Models and algorithms for robust network design with several traffic scenarios

Authors:
Eduardo Álvarez-Miranda;Valentina Cacchiani;Tim Dorneth;Michael Jünger;Frauke Liers;Andrea Lodi;Tiziano Parriani;Daniel R. Schmidt
Affiliations:
DEIS, University of Bologna, Bologna, Italy;DEIS, University of Bologna, Bologna, Italy;Institut für Informatik, Universität zu Köln, Köln, Germany;Institut für Informatik, Universität zu Köln, Köln, Germany;Department Mathematik, Friedrich-Alexander Universität Erlangen-Nürnberg, Erlangen, Germany;DEIS, University of Bologna, Bologna, Italy;DEIS, University of Bologna, Bologna, Italy;Institut für Informatik, Universität zu Köln, Köln, Germany
Venue:
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Year:
2012

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Abstract

We consider a robust network design problem: optimum integral capacities need to be installed in a network such that supplies and demands in each of the explicitly known traffic scenarios can be satisfied by a single-commodity flow. In Buchheim et al. (LNCS 6701, 7---17 (2011)), an integer-programming (IP) formulation of polynomial size was given that uses both flow and capacity variables. We introduce an IP formulation that only uses capacity variables and exponentially many, but polynomial time separable constraints. We discuss the advantages of the latter formulation for branch-and-cut implemenations and evaluate preliminary computational results for the root bounds. We define a class of instances that is difficult for IP-based approaches. Finally, we design and implement a heuristic solution approach based on the exploration of large neighborhoods of carefully selected size and evaluate it on the difficult instances. The results are encouraging, with a good understanding of the trade-off between solution quality and neighborhood size.