a particle swarm optimization method for periodic vehicle routing problem with pickup and delivery in transportation

in this article, multiple-product pvrp with pickup and delivery that is used widely in goods distribution or other service companies, especially by railways, was introduced. a mathematical formulation was provided for this problem. each product had a set of vehicles which could carry the product and pickup and delivery could simultaneously occur. to solve the problem, two meta-heuristic methods, both based on particle swarm optimization, were provided and ran for small and large class problems and their efficiency were demonstrated. also, efficiency of binary pso to general pso was tested and bpso was shown to outperform the general method. this approach can be used in railway transportation. key words: periodic vehicle routing, particle swarm optimization, binary particle swarm optimization, railway key words: periodic vehicle routing, particle swarm optimization, binary particle swarm optimization, railway key words: periodic vehicle routing, particle swarm optimization, binary particle swarm optimization, railway key words: periodic vehicle routing, particle swarm optimization, binary particle swarm optimization, railway