A hybridization of granular adaptive tabu search with path relinking for the multi-depot open vehicle routing problem

The multi-depot open vehicle routing problem (MDOVRP) differs from the classical VRP in that there is more than one depot and the vehicle does not need to return to a depot after serving the last customer. For solving this challenging problem, we propose a hybrid metaheuristic algorithm (GATS-PR) which integrates the granular adaptive tabu search with path relinking. The main contributions of this work consist of introducing a solution-based tabu search technique in granular tabu search, designing an adaptive neighborhood selection method for the large neighborhoods with 22 kinds of move types, and adopting path relinking with a new similarity definition to the MDOVRP for the first time. Computational results on 24 public instances demonstrate that GATS-PR outperforms the previous state-of-the-art algorithms in the literature. Specifically, GATS-PR improved and matched the previous best known results on 4 and 19 instances, respectively.