Single-Commodity Robust Network Design with Finite and Hose Demand Sets

Cacchiani, Valentina and Jünger, Michael and Liers, Frauke and Lodi, Andrea and Schmidt, Daniel R. (2014) Single-Commodity Robust Network Design with Finite and Hose Demand Sets.
Technical Report , 32 p.
Submitted

Abstract

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 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.


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Item Type: Paper (Technical Report)
Citations: [error in script] [error in script]
Subjects:
  • 90-XX Operations research, mathematical programming > 90Bxx Operations research and management science > 90B10 Network models, deterministic

  • 90-XX Operations research, mathematical programming > 90Bxx Operations research and management science > 90B18 Communication networks

  • 90-XX Operations research, mathematical programming > 90Cxx Mathematical programming > 90C05 Linear programming

  • 90-XX Operations research, mathematical programming > 90Cxx Mathematical programming > 90C11 Mixed integer programming

  • 90-XX Operations research, mathematical programming > 90Cxx Mathematical programming > 90C27 Combinatorial optimization

  • 90-XX Operations research, mathematical programming > 90Cxx Mathematical programming > 90C35 Programming involving graphs or networks

  • 90-XX Operations research, mathematical programming > 90Cxx Mathematical programming > 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut

  • Additional Information: Also appeared as technical report OR-14-11 at the University of Bologna, Italy.
    Subjects: 90-XX Operations research, mathematical programming > 90Bxx Operations research and management science > 90B10 Network models, deterministic
    90-XX Operations research, mathematical programming > 90Bxx Operations research and management science > 90B18 Communication networks
    90-XX Operations research, mathematical programming > 90Cxx Mathematical programming > 90C05 Linear programming
    90-XX Operations research, mathematical programming > 90Cxx Mathematical programming > 90C11 Mixed integer programming
    90-XX Operations research, mathematical programming > 90Cxx Mathematical programming > 90C27 Combinatorial optimization
    90-XX Operations research, mathematical programming > 90Cxx Mathematical programming > 90C35 Programming involving graphs or networks
    90-XX Operations research, mathematical programming > 90Cxx Mathematical programming > 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
    Divisions: Institute of Computer Science > Computer Science Department - Prof. Dr. Juenger
    Depositing User: Daniel R. Schmidt
    Date Deposited: 03 Apr 2014 10:15
    Last Modified: 15 Apr 2014 15:46
    Deposit Information:
    ZAIK Number: [error in script]
    Depositing User: Daniel R. Schmidt
    Date Deposited: 03 Apr 2014 10:15
    Last Modified: 15 Apr 2014 15:46
    URI: http://e-archive.informatik.uni-koeln.de/id/eprint/771