A Method for Avoiding the Feedback Searching Bias in Ant Colony Optimization

  • Bolun Chen
  • Ling Chen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7331)


One of the obstacles in applying ant colony optimization (ACO) to the combinatorial optimization is that the search process is sometimes biased by algorithm features such as the pheromone model and the solution construction process. Due to such searching bias, ant colony optimization cannot converge to the optimal solution for some problems. In this paper, we define a new type of searching bias in ACO named feedback bias taking the k-cardinality tree problem as the test instance. We also present a method for avoiding the feedback searching bias. Convergence analysis of our method is also given. Experimental results confirm the correctness of our analysis and show that our method can effectively avoid the searching bias and can ensure the convergence for the problem.


ant colony optimization deceptive problems K-cardinality tree problem solution convergence 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press (2004)Google Scholar
  2. 2.
    Dorigo, M., Blum, C.: Ant colony optimization theory: A survey. Theoretical Computer Science 344, 243–278 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Blum, C.: Ant colony optimization: Introduction and recent trends. Physics of Life Reviews 2, 353–373 (2005)CrossRefGoogle Scholar
  4. 4.
    Shtovba, S.: Ant Algorithms: Theory and Applications. Programming and Computer Software 31, 167–178 (2005)zbMATHCrossRefGoogle Scholar
  5. 5.
    Blum, C., Sampels, M.: Ant colony optimization for FOP shop scheduling: A case study on different pheromone representation. In: Proceedings of Congress on Evolutionary Computation 2002, vol. 2, pp. 1558–1563 (2002)Google Scholar
  6. 6.
    Blum, C., Sampels, M.: When Model Bias Is Stronger than Selection Pressure. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) PPSN VII 2002. LNCS, vol. 2439, pp. 893–902. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Merkle, D., Middendorf, M.: Modeling the dynamics of ant colony optimization algorithms. Evolutionary Computation 10(3), 235–262 (2002)CrossRefGoogle Scholar
  8. 8.
    Merkle, D., Middendorf, M.: Modelling ACO: Composed Permutation Problems. In: Dorigo, M., Di Caro, G.A., Sampels, M. (eds.) ANTS 2002. LNCS, vol. 2463, pp. 149–162. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Montgomery, J., Randall, M., Hendtlass, T.: Solution bias in ant colony optimization: Lessons for selecting pheromone models. Computers and Operations Research 35(9), 2728–2749 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Montgomery, J., Randall, M., Hendtlass, T.: Structural Advantages for Ant Colony Optimisation Inherent in Permutation Scheduling Problems. In: Ali, M., Esposito, F. (eds.) IEA/AIE 2005. LNCS (LNAI), vol. 3533, pp. 218–228. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Chen, L., Sun, H., Wang, S.: First Order Deceptive Problem of ACO and Its Performance Analysis. Journal of Networks 4(10), 993–1000 (2009)CrossRefGoogle Scholar
  12. 12.
    Blum, C., Dorigo, M.: Deception in Ant Colony Optimization. In: Dorigo, M., Birattari, M., Blum, C., Gambardella, L.M., Mondada, F., Stützle, T. (eds.) ANTS 2004. LNCS, vol. 3172, pp. 118–129. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Blum, C., Dorigo, M.: Search bias in ant colony optimization: on the role of competition-balanced systems. IEEE Transactions on Evolutionary Computation 9, 159–174 (2005)CrossRefGoogle Scholar
  14. 14.
    Gutjahr, W.J.: A Graph-based Ant System and its convergence. Future Generation Computer Systems 16, 873–888 (2000)CrossRefGoogle Scholar
  15. 15.
    Gutjahr, W.J.: ACO algorithms with guaranteed convergence to the optimal solution. Info. Processing Lett. 82, 145–153 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Stützle, T., Dorigo, M.: A Short Convergence Proof for a Class of Ant Colony Optimization Algorithms. IEEE Transactions on Evolutionary Computation 6, 358–365 (2002)CrossRefGoogle Scholar
  17. 17.
    Blum, C., Dorigo, M.: The hypercube framework for ant colony optimization. IEEE Transaction on Systems, Man, and Cybernetics—Part B 43, 1161–1172 (2004)CrossRefGoogle Scholar
  18. 18.
    Blum, C.: Theoretical and practical aspects of ant colony optimization. Dissertations in Artificial Intelligence, vol. 2463. Akademische Verlagsgesellschaft Aka CmbH, Berlin (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bolun Chen
    • 1
  • Ling Chen
    • 1
    • 2
  1. 1.Department of Computer ScienceYangzhou UniversityYangzhouChina
  2. 2.State Key Lab of Novel Software TechNanjing UniversityNanjingChina

Personalised recommendations