Solving nonlinear multicommodity flow problems with the analytic center cutting plane method
A talk deals with nonlinear multicommodity flow problems with convex costs. A decomposition method is proposed to solve them. The approach applies a potential reduction algorithm to (approximately) solve the master problem and a column generation technique defining a sequence of primal linear programming problems. Each subproblem consists in finding a minimum cost flow between an origin and a destination node on an uncapacited network. It is thus formulated as a shortest path problem and it is solved with the Dijkstra`s d-heap algorithm. An experimental implementation is described that takes full advantage of the supersparsity of the network in the linear algebra operations. Computational results show high efficiency of the approach on (known from the literature) nondifferentiable problems, real-life large scale France Telecom problem and other large scale randomly generated problems (sized up to 1000 arcs and 4000 commodities).
- OSTI ID:
- 36070
- Report Number(s):
- CONF-9408161-; TRN: 94:009753-0341
- Resource Relation:
- Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 15-19 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.
- Country of Publication:
- United States
- Language:
- English
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