Álvarez-Miranda, Eduardo, Cacchiani, Valentina, Lodi, Andrea, Parriani, Tiziano and Schmidt, Daniel R. ORCID: 0000-0001-7381-912X (2014). Single-commodity robust network design problem: Complexity, instances and heuristic solutions. European Journal of Operational Research, 238 (3). pp. 711-723. Elsevier.


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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.

Item Type: Journal Article
CreatorsEmailORCIDORCID Put Code
Schmidt, Daniel R.UNSPECIFIEDorcid.org/0000-0001-7381-912XUNSPECIFIED
URN: urn:nbn:de:hbz:38-550509
Journal or Publication Title: European Journal of Operational Research
Volume: 238
Number: 3
Page Range: pp. 711-723
Date: 2014
Publisher: Elsevier
Language: English
Faculty: Faculty of Mathematics and Natural Sciences
Divisions: Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Institute of Computer Science
Subjects: Data processing Computer science
Refereed: No
URI: http://kups.ub.uni-koeln.de/id/eprint/55050


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