SOLVING TRANSPORTATION PROBLEMS WITH CONCAVE COST FUNCTIONS USING GENETIC ALGORITHMS

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 large-scale problems. We prove that the complexity of a single iteration of the algorithm is O(nm) and converges to anǫ -optimum solution. We also present some implementation and testing examples of the algorithm using Wolfram Mathematica.