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An Analysis of Problem Difficulty for a Class of Optimisation Heuristics

  • Enda Ridge
  • Daniel Kudenko
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4446)

Abstract

This paper investigates the effect of the cost matrix standard deviation of Travelling Salesman Problem (TSP) instances on the performance of a class of combinatorial optimisation heuristics. Ant Colony Optimisation (ACO) is the class of heuristic investigated. Results demonstrate that for a given instance size, an increase in the standard deviation of the cost matrix of instances results in an increase in the difficulty of the instances. This implies that for ACO, it is insufficient to report results on problems classified only by problem size, as has been commonly done in most ACO research to date. Some description of the cost matrix distribution is also required when attempting to explain and predict the performance of these algorithms on the TSP.

Keywords

Problem Instance Travelling Salesperson Problem Cost Matrix Optimisation Heuristic Instance Size 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Applegate, D., Bixby, R., Chvatal, V., Cook, W.: Implementing the Dantzig-Fulkerson-Johnson algorithm for large traveling salesman problems. Mathematical Programming Series B97(1-2), 91–153 (2003)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Cheeseman, P., Kanefsky, B., Taylor, W.M.: Where the Really Hard Problems Are. In: Proceedings of the Twelfth International Conference on Artificial Intelligence, vol. 1, pp. 331–337. Morgan Kaufmann Publishers, San Francisco (1991)Google Scholar
  3. 3.
    Dorigo, M., Gambardella, L.M.: Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem. IEEE Transactions on Evolutionary Computation 1(1), 53–66 (1997)CrossRefGoogle Scholar
  4. 4.
    Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)zbMATHGoogle Scholar
  5. 5.
    Fischer, T., Stützle, T., Hoos, H., Merz, P.: An Analysis Of The Hardness Of TSP Instances For Two High Performance Algorithms. In: Proceedings of the Sixth Metaheuristics International Conference, pp. 361–367 (2005)Google Scholar
  6. 6.
    Helsgaun, K.: An effective implementation of the Lin-Kernighan traveling salesman heuristic. European Journal of Operational Research 126(1), 106–130 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Johnson, D.S.: A Theoretician’s Guide to the Experimental Analysis of Algorithms. In: Goldwasser, Johnson, and McGeoch (eds.) Proceedings of the Fifth and Sixth DIMACS Implementation Challenges, pp. 215–250. American Mathematical Society (2002) Google Scholar
  8. 8.
    Montgomery, D.C.: Design and Analysis of Experiments, 6th edn. John Wiley and Sons Inc., New York (2005)zbMATHGoogle Scholar
  9. 9.
    Stützle, T., Hoos, H.H.: Max-Min Ant System. Future Generation Computer Systems 16(8), 889–914 (2000)CrossRefGoogle Scholar
  10. 10.
    van Hemert, J.I.: Property Analysis of Symmetric Travelling Salesman Problem Instances Acquired Through Evolution. In: Raidl, G.R., Gottlieb, J. (eds.) EvoCOP 2005. LNCS, vol. 3448, pp. 122–131. Springer, Heidelberg (2005)Google Scholar
  11. 11.
    Zlochin, M., Dorigo, M.: Model based search for combinatorial optimization: A comparative study. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) Parallel Problem Solving from Nature - PPSN VII. LNCS, vol. 2439, pp. 651–661. Springer, Heidelberg (2002)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Enda Ridge
    • 1
  • Daniel Kudenko
    • 1
  1. 1.Department of Computer Science, The University of York, York YO10 5DDEngland

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