Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 104279, 11 pages
Research Article

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

College of Management, Shenzhen University, Shenzhen 518060, China

Received 19 April 2012; Accepted 6 June 2012

Academic Editor: Yuping Wang

Copyright © 2012 Xiaobing Gan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.