Optimal Trees for General Nonlinear Network Flow Problems: A Dynamic Programming Approach
نویسنده
چکیده
In this paper, we describe a dynamic programming approach to find optimal trees to the singlesource minimum cost network flow problem with general nonlinear costs. This class of problems is known to be NP-Hard and there is a scarcity of methods to address them. The algorithms previously developed have considered only two particular types of cost functions: “staircase” and “sawtooth”. Here, a dynamic programming approach to find optimal trees, that can be used with any kind of separable and additive cost function, is proposed. Computational experiments were performed using randomly generated problems and the results reported, for small and medium size problems, indicate the effectiveness of the proposed approach. keywords Dynamic programming, network flows, optimal trees, general nonlinear costs
منابع مشابه
A dynamic programming approach for solving nonlinear knapsack problems
Nonlinear Knapsack Problems (NKP) are the alternative formulation for the multiple-choice knapsack problems. A powerful approach for solving NKP is dynamic programming which may obtain the global op-timal solution even in the case of discrete solution space for these problems. Despite the power of this solu-tion approach, it computationally performs very slowly when the solution space of the pr...
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 کاملAn efficient modified neural network for solving nonlinear programming problems with hybrid constraints
This paper presents the optimization techniques for solving convex programming problems with hybrid constraints. According to the saddle point theorem, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalleinvariance principle, a neural network model is constructed. The equilibrium point of the proposed model is proved to be equivalent to the optima...
متن کاملInverse Maximum Dynamic Flow Problem under the Sum-Type Weighted Hamming Distance
Inverse maximum flow (IMDF), is among the most important problems in the field ofdynamic network flow, which has been considered the Euclidean norms measure in previousresearches. However, recent studies have mainly focused on the inverse problems under theHamming distance measure due to their practical and important applications. In this paper,we studies a general approach for handling the inv...
متن کاملA Mixed Integer Programming Approach to Optimal Feeder Routing for Tree-Based Distribution System: A Case Study
A genetic algorithm is proposed to optimize a tree-structured power distribution network considering optimal cable sizing. For minimizing the total cost of the network, a mixed-integer programming model is presented determining the optimal sizes of cables with minimized location-allocation cost. For designing the distribution lines in a power network, the primary factors must be considered as m...
متن کامل