Finding Near Optimal Solutions for Vehicle Routing Problems with Time Windows using Hybrid Genetic Algorithm

The Vehicle Routing Problem with Time Windows (VRPTW) is a well-know and complex combinatorial problem, which has received considerable attention in recent years. This problem has been addressed using many different techniques including both exact and heuristic methods. The VRPTW benchmark problems of Solomon (1987) have been most commonly chosen to evaluate and to compare all solutions proposed in the literature. Results from exact methods have been improved considerably because of parallel implementations and modern branch-and-cut techniques. However, 25 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. Unfortunately, while all publications on exact methods have considered the total traveled distance as their main objective, almost all of the heuristic attempts have considered the total number of vehicles as their main objective. Consequently, it is more difficult to compare and to take advantage of the strong points from each approach. With travelled distance as the main objective, this paper proposes a robust heuristic approach for the VRPTW problem using an efficient Genetic Algorithm and a MIP formulation. With this innovative approach it is possible to compare the results with the exact methods published. Additionally, computational results show that the heuristic approach proposed here outperforms all previously known heuristic methods published, in terms of minimization of traveled distance.