A two-phase genetic and set partitioning approach for the vehicle routing problem with time windows

The vehicle routing problem with time windows (VRPTW) is a well-known and complex combinatorial problem, which has received considerable attention in recent years. Results from exact methods have been improved exploring parallel implementations and modern branch-and-cut techniques. However, 23 out of the 56 high order instances from Solomon´s test set still remain unsolved. Additionally, in many cases a prohibitive time is needed to find the exact solution. Many efficient heuristic methods have been developed to make possible a good solution in a reasonable amount of time. Using travel distance as the main objective, this paper proposes a robust heuristic approach for the VRPTW using an efficient genetic algorithm and a set partitioning formulation. The tests were produced using both real numbers and truncated data type, making it possible to compare the results with previous heuristic and exact methods published. Furthermore, computational results show that the proposed heuristic approach outperforms all previous known heuristic methods in the literature, in terms of the minimal travel distance.