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Journal of Optimization
Volume 2016, Article ID 4786268, 15 pages
Research Article

Introducing Complexity Curtailing Techniques for the Tour Construction Heuristics for the Travelling Salesperson Problem

1School of Mathematical and Computer Sciences, Heriot Watt University, Edinburgh EH14 4AS, UK
2Route Monkey Ltd., Livingston EH54 5DW, UK

Received 22 March 2016; Revised 23 May 2016; Accepted 8 June 2016

Academic Editor: Ling Wang

Copyright © 2016 Ziauddin Ursani and David W. Corne. 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.


In this paper, complexity curtailing techniques are introduced to create faster version of insertion heuristics, that is, cheapest insertion heuristic (CIH) and largest insertion heuristic (LIH), effectively reducing their complexities from to with no significant effect on quality of solution. This paper also examines relatively not very known heuristic concept of max difference and shows that it can be culminated into a full-fledged max difference insertion heuristic (MDIH) by defining its missing steps. Further to this the paper extends the complexity curtailing techniques to MDIH to create its faster version. The resultant heuristic, that is, fast max difference insertion heuristic (FMDIH), outperforms the “farthest insertion” heuristic (FIH) across a wide spectrum of popular datasets with statistical significance, even though both the heuristics have the same worst case complexity of . It should be noted that FIH is considered best among lowest order complexity heuristics. The complexity curtailing techniques presented here open up the new area of research for their possible extension to other heuristics.