The interactive fixed charge inhomogeneous flows optimization problem |
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Authors: | Boris V. Pelzwerger Anatoly Yu. Shafir |
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Affiliation: | (1) Department of Applied Mathematics, Polytechnical Institute, 76, Lenin Avenue, 454080 Chelyabinsk, USSR |
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Abstract: | An optimization problem of interactive inhomogenous flows (Steiner multicommodity network flow problem) is formulated. The problem's main characteristic is a fixed charge change when combining multicommodity communications. In this paper we propose a method for solving this problem which, in order to restrict the search on the feasible domain, reduces the original problem to a concave programming problem in the form: min {f(x)|xX} wheref:n is a concave function, andX0n is a flow polytope defined by network transportation constraints. For practical large-scale problems arising from planning transportation networks on inhomogeneous surfaces defined by a digital model, a method of local optimization over a flow polytope vertex set is proposed, which is far more effective in comparison with the Gallo and Sodini method under polytope strong degeneracy conditions. |
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