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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.

The Vehicle Routing Problem with Time Windows (VRPTW) is a well-known and complex combinatorial problem. The static version of this problem has received special attention in last years. However, the most real world vehicle routing problems are dynamic, where information relevant to the routing can change after the initial routes have been constructed. The common approach in this scenario is restart the algorithm when novel information arrives, but his type of restart methods does not use the memory to improve the quality of the final result. In this paper, the hybrid CGH Column Generation Heuristic (Alvarenga et al. 2005) is modified in order to use the routes generated during the optimization process.

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The Vehicle Routing Problem with Time Windows (VRPTW) is a well-known and complex combinatorial problem, which has received considerable attention in recent years. The VRPTW benchmark problems of Solomon (1987) have been most commonly chosen to evaluate and compare all exact and heuristic algorithms. A genetic algorithm and a set partitioning two phases approach has obtained competitive results in terms of total travel distance minimization. However, a great number of heuristics has used the number of vehicles as the first objective and travel distance as the second, subject to the first. This paper proposes a three phases approach considering both objectives. Initially, a hierarchical tournament selection genetic algorithm is applied. It can reach all best results in number of vehicles of the 56 Solomon's problems explored in the literature. After then, the two phase approach, the genetic and the set partitioning, is applied to minimize the travel distance as the second objective.