Hierarchical tournament selection genetic algorithm 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. 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.