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

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Abstract

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.

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References

  1. Glover, F.: Tabu search: Part I. ORSA J. Comput. 3, 190–206 (1989)

    MathSciNet  Google Scholar 

  2. Glover, F.: Tabu search: Part II. ORSA J. Comput. 1, 4–32 (1990)

    Google Scholar 

  3. Hu, N.: Tabu search method with random moves for globally optimal design. Int. J. Numer. Methods Eng. 35, 1055–1070 (1992)

    Article  Google Scholar 

  4. Cvijovic, D., Klinowski, J.: Taboo search: an approach to the multiple minima problem. Science 667, 664–666 (1995)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  6. Siarry, P., Berthiau, G.: Fitting of tabu search to optimize functions of continuous variables. Int. J. Numer. Methods Eng. 40, 2449–2457 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  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. Chelouah, R., Siarry, P.: Tabu search applied to global optimization. Eur. J. Oper. Res. 123, 256–270 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dorigo, M.: Optimization, learning and natural algorithms. Ph.D. thesis, Univ. of Milan, Milan (1992)

  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. 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)

    Article  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  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)

  15. Costa, D., Hertz, A.: Ants can colour graphs. J. Oper. Res. Soc. 48, 295–305 (1997)

    MATH  Google Scholar 

  16. Dorigo, M., Caro, G.D., Gambardella, L.M.: Ant algorithms for discrete optimization. Artif. Life 3, 137–172 (1999)

    Article  Google Scholar 

  17. Dorigo, M., Bonabeau, E., Theraulaz, G.: Ant algorithms and stigmergy. Future Gener. Comput. Syst. 16, 851–871 (2000)

    Article  Google Scholar 

  18. Wodrich, M., Bilchev, G.: Cooperative distributed search: the ants’ way. Control Cybern. 26(3), 413–445 (1997)

    MathSciNet  MATH  Google Scholar 

  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. Monmarché, N., Venturini, G., Slimane, M.: On how Pachycondyla apicalis ants suggest a new search algorithm. Future Gener. Comput. Syst. 16, 937–946 (2000)

    Article  Google Scholar 

  21. Dréo, J., Siarry, P.: Continuous interacting ant colony algorithm based on dense heterarchy. Future Gener. Comput. Syst. 20, 841–856 (2004)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. Pourtakdoust, S.H., Nobahari, H.: An extension of ant colony system to continuous optimization problems. Lect. Notes Comput. Sci. 3172, 294–301 (2004)

    Article  Google Scholar 

  26. Socha, K.: ACO for continuous and mixed-variable optimization. Lect. Notes Comput. Sci. 3172, 25–36 (2004)

    Article  Google Scholar 

  27. Socha, K., Dorigo, M.: Ant colony optimization for continuous domains. IRIDIA Technical Report, TR/IRIDIA/2005-037

  28. Socha, K., Dorigo, M.: Ant colony optimization for continuous domains. Eur. J. Oper. Res. 185, 1155–1173 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  30. Nobahari, H., Pourtakdoust, S.H.: Optimal fuzzy CLOS guidance law design using ant colony optimization. Lect. Notes Comput. Sci. 3777, 95–106 (2005)

    Article  Google Scholar 

  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

  32. Chelouah, R., Siarry, P.: A continuous genetic algorithm designed for the global optimization of multimodal functions. J. Heuristics 6, 191–213 (2000)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Aerospace Engineering, Sharif University of Technology, P.O. Box 11365-8639, Tehran, Iran

    Akbar Karimi & Hadi Nobahari

  2. Laboratoire Images, Signaux et Systèmes Intelligents (LiSSi), Université Paris 12 Val-de-Marne, 94010, Créteil, France

    Patrick Siarry

Authors
  1. Akbar Karimi
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  2. Hadi Nobahari
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  3. Patrick Siarry
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Correspondence to Patrick Siarry.

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Karimi, A., Nobahari, H. & Siarry, P. Continuous ant colony system and tabu search algorithms hybridized for global minimization of continuous multi-minima functions. Comput Optim Appl 45, 639–661 (2010). https://doi.org/10.1007/s10589-008-9176-7

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  • DOI: https://doi.org/10.1007/s10589-008-9176-7

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