Supervision in the Self-Organizing Feature Map: Application to the Vehicle Routing Problem

In this paper, we describe a neural heuristic to find an approximate optimal solution to the vehicle routing problem (VRP) with capacity and time limits constraints. This heuristic is based upon the hierarchical deformable nets (HDN) with stochastic competition introduced by Ghaziri [1991] to solve the VRP with capacity constraints only. For the time limits constraint we have added a constructive procedure to the HDN algorithm. Partial trial solutions are generated one of them is selected using a stochastic competition. In order to improve the results of this approach we have introduced a supervision process to the primary unsupervised algorithm. The performance of this hybrid approach is compared with the unsupervised algorithm and the methods based on other heuristics. We have tested the performance in terms of quality and CPU time consumption. We found that the solutions of the traditional heuristics are still better than the neural heuristics but their CPU time consumption is higher.