Multicommodity network flows: the impact of formulation on decomposition
Mathematical Programming: Series A and B
Fast approximation algorithms for multicommodity flow problems
Selected papers of the 23rd annual ACM symposium on Theory of computing
Fast approximation algorithm for minimum cost multicommodity flow
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
SIAM Journal on Discrete Mathematics
A Specialized Interior-Point Algorithm for Multicommodity Network Flows
SIAM Journal on Optimization
Improved Empty Freight Car Distribution
Transportation Science
A Scaling Algorithm for Multicommodity Flow Problems
Operations Research
A Bundle Type Dual-Ascent Approach to Linear Multicommodity Min-Cost Flow Problems
INFORMS Journal on Computing
A Survey of Algorithms for Convex Multicommodity Flow Problems
Management Science
A Multicommodity Network-Flow Problem with Side Constraints on Paths Solved by Column Generation
INFORMS Journal on Computing
A linear model for compound multicommodity network flow problems
Computers and Operations Research
Power-efficient radio configuration in fixed broadband wireless networks
Computer Communications
A chance-constrained model and cutting planes for fixed broadband wireless networks
INOC'11 Proceedings of the 5th international conference on Network optimization
| Hi-index | 0.00 |
The linear multicommodity network flow (MCNF) problem has many applications in the areas of transportation and telecommunications. It has therefore received much attention, and many algorithms that exploit the problem structure have been suggested and implemented. The practical difficulty of solving MCNF models increases fast with respect to the problem size, and especially with respect to the number of commodities. Applications in telecommunications typically lead to instances with huge numbers of commodities, and tackling such instances computationally is challenging.In this paper, we describe and evaluate a fast and convergent lower-bounding procedure which is based on an augmented Lagrangian reformulation of MCNF, that is, a combined Lagrangian relaxation and penalty approach. The algorithm is specially designed for solving very large scale MCNF instances. Compared to a standard Lagrangian relaxation approach, it has more favorable convergence characteristics. To solve the nonlinear augmented Lagrangian subproblem, we apply a disaggregate simplicial decomposition scheme, which fully exploits the structure of the subproblem and has good reoptimization capabilities. Finally, the augmented Lagrangian algorithm can also be used to provide heuristic upper bounds.The efficiency of the augmented Lagrangian method is demonstrated through computational experiments on large scale instances. In particular, it provides near-optimal solutions to instances with over 3,600 nodes, 14,000 arcs and 80,000 commodities within reasonable computing time.