Integer and combinatorial optimization
Integer and combinatorial optimization
L-shaped decomposition of two-stage stochastic programs with integer recourse
Mathematical Programming: Series A and B
Design of Survivable Networks with Bounded Rings
Design of Survivable Networks with Bounded Rings
A Cutting Plane Algorithm for Multicommodity Survivable Network Design Problems
INFORMS Journal on Computing
INFORMS Journal on Computing
Two-Connected Networks with Rings of Bounded Cardinality
Computational Optimization and Applications
Two Edge-Disjoint Hop-Constrained Paths and Polyhedra
SIAM Journal on Discrete Mathematics
Networks
Two-edge connected subgraphs with bounded rings: Polyhedral results and Branch-and-Cut
Mathematical Programming: Series A and B
The two-edge connected hop-constrained network design problem: Valid inequalities and branch-and-cut
Networks - Special Issue on Multicommodity Flows and Network Design
A survey on benders decomposition applied to fixed-charge network design problems
Computers and Operations Research
Combinatorial Benders Cuts for the Minimum Tollbooth Problem
Operations Research
SNDlib 1.0—Survivable Network Design Library
Networks - Network Optimization (INOC 2007)
A note on the selection of Benders’ cuts
Mathematical Programming: Series A and B - Series B - Special Issue: Combinatorial Optimization and Integer Programming
Introduction to Stochastic Programming
Introduction to Stochastic Programming
Approximability of 3- and 4-hop bounded disjoint paths problems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
An improved Benders decomposition applied to a multi-layer network design problem
Operations Research Letters
On the k edge-disjoint 2-hop-constrained paths polytope
Operations Research Letters
Notes on polyhedra associated with hop-constrained paths
Operations Research Letters
On the directed hop-constrained shortest path problem
Operations Research Letters
A note on hop-constrained walk polytopes
Operations Research Letters
On the hop constrained steiner tree problem with multiple root nodes
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Optimal design and augmentation of strongly attack-tolerant two-hop clusters in directed networks
Journal of Combinatorial Optimization
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Given a graph with nonnegative edge weights and node pairs Q, we study the problem of constructing a minimum weight set of edges so that the induced subgraph contains at least K edge-disjoint paths containing at most L edges between each pair in Q. Using the layered representation introduced by Gouveia [Gouveia, L. 1998. Using variable redefinition for computing lower bounds for minimum spanning and Steiner trees with hop constraints. INFORMS J. Comput.102 180--188], we present a formulation for the problem valid for any K, L ≥ 1. We use a Benders decomposition method to efficiently handle the large number of variables and constraints. We show that our Benders cuts contain constraints used in previous studies to formulate the problem for L = 2, 3, 4, as well as new inequalities when L ≥ 5. Whereas some recent works on Benders decomposition study the impact of the normalization constraint in the dual subproblem, we focus here on when to generate the Benders cuts. We present a thorough computational study of various branch-and-cut algorithms on a large set of instances including the real-based instances from SNDlib. Our best branch-and-cut algorithm combined with an efficient heuristic is able to solve the instances significantly faster than CPLEX 12 on the extended formulation.