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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 726564, 17 pages
Research Article

A Hybrid Algorithm Based on ACO and PSO for Capacitated Vehicle Routing Problems

Department of Information Management, Tatung University, 40 Chungshan N. Road, Sec. 3, Taipei 104, Taiwan

Received 24 February 2012; Revised 5 May 2012; Accepted 8 May 2012

Academic Editor: Jung-Fa Tsai

Copyright © 2012 Yucheng Kao 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 vehicle routing problem (VRP) is a well-known combinatorial optimization problem. It has been studied for several decades because finding effective vehicle routes is an important issue of logistic management. This paper proposes a new hybrid algorithm based on two main swarm intelligence (SI) approaches, ant colony optimization (ACO) and particle swarm optimization (PSO), for solving capacitated vehicle routing problems (CVRPs). In the proposed algorithm, each artificial ant, like a particle in PSO, is allowed to memorize the best solution ever found. After solution construction, only elite ants can update pheromone according to their own best-so-far solutions. Moreover, a pheromone disturbance method is embedded into the ACO framework to overcome the problem of pheromone stagnation. Two sets of benchmark problems were selected to test the performance of the proposed algorithm. The computational results show that the proposed algorithm performs well in comparison with existing swarm intelligence approaches.