Optimal flow in dynamic networks with nonlinear cost functions on edges
نویسندگان
چکیده
In this paper we study the dynamic version of the nonlinear minimumcost flow problem on networks. We consider the problem on dynamic networks with nonlinear cost functions on edges that depend on time and flow. Moreover, we assume that the demand function and capacities of edges also depend on time. To solve the problem we propose an algorithm, which is based on reducing the dynamic problem to the classical minimum-cost problem on a time-expanded network. We also study some generalization of the proposed problem. Mathematics subject classification: 90B10, 90C35, 90C27.
منابع مشابه
Optimal multicommodity flows in dynamic networks and algorithms for their finding
In this paper we study two basic problems related to dynamic flows: maximum multicommodity flow and the minimum cost multicommodity flow problems. We consider these problems on dynamic networks with time-varying capacities of edges. For minimum cost multicommodity flow problem we assume that cost functions, defined on edges, are nonlinear and depending on time and flow, and the demand function ...
متن کاملA class of multi-agent discrete hybrid non linearizable systems: Optimal controller design based on quasi-Newton algorithm for a class of sign-undefinite hessian cost functions
In the present paper, a class of hybrid, nonlinear and non linearizable dynamic systems is considered. The noted dynamic system is generalized to a multi-agent configuration. The interaction of agents is presented based on graph theory and finally, an interaction tensor defines the multi-agent system in leader-follower consensus in order to design a desirable controller for the noted system. A...
متن کاملThe minimum cost multicommodity flow problem in dynamic networks and an algorithm for its solving
The dynamic version of the minimum cost multicommodity flow problem that generalizes the static minimum cost multicommodity flow problem is formulated and studied. This dynamic problem is considered on directed networks with a set of commodities, time-varying capacities, fixed transit times on arcs, and a given time horizon. We assume that cost functions, defined on edges, are nonlinear and dep...
متن کاملNumerical treatment for nonlinear steady flow of a third grade fluid in a porous half space by neural networks optimized
In this paper, steady flow of a third-grade fluid in a porous half space has been considered. This problem is a nonlinear two-point boundary value problem (BVP) on semi-infinite interval. The solution for this problem is given by a numerical method based on the feed-forward artificial neural network model using radial basis activation functions trained with an interior point method. ...
متن کاملOptimal Flow Trees for Networks with General Nonlinear Arc Costs
This paper describes the application of a dynamic programming approach to find minimum flow cost spanning trees on a network with general nonlinear arc costs. Thus, this problem is an extension of the Minimum Spanning Tree (MST) problem since we also consider flows that must be routed in order to satisfy user needs. In fact, the MST, usually, considers fixed arc costs and in our case the arc co...
متن کامل