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)|x∈X} wheref:ℝn→ℝ is a concave function, andX⊂ℝ n≥0 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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Pelzwerger, B.V., Shafir, A.Y. The interactive fixed charge inhomogeneous flows optimization problem. Ann Oper Res 25, 223–242 (1990). https://doi.org/10.1007/BF02283697
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DOI: https://doi.org/10.1007/BF02283697