Computational Optimization and Applications

, Volume 45, Issue 3, pp 639–661 | Cite as

Continuous ant colony system and tabu search algorithms hybridized for global minimization of continuous multi-minima functions

  • Akbar Karimi
  • Hadi Nobahari
  • Patrick SiarryEmail author


A new hybrid optimization method, combining Continuous Ant Colony System (CACS) and Tabu Search (TS) is proposed for minimization of continuous multi-minima functions. The new algorithm incorporates the concepts of promising list, tabu list and tabu balls from TS into the framework of CACS. This enables the resultant algorithm to avoid bad regions and to be guided toward the areas more likely to contain the global minimum. New strategies are proposed to dynamically tune the radius of the tabu balls during the execution and also to handle the variable correlations. The promising list is also used to update the pheromone distribution over the search space. The parameters of the new method are tuned based on the results obtained for a set of standard test functions. The results of the proposed scheme are also compared with those of some recent ant based and non-ant based meta-heuristics, showing improvements in terms of accuracy and efficiency.


Ant colony optimization Tabu search Hybrid meta-heuristics Global optimization Continuous optimization 


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  1. 1.
    Glover, F.: Tabu search: Part I. ORSA J. Comput. 3, 190–206 (1989) MathSciNetGoogle Scholar
  2. 2.
    Glover, F.: Tabu search: Part II. ORSA J. Comput. 1, 4–32 (1990) Google Scholar
  3. 3.
    Hu, N.: Tabu search method with random moves for globally optimal design. Int. J. Numer. Methods Eng. 35, 1055–1070 (1992) CrossRefGoogle Scholar
  4. 4.
    Cvijovic, D., Klinowski, J.: Taboo search: an approach to the multiple minima problem. Science 667, 664–666 (1995) CrossRefMathSciNetGoogle Scholar
  5. 5.
    Battiti, R., Tecchiolli, G.: The continuous reactive tabu search: blending combinatorial optimization and stochastic search for global optimization. Ann. Oper. Res. 63, 53–188 (1996) CrossRefGoogle Scholar
  6. 6.
    Siarry, P., Berthiau, G.: Fitting of tabu search to optimize functions of continuous variables. Int. J. Numer. Methods Eng. 40, 2449–2457 (1997) CrossRefMathSciNetzbMATHGoogle Scholar
  7. 7.
    Chelouah, R., Siarry, P.: Enhanced continuous tabu search: an algorithm for the global optimization of multiminima functions. In: Voss, S., Martello, S., Osman, I.H., Roucairol, C. (eds.) Meta-Heuristics, Advances and Trends in Local Search Paradigms for Optimization, vol. 4, pp. 49–61. Kluwer Academic, Dordrecht (1999) Google Scholar
  8. 8.
    Chelouah, R., Siarry, P.: Tabu search applied to global optimization. Eur. J. Oper. Res. 123, 256–270 (2000) CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Dorigo, M.: Optimization, learning and natural algorithms. Ph.D. thesis, Univ. of Milan, Milan (1992) Google Scholar
  10. 10.
    Colorni, A., Dorigo, M., Maniezzo, V.: Distributed optimization by ant colonies. In: Proceedings of the First European Conference on Artificial Life, pp. 134–142. Elsevier, Amsterdam (1992) Google Scholar
  11. 11.
    Dorigo, M., Maniezzo, V., Colorni, A.: The ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. B 1, 29–41 (1996) CrossRefGoogle Scholar
  12. 12.
    Stutzle, T., Hoos, H.: The MAX–MIN ant system and local search for the traveling salesman problem. In: Proceedings of IEEE International Conference on Evolutionary Computation and Evolutionary Programming, pp. 309–314 (1997) Google Scholar
  13. 13.
    Dorigo, M., Gambardella, L.M.: Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans. Evol. Comput. 1, 53–66 (1997) CrossRefGoogle Scholar
  14. 14.
    Gambardella, L.M., Dorigo, M.: Ant-Q: a reinforcement learning approach to the traveling salesman problem. In: Proceedings of the Twelfth International Conference on Machine Learning, Palo Alto, pp. 252–260 (1995) Google Scholar
