A neural heuristic for the Multisource Weber Problem

The Multisource Weber Problem consists of finding the location of α facilities in the Euclidean space such that the total transportation cost needed to satisfy the demand of n fixed customers is minimized. This problem is an NP-Hard problem. As a consequence, exact methods are restricted to small size problems and many heuristics have been proposed to find quickly approximate optimal solutions for real size problems. In this paper, we propose a new heuristic based on artificial neural networks. Several variations of this approach are presented. Their performance is compared to the best results obtained for a set of two problems, one with 654 customers and the other one with 1060 customers, with a various number of facilities.