together with a discrete set of balance matrices, representing different supply/demand scenarios. In each scenario, a subset of the nodes is exchanging flow. The goal is to determine the minimum cost installation of capacities on the edges such that the flow exchange is feasible for every scenario. Previously conducted computational investigations on the problem motivated the study of the complexity of some special cases and we present complexity results on them, including hypercubes. In turn, these results lead to the definition of new instances (random graphs with {-1,0,1} balances) that are computationally hard for the natural flow formulation. These instances are then solved by means of a new heuristic algorithm for RND, which consists of three phases. In the first phase the graph representing the network is reduced by heuristically deleting a subset of the arcs, and a feasible solution is built. The second phase consists of a neighborhood search on the reduced graph based on a Mixed-Integer (Linear) Programming (MIP) flow model. Finally, the third phase applies a proximity search approach to further improve the solution, taking into account the original graph. The heuristic is tested on the new instances, and the comparison with the solutions obtained by Cplex on a natural flow formulation shows the effectiveness of the proposed method.

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Section: Related Literaturementioning

confidence: 99%

“…Motivated by the computational investigations in [9,2], in the following, we analyze some special cases:…”

Section: Complexitymentioning

confidence: 99%

Section: Complexitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Álvarez-Miranda

Cacchiani

Lodi

et al. 2014

European Journal of Operational Research

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Branch‐and‐price for energy optimization in multi‐hop wireless sensor networks

Vanier

2021

Networks

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Wireless sensor networks (WSNs) are widely deployed to support transmissions of the huge data emitted by heterogeneous connected devices. The quality of service (QoS) and energy requirements in WSNs are dramatically increasing and becoming challenging issues. Integrating network coding, in the data transmission process, leads to reduced energy consumption and improved QoS. In this work, we study the problem of energy efficiency in multi-hop WSNs, namely wireless unsplittable multi-commodity flow with network coding (wUMCFC). We propose mixed-integer programming formulations of the wUMCFC problem, and we implement an open source solver wUMCFC based on the branch-and-price algorithm. To the best of our knowledge, this work is the first study of the wUMCFC problem by mathematical programming tools. We perform a computational study on realistic instances with an analysis of the performance of the proposed algorithm. The computational results show the efficiency of the network coding and provide important information for strategic decisions on routing policies and network management https://github.com/ lidingxu/wUMCFC.

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Optimization in Wireless Networks

Oustry

Haddad-Vanier

et al. 2022

Encyclopedia of Optimization

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Models and Algorithms for Robust Network Design with Several Traffic Scenarios

Cited by 6 publications

References 25 publications

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

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

Branch‐and‐price for energy optimization in multi‐hop wireless sensor networks

Optimization in Wireless Networks

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