Abstract: The purpose of the vehicle routing problem(VRP) is to search the service route of each vehicle,so as to minimize the sum of driving distances in the case of completing all of the distribution tasks.CVRP,a classical combinatorial optimization problem in operations research,belongs to NP-hard problem and has high theoretical significance and practical value.In order to solve this problem,a hybrid particle swarm optimization algorithm based on hierarchical learning and different evolution(DE-HSLPSO) is proposed.First,the hierarchical learning strategy is introduced and the population particles are divided into three layers according to their fitness values and number of iterations.Secondly,the social learning mechanism is introduced in the evolution of the first two layers of particles,while particles in the third layer carry out differential evolution which effectively increases the diversity of particles,thus expanding the space and jumping out of local optimal.Simulation experiment whose examples are taken from the classical CVRP data sets explores the impact of each part of DE-HSLPSO on the overall performance.It is found that both hierarchical strategy and differential evolution can improve the overall performance of the algorithm.In addition,DE-HSLPSO and other algorithms are tested on seven benchmark examples.With comprehensive comparison of time and optimal solution,the result shows that the solution performance of DE-HSLPSO is better than that of other algorithms.

Key words: Hierarchical learning, Social learning, Differential evolution, Particle swarm optimization algorithm, Capacitated vehicle routing problem