Copyright Statement: This is an open access article licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, even commercially as long as the original work is properly cited.
Digital Object Identifier (DOI) : 10.14569/IJACSA.2014.050110
Article Published in International Journal of Advanced Computer Science and Applications(IJACSA), Volume 5 Issue 1, 2014.
Abstract: The Traveling Salesman Problem (TSP) is the problem of finding the shortest path passing through all given cities while only passing by each city once and finishing at the same starting city. This problem has NP-hard complexity making it extremely impractical to get the most optimal path even for problems as small as 20 cities since the number of permutations becomes too high. Many heuristic methods have been devised to reach “good” solutions in reasonable time. In this paper, we present the idea of utilizing a spatial “geographical” Divide and Conquer technique in conjunction with heuristic TSP algorithms specifically the Nearest Neighbor 2-opt algorithm. We have found that the proposed algorithm has lower complexity than algorithms published in the literature. This comes at a lower accuracy expense of around 9%. It is our belief that the presented approach will be welcomed to the community especially for large problems where a reasonable solution could be reached in a fraction of the time.
Hoda A. Darwish and Ihab Talkhan, “Reduced Complexity Divide and Conquer Algorithm for Large Scale TSPs” International Journal of Advanced Computer Science and Applications(IJACSA), 5(1), 2014. http://dx.doi.org/10.14569/IJACSA.2014.050110