A VNS-Based Algorithm with Adaptive Local Search for Solving the Multi-Depot Vehicle Routing Problem

The Multi-Depot Vehicle Routing Problem (MDVRP) is a variant of the Vehicle Routing Problem (VRP) that consists in designing a set of vehicle routes to serve all customers, such that the maximum number of vehicle per depot, the vehicle capacity and the maximum time for each route are respected. The objective is to minimize the total cost of transportation. This paper presents an algorithm, named VNSALS, based on the Variable Neighborhood Search (VNS) with Adaptive Local Search (ALS) for solving it. The main procedures of VNSALS are perturbation, ALS and cluster refinement. The perturbation procedure of VNS is important to diversify the solutions and avoid getting stuck in local optima. The ALS procedure consists in memorizing the results found after applying a local search and in using this memory to select the most promising neighborhood for the next local search application. The choice of the neighborhood is very important to improve the solution in heuristic methods because the complexity of the local search is high and expensive. On the other hand, customer’s reallocation keeps the clusters more balanced. VNSALS is tested in classical instances of MDVRP for evaluating its efficiency and the results are presented and discussed.