  15. 15.
    Costa, D., Hertz, A.: Ants can colour graphs. J. Oper. Res. Soc. 48, 295–305 (1997) zbMATHGoogle Scholar
  16. 16.
    Dorigo, M., Caro, G.D., Gambardella, L.M.: Ant algorithms for discrete optimization. Artif. Life 3, 137–172 (1999) CrossRefGoogle Scholar
  17. 17.
    Dorigo, M., Bonabeau, E., Theraulaz, G.: Ant algorithms and stigmergy. Future Gener. Comput. Syst. 16, 851–871 (2000) CrossRefGoogle Scholar
  18. 18.
    Wodrich, M., Bilchev, G.: Cooperative distributed search: the ants’ way. Control Cybern. 26(3), 413–445 (1997) MathSciNetzbMATHGoogle Scholar
  19. 19.
    Bilchev, G., Parmee, I.C.: The ant colony metaphor for searching continuous design spaces. Lect. Notes Comput. Sci. 993, 25–39 (1995) Google Scholar
  20. 20.
    Monmarché, N., Venturini, G., Slimane, M.: On how Pachycondyla apicalis ants suggest a new search algorithm. Future Gener. Comput. Syst. 16, 937–946 (2000) CrossRefGoogle Scholar
  21. 21.
    Dréo, J., Siarry, P.: Continuous interacting ant colony algorithm based on dense heterarchy. Future Gener. Comput. Syst. 20, 841–856 (2004) CrossRefGoogle Scholar
  22. 22.
    Dréo, J., Siarry, P.: A new ant colony algorithm using the heterarchical concept aimed at optimization of multi-minima continuous functions. Lect. Notes Comput. Sci. 2463, 216–221 (2002) CrossRefGoogle Scholar
  23. 23.
    Ling, C., Jie, S., Ling, O., Hongjian, C.: A method for solving optimization problems in continuous space using ant colony algorithm. Lect. Notes Comput. Sci. 2463, 288–289 (2002) CrossRefGoogle Scholar
  24. 24.
    Jun, L.Y., Jun, W.T.: An adaptive ant colony system algorithm for continuous-space optimization problems. J. Zhejiang Univ. Sci. 1, 40–46 (2003) Google Scholar
  25. 25.
    Pourtakdoust, S.H., Nobahari, H.: An extension of ant colony system to continuous optimization problems. Lect. Notes Comput. Sci. 3172, 294–301 (2004) CrossRefGoogle Scholar
  26. 26.
    Socha, K.: ACO for continuous and mixed-variable optimization. Lect. Notes Comput. Sci. 3172, 25–36 (2004) CrossRefGoogle Scholar
  27. 27.
    Socha, K., Dorigo, M.: Ant colony optimization for continuous domains. IRIDIA Technical Report, TR/IRIDIA/2005-037 Google Scholar
  28. 28.
    Socha, K., Dorigo, M.: Ant colony optimization for continuous domains. Eur. J. Oper. Res. 185, 1155–1173 (2008) CrossRefMathSciNetzbMATHGoogle Scholar
  29. 29.
    Nobahari, H., Pourtakdoust, S.H.: Optimization of fuzzy rule bases using continuous ant colony system. In: Proceedings of the First International Conference on Modeling, Simulation and Applied Optimization, Sharjah, U.A.E., Paper No. 243 (2005) Google Scholar
  30. 30.
    Nobahari, H., Pourtakdoust, S.H.: Optimal fuzzy CLOS guidance law design using ant colony optimization. Lect. Notes Comput. Sci. 3777, 95–106 (2005) CrossRefGoogle Scholar
  31. 31.
    Nobahari, H., Nabavi, S.Y., Pourtakdoust, S.H.: Aerodynamic shape optimization of unguided projectiles using ant colony optimization. In: Proceedings of ICAS 2006, Hamburg, Germany, 3–8 Sept. 2006 Google Scholar
  32. 32.
    Chelouah, R., Siarry, P.: A continuous genetic algorithm designed for the global optimization of multimodal functions. J. Heuristics 6, 191–213 (2000) CrossRefzbMATHGoogle Scholar
  33. 33.
    Siarry, P., Berthiau, G., Durbin, F., Haussy, J.: Enhanced simulated annealing for globally minimizing functions of many continuous variables. ACM Trans. Math. Softw. 23(2), 209–228 (1997) CrossRefMathSciNetzbMATHGoogle Scholar
  34. 34.
    Chelouah, R., Siarry, P.: Genetic and Nelder–Mead algorithms hybridized for a more accurate global optimization of continuous multiminima functions. Eur. J. Oper. Res. 148, 335–348 (2003) CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringSharif University of TechnologyTehranIran
  2. 2.Laboratoire Images, Signaux et Systèmes Intelligents (LiSSi)Université Paris 12 Val-de-MarneCréteilFrance

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