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This paper considers two additional factors of the widely researched vehicle routing problem with time windows (VRPTW). The two factors, which are very common characteristics in realworld, are uncertain number of vehicles and simultaneous delivery and pick-up service. Using minimization of the total transport costs as the objective of the extension VRPTW, a mathematic model is constructed. To solve the problem, an efficient multiswarm cooperative particle swarm optimization (MCPSO) algorithm is applied. And a new encoding method is proposed for the extension VRPTW. Finally, comparing with genetic algorithm (GA) and particle swarm optimization (PSO) algorithm, the MCPSO algorithm performs best for solving this problem.

Vehicle Routing Problem with Time Windows and Simultaneous Delivery and Pick-Up Service Based on MCPSO