Skip to main content

Ant Colonies Discover Knight’s Tours

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNAI,volume 3339)


In this paper we introduce an Ant Colony Optimisation (ACO) algorithm to find solutions for the well-known Knight’s Tour problem. The algorithm utilizes the implicit parallelism of ACO’s to simultaneously search for tours starting from all positions on the chessboard. We compare the new algorithm to a recently reported genetic algorithm, and to a depth-first backtracking search using Warnsdorff’s heuristic. The new algorithm is superior in terms of search bias and also in terms of the rate of finding solutions.

This is a preview of subscription content, access via your institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD   149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Murray, H.J.R.: History of Chess (1913)

    Google Scholar 

  2. Euler, L.: Mémoires de l’Academie Royale des Sciences et Belles Lettres. Année 15, 310–337 (1766)

    Google Scholar 

  3. Mordecki, E.: On the Number of Knight’s Tours. Pre-publicaciones de Matematica de la Universidad de la Republica, Uruguay, 2001/57 (2001),

  4. Löbbing, M., Wegener, I.: The Number of Knight’s Tours Equals 33,439,123,484,294 – Counting with Binary Decision Diagrams. Electronic Journal of Combinatorics 3(1), R5 (1996)

    Google Scholar 

  5. McKay, B.D.: Knight’s tours of an 8x8 chessboard, Tech. Rpt. TR-CS-97-03, Dept. Computer Science, Australian National University (1997)

    Google Scholar 

  6. Warnsdorff, H.C.: Des Rösselsprungs einfachste und allgemeinste Lösung. Schmalkalden (1823)

    Google Scholar 

  7. Gordon, V.S., Slocum, T.J.: The Knight’s Tour – Evolutionary vs. Depth-First Search. In: Proceedings of the Congress of Evolutionary Computation 2004 (CEC 2004), Portland, Oregon, pp. 1435–1440 (2004)

    Google Scholar 

  8. Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  9. Dorigo, M.: Optimization, Learning and Natural Algorithms. Ph.D.Thesis, Politecnico di Milano, Italy (in Italian) (1992)

    Google Scholar 

  10. Dorigo, M., Maniezzo, V., Colorni, A.: The Ant System: Optimization by a Colony of Cooperating Agents. IEEE Transactions on Systems, Man, and Cybernetics-Part B 26(1), 29–41 (1996)

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations


Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hingston, P., Kendall, G. (2004). Ant Colonies Discover Knight’s Tours. In: Webb, G.I., Yu, X. (eds) AI 2004: Advances in Artificial Intelligence. AI 2004. Lecture Notes in Computer Science(), vol 3339. Springer, Berlin, Heidelberg.

Download citation

  • DOI:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24059-4

  • Online ISBN: 978-3-540-30549-1

  • eBook Packages: Computer ScienceComputer Science (R0)