A hybrid algorithm between the ant system and the harmonic search for solving the vehicle routing problem with time windows (VRP-TW).

In this paper, we present a hybrid method between the Ant System (AS) and the Harmonic Search (HS), which was used to solve vehicle routing problem with time-windows (VRP-TW). This method has been called AS-HS. In this sense, both metaheuristics are intertwined. The AS technique guides the behavior through changes in the pheromone matrix, and takes advantage of information from a number of HS executions stored in the harmonic memory (HM). In the proposed procedure, the best solutions are taken to update the pheromone level. This allows the ants to intensify in a promising region and the elements of diversity in the techniques avoid the premature convergence of the algorithm.   On the other hand, for a more efficient construction of the solutions, we took advantage of the structure of the problem that used the time window, the distance between the customers to visit and the load assigned to each vehicle as factors within the update of the pheromone level.