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Entropy 2013, 15(4), 1247-1270; doi:10.3390/e15041247
Article

A Hybrid Chaos-Particle Swarm Optimization Algorithm for the Vehicle Routing Problem with Time Window

1,2,* , 1
,
1
,
1
 and
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1 School of Computer, Wuhan University, Wuhan City, Hubei Province 430072, China 2 State Key Laboratory of Software Engineering, Wuhan University, Wuhan City, Hubei Province 430072, China
* Author to whom correspondence should be addressed.
Received: 11 January 2013 / Revised: 13 March 2013 / Accepted: 1 April 2013 / Published: 9 April 2013
Download PDF [276 KB, 24 February 2015; original version 24 February 2015]

Abstract

State-of-the-art heuristic algorithms to solve the vehicle routing problem with time windows (VRPTW) usually present slow speeds during the early iterations and easily fall into local optimal solutions. Focusing on solving the above problems, this paper analyzes the particle encoding and decoding strategy of the particle swarm optimization algorithm, the construction of the vehicle route and the judgment of the local optimal solution. Based on these, a hybrid chaos-particle swarm optimization algorithm (HPSO) is proposed to solve VRPTW. The chaos algorithm is employed to re-initialize the particle swarm. An efficient insertion heuristic algorithm is also proposed to build the valid vehicle route in the particle decoding process. A particle swarm premature convergence judgment mechanism is formulated and combined with the chaos algorithm and Gaussian mutation into HPSO when the particle swarm falls into the local convergence. Extensive experiments are carried out to test the parameter settings in the insertion heuristic algorithm and to evaluate that they are corresponding to the data’s real-distribution in the concrete problem. It is also revealed that the HPSO achieves a better performance than the other state-of-the-art algorithms on solving VRPTW.
Keywords: VRPTW; PSO; chaos algorithm; insertion heuristic algorithm; Gaussian mutation VRPTW; PSO; chaos algorithm; insertion heuristic algorithm; Gaussian mutation
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.

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Hu, W.; Liang, H.; Peng, C.; Du, B.; Hu, Q. A Hybrid Chaos-Particle Swarm Optimization Algorithm for the Vehicle Routing Problem with Time Window. Entropy 2013, 15, 1247-1270.

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