A Hopfield neural net approach to the vehicle routing problem with stochastic demands

Various vehicle routing problems (VRPs) are encountered in many service systems such as delivery, customer pick-up, repair and maintenance services. Most existing VRP studies have been concentrated on the case of deterministic demands. Because of practical needs, research on the vehicle routing problem with stochastic demands is beginning to draw much attention. This paper proposes an algorithm based on a Hopfield neural network to solve the VRP with some stochastic demands. The specific energy function and the network equations corresponding to the stochastic VRP are derived. The behavior of the algorithm is tested with numerical examples. The results show that the algorithm has good performance in both global and local searching. It is believed that the concurrent and adaptive mechanisms of a neural network make the algorithm so efficient.