Grasp Embedded Scatter Search for the Multicommodity Capacitated Network Design Problem
Journal of Heuristics
Variable Disaggregation in Network Flow Problems with Piecewise Linear Costs
Operations Research
An Integrated Model and Solution Approach for Fleet Sizing with Heterogeneous Assets
Transportation Science
Heuristics for the rural postman problem
Computers and Operations Research
Efficient routing from multiple sources to multiple sinks in wireless sensor networks
EWSN'07 Proceedings of the 4th European conference on Wireless sensor networks
The k-Cardinality Tree Problem: Reformulations and Lagrangian Relaxation
Discrete Applied Mathematics
A Freight Service Design Problem for a Railway Corridor
Transportation Science
Optimizing single-source capacitated FLP in fuzzy decision systems
ICSI'11 Proceedings of the Second international conference on Advances in swarm intelligence - Volume Part I
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The network design problem is a multicommodity minimal cost network flow problem with fixed costs on the arcs, i.e., a structured linear mixed-integer programming problem. It has various applications, such as construction of new links in transportation networks, topological design of computer communication networks, and planning of empty freight car transportation on railways. We present a Lagrangean heuristic within a branch-and-bound framework as a method for finding the exact optimal solution of the uncapacitated network design problem with single origins and destinations for each commodity (the simplest problem in this class, but still NP-hard). The Lagrangean heuristic uses a Lagrangean relaxation as subproblem, solving the Lagrange dual with subgradient optimization, combined with a primal heuristic (the Benders subproblem) yielding primal feasible solutions. Computational tests on problems of various sizes (up to 1000 arcs, 70 nodes and 138 commodities or 40 nodes and 600 commodities) and of several different structures lead to the conclusion that the method is quite powerful, outperforming for example a state-of-the-art mixed-integer code, both with respect to problem size and solution time.