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## Solving transportation problems with concave cost functions using genetic algorithms

Authors: Tatiana Pașa
Keywords: genetic algorithm, population, minimum cost flow, non-linear transport problem, large-scale problem, concave function.

### Abstract

In this paper we propose a genetic algorithm for solving the non-linear 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 %{\color{red}large-scale} 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.

Moldova State University
60 A. Mateevici, MD-2009, Chisinau
Republic of Moldova
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