Solving the capacitated multi-facility weber problem by simulated annealing, threshold accepting and genetic algorithms

Abstract

In this paper we focus on the capacitated multi-facility Weber problem with rectilinear, Euclidean, squared Euclidean and ℓp distances. This problem deals with locating m capacitated facilities in the Euclidean plane so as to satisfy the demand of n customers at the minimum total transportation cost. The location and the demand of each customer is known a priori and the transportation cost is proportional to the distance and the amount of flow between customers and facilities. We present three new heuristic methods each of which is based on one of the three well-known metaheuristic approaches: simulated annealing, threshold accepting, and genetic algorithms. Computational results on benchmark instances indicate that the heuristics perform well in terms of the quality of solutions they generate. Furthermore, the simulated annealing-based heuristic implemented with the two-variable exchange neighborhood structure outperforms the other heuristics considered in the paper. © 2007 by Springer Science+Business Media, LLC.