A Direct Application of Ant Colony Optimization to Function Optimization Problem in Continuous Domain

  • Min Kong
  • Peng Tian
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4150)


This paper proposes a direct application of Ant Colony Optimization to the function optimization problem in continuous domain. In the proposed algorithm, artificial ants construct solutions by selecting values for each variable randomly biased by a specific variable-related normal distribution, of which the mean and deviation values are represented by pheromone modified by ants according to the previous search experience. Some methods to avoid premature convergence, such as local search in different neighborhood structure, pheromone re-initialization and different solutions for pheromone intensification are incorporated into the proposed algorithm. Experimental setting of the parameters are presented, and the experimental results show the potential of the proposed algorithm in dealing with the function optimization problem of different characteristics.


Local Search Premature Convergence Continuous Domain Global Good Solution Function Optimization Problem 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Oxford University Press, Oxford (1999)MATHGoogle Scholar
  2. 2.
    Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)CrossRefMATHGoogle Scholar
  3. 3.
    Bilchev, G., Parmee, I.: The ant colony metaphor for searching continuous design spaces. In: Fogarty, T.C. (ed.) AISB-WS 1995. LNCS, vol. 993, pp. 25–39. Springer, Heidelberg (1995)Google Scholar
  4. 4.
    Bilchev, G., Parmee, I.: Constrained optimization with an ant colony search model. In: 2nd International Conference on Adaptive Computing in Engineering Design and Control, pp. 26–28 (1996)Google Scholar
  5. 5.
    Mathur, M., Karale, S., Priye, S., Jyaraman, V., Kulkarni, B.: Ant colony approach to continuous function optimization. Ind. Eng. Chem. Res. 39(10), 3814–3822 (2000)CrossRefGoogle Scholar
  6. 6.
    Wodrich, M., Bilchev, G.: Cooperative distributed search: the ant’s way. Control & Cybernetics 3, 413–446 (1997)MathSciNetGoogle Scholar
  7. 7.
    Monmarche, N., Venturini, G., Slimane, M.: On how pachycondyla apicalis ants suggest a new search algorithm. Future Generation Computer Systems 16(8), 937–946 (2000)CrossRefGoogle Scholar
  8. 8.
    Dréo, J., Siarry, P.: A new ant colony algorithm using the heterarchical concept aimed at optimization of multiminima continuous functions. In: Dorigo, M., Di Caro, G.A., Sampels, M. (eds.) Ant Algorithms 2002. LNCS, vol. 2463, pp. 216–221. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Dreo, J., Siarry, P.: Continuous interacting ant colony algorithm based on dense heterarchy. Future Generation Computer Systems 20(5), 841–856 (2004)CrossRefGoogle Scholar
  10. 10.
    Socha, K.: Aco for continuous and mixed variable optimization. In: Dorigo, M., Birattari, M., Blum, C., Gambardella, L.M., Mondada, F., Stützle, T. (eds.) ANTS 2004. LNCS, vol. 3172, pp. 25–36. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Kong, M., Tian, P.: A binary ant colony optimization for the unconstrained function optimization problem. In: Hao, Y., Liu, J., Wang, Y.-P., Cheung, Y.-m., Yin, H., Jiao, L., Ma, J., Jiao, Y.-C. (eds.) CIS 2005. LNCS (LNAI), vol. 3801, pp. 682–687. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Blum, C., Dorigo, M.: The hyper-cube framework for ant colony optimization. IEEE Transactions on Systems, Man and Cybernetics, Part B 34(2), 1161–1172 (2004)CrossRefGoogle Scholar
  13. 13.
    Chelouah, R., Siarry, P.: A continuous genetic algorithm designed for the global optimization of multimodal functions. Journal of Heuristics 6, 191–213 (2000)CrossRefMATHGoogle Scholar
  14. 14.
    Chelouah, R., Siarry, P.: Enhanced continuous tabu search. In: Voss, S., Martello, S., Osman, I., Roucairol, C. (eds.) Meta-heuristics: advances and trends in local search paradigms for optimization, ch. 4, pp. 49–61. Kluwer Academic Publishers, Dordrecht (1999)Google Scholar
  15. 15.
    Siarry, P., Berthiau, G., Durbin, F., Haussy, J.: Enhanced simulated annealing for globally minimizing functions of many continuous variables. ACM Transactions on Mathematical Software 23(2), 209–228 (1997)CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Min Kong
    • 1
  • Peng Tian
    • 1
  1. 1.Shanghai Jiaotong UniversityShanghaiChina

Personalised recommendations