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Mathematical Problems in Engineering
Volume 2011, Article ID 750968, 18 pages
Research Article

A Data-Guided Lexisearch Algorithm for the Asymmetric Traveling Salesman Problem

Department of Computer Science, Al-Imam Muhammad Ibn Saud Islamic University, P.O. Box 5701, Riyadh 11432, Saudi Arabia

Received 23 October 2010; Revised 15 March 2011; Accepted 26 April 2011

Academic Editor: Tamas Kalmar-Nagy

Copyright © 2011 Zakir Hussain Ahmed. 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.


A simple lexisearch algorithm that uses path representation method for the asymmetric traveling salesman problem (ATSP) is proposed, along with an illustrative example, to obtain exact optimal solution to the problem. Then a data-guided lexisearch algorithm is presented. First, the cost matrix of the problem is transposed depending on the variance of rows and columns, and then the simple lexisearch algorithm is applied. It is shown that this minor preprocessing of the data before the simple lexisearch algorithm is applied improves the computational time substantially. The efficiency of our algorithms to the problem against two existing algorithms has been examined for some TSPLIB and random instances of various sizes. The results show remarkably better performance of our algorithms, especially our data-guided algorithm.