A novel approach based on heuristics and a neural network to solve a capacitated location routing problem

In this work, we describe a method to solve the capacitated location-routing problem (CLRP) to minimize the delivery distance for a vehicle. The CLRP consists of locating depots, assigning each customer to one depot, and determining routes. The objective is to minimize the cost (distance). In the locating problem, we use a self-organizing map (SOM) to determine the depots and assign customers to depots. The SOM is an unsupervised learning method with two layers and has proven effective in several research areas, such as clustering. In the routing problem, we use the Clarke and Wright technique to determine routes. In the present work, we propose an improvement of the capacitated self-organizing map (CSOM) to optimize the location of depots and the Or-Opt algorithm to ameliorate the routes obtained by Clarke and Write (CSOM&CW). The numerical results show that the proposed method can meet many benchmarks of small and medium instances. Computational results assess the higher performance of our approach and demonstrate its efficiency in solving large-size instances.