A reactive variable neighborhood search for the vehicle-routing problem with time windows

The purpose of this paper is to present a new deterministic metaheuristic based on a modification of the variable neighborhood search of Mladenovic & Hansen for solving the vehicle-routing problem with time windows. Results are reported for the standard 100, 200, and 400 customer data sets by Solomon and Gehring & Homberger, and two real-life problems by Russell. The findings indicate that the proposed procedure outperforms other recent local searches and metaheuristics. In addition, four new best-known solutions were obtained. The proposed procedure is based on a new four-phase approach. In this approach an initial solution is first created using new route-construction heuristics followed by a route-elimination procedure to improve the solutions regarding the number of vehicles. In the third phase the solutions are improved in terms of total traveled distance using four new local-search procedures proposed in this paper. Finally, in phase four, the best solution obtained is improved by modifying the objective function to escape from a local minimum.