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Mathematical Problems in Engineering
Volume 2015, Article ID 165476, 11 pages
http://dx.doi.org/10.1155/2015/165476
Research Article

A Problem-Reduction Evolutionary Algorithm for Solving the Capacitated Vehicle Routing Problem

Wanfeng Liu1,2 and Xia Li1,2

1College of Information Engineering, Shenzhen University, Shenzhen 518060, China
2Shenzhen Key Lab of Communication and Information Processing, Shenzhen 518060, China

Received 30 April 2014; Accepted 13 October 2014

Academic Editor: Pandian Vasant

Copyright © 2015 Wanfeng Liu and Xia Li. 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.

Abstract

Assessment of the components of a solution helps provide useful information for an optimization problem. This paper presents a new population-based problem-reduction evolutionary algorithm (PREA) based on the solution components assessment. An individual solution is regarded as being constructed by basic elements, and the concept of acceptability is introduced to evaluate them. The PREA consists of a searching phase and an evaluation phase. The acceptability of basic elements is calculated in the evaluation phase and passed to the searching phase. In the searching phase, for each individual solution, the original optimization problem is reduced to a new smaller-size problem. With the evolution of the algorithm, the number of common basic elements in the population increases until all individual solutions are exactly the same which is supposed to be the near-optimal solution of the optimization problem. The new algorithm is applied to a large variety of capacitated vehicle routing problems (CVRP) with customers up to nearly 500. Experimental results show that the proposed algorithm has the advantages of fast convergence and robustness in solution quality over the comparative algorithms.