A particle swarm optimization algorithm with crossover for vehicle routing problem with time windows

The vehicle routing problem (VRP) is a very important combinatorial optimization and nonlinear programming problem in the fields of transportation, distribution and logistics. In this paper, a particle swarm optimization (PSO) algorithm with crossover for VRP is proposed. The PSO algorithm combined with the crossover operation of genetic algorithm (GA) can avoid being trapped in local optimum due to using probability searching. We apply the proposed algorithm to an example of VRP, and compare its result with those generated by PSO, GA, and parallel PSO algorithms. The experimental comparison result demonstrates that the performance of PSO algorithm with crossover is competitive with others and will be an effective method for solving discrete combinatory problems.