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

• 成果类型: Article
• 署名作者: Cacchiani, Valentina; Juenger, Michael; Liers, Frauke; Lodi, Andrea; Schmidt, Daniel R.
• 署名单位: University of Bologna; University of Cologne; University of Erlangen Nuremberg; Universite de Montreal; Polytechnique Montreal
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-016-0991-9
• 发表日期: 2016
• 页码: 297-342
• 关键词: cost

摘要

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-and-cut algorithm to derive optimal solutions to sRND, built on a capacity-based integer linear programming formulation. It is strengthened with valid inequalities derived as -Chvatal-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.