A memory-based iterated local search algorithm for the multi-depot open vehicle routing problem

The problem studied in this paper is the multi-depot open vehicle routing problem, which has the following two differences in relation to the classical vehicle routing problem: there are several depots; the vehicles do not return to the depot after delivering the goods to the customers, i.e., the end of the route is not the starting point. There are many practical applications for this problem, however the great majority of the studies have only addressed the open vehicle routing problem with a single depot. In this paper, we present an iterated local search algorithm, in which the moves performed during the local search are recalled and this historical search information is then used to define the moves executed inside the perturbation procedures. Therefore, it is recorded the number of times that each customer is moved during the local search. Since this information is continuously updated and changes in each iteration, the search is driven to potentially better regions of the solution space, and increases the chance of avoiding cycling, even when using deterministic perturbations. The performance of this algorithm was tested using a large set of benchmark problems and was compared with other algorithms, and the results show that it is very competitive.