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Solving transportation problems with concave cost functions using genetic algorithms. (English) Zbl 1451.90019

Summary: In this paper we propose a genetic algorithm for solving the nonlinear transportation problem on a network with concave cost functions and the restriction that the flow must pass through all arcs of the network. We show that the algorithm can be used in solving large-scale problems. We prove that the complexity of a single iteration of the algorithm is \(O(nm)\) and converges to an \(\epsilon \)-optimum solution. We also present some implementation and testing examples of the algorithm using Wolfram Mathematica.

MSC:

90B06 Transportation, logistics and supply chain management
90C59 Approximation methods and heuristics in mathematical programming
90B10 Deterministic network models in operations research
90C06 Large-scale problems in mathematical programming

Software:

Mathematica
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