A hybrid generational genetic algorithm for the periodic vehicle routing problem with time windows

We propose a new population-based hybrid meta-heuristic for the periodic vehicle routing problem with time windows. This meta-heuristic is a generational genetic algorithm that uses two neighborhood-based meta-heuristics to optimize offspring. Local search methods have previously been proposed to enhance the fitness of offspring generated by crossover operators. In the proposed method, neighborhood-based meta-heuristics are used for their capacity to escape local optima, and deliver optimized and diversified solutions to the population of the next generation. Furthermore, the search performed by the neighborhood-based meta-heuristics repairs most of the constraint violations that naturally occur after the application of the crossover operators. The genetic algorithm we propose introduces two new crossover operators addressing the periodic vehicle routing problem with time windows. The two crossover operators are seeking the diversification of the exploration in the solution space from solution recombination, while simultaneously aiming not to destroy information about routes in the population as computing routes is NP-hard. Extensive numerical experiments and comparisons with all methods proposed in the literature show that the proposed methodology is highly competitive, providing new best solutions for a number of large instances.