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Mathematical Problems in Engineering
Volume 2012, Article ID 879614, 19 pages
Research Article

Multiobjective Quantum Evolutionary Algorithm for the Vehicle Routing Problem with Customer Satisfaction

1College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310014, China
2College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310014, China
3Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

Received 20 August 2012; Accepted 10 October 2012

Academic Editor: Sheng-yong Chen

Copyright © 2012 Jingling Zhang 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.


The multiobjective vehicle routing problem considering customer satisfaction (MVRPCS) involves the distribution of orders from several depots to a set of customers over a time window. This paper presents a self-adaptive grid multi-objective quantum evolutionary algorithm (MOQEA) for the MVRPCS, which takes into account customer satisfaction as well as travel costs. The degree of customer satisfaction is represented by proposing an improved fuzzy due-time window, and the optimization problem is modeled as a mixed integer linear program. In the MOQEA, nondominated solution set is constructed by the Challenge Cup rules. Moreover, an adaptive grid is designed to achieve the diversity of solution sets; that is, the number of grids in each generation is not fixed but is automatically adjusted based on the distribution of the current generation of nondominated solution set. In the study, the MOQEA is evaluated by applying it to classical benchmark problems. Results of numerical simulation and comparison show that the established model is valid and the MOQEA is effective for MVRPCS.