Cluster Computing

, Volume 20, Issue 2, pp 1247–1257 | Cite as

Ant colony optimization with different crossover schemes for global optimization

  • Zhiqiang ChenEmail author
  • Rong-Long Wang


Global optimization, especially large scale optimization problems arise as a very interesting field of research, because they appear in many real-world problems. Ant colony optimization is one of optimization techniques for these problems. In this paper, we improve the continuous ant colony optimization (ACO\(_\mathrm{R})\) with crossover operator. Three crossover methods are employed to generate some new probability density function set of ACO\(_\mathrm{R}\). The proposed algorithms are evaluated by using 21 benchmark functions whose dimensionality is 30–1000. The simulation results show that the proposed ACO\(_\mathrm{R}\) with different crossover operators significantly enhance the performance of ACO\(_\mathrm{R}\) for global optimization. In the case the dimensionality is 1000, the proposed algorithm also can efficiently solves them. Compared with state-of-art algorithms, the proposal is a very competitive optimization algorithm for global optimization problems.


Ant colony optimization Large scale Continuous optimization problem Crossover operator 



This work is supported by Scientific and Technological Research Program of Chongqing Municipal Education Commission [Nos. KJ1500607, KJ1400629], Science Research Fund of Chongqing Technology and Business University [No. 2011-56-05], and the National Natural Science Foundation of China [51375517, 61402063].


  1. 1.
    Zhang, X., Tian, Y., Jin, Y.: A knee point driven evolutionary algorithm for many-objective optimization. IEEE Trans. Evol. Comput. 19(6), 761–776 (2015)CrossRefGoogle Scholar
  2. 2.
    Zhang, X., Tian, Y., Cheng, R., Jin, Y.: An efficient approach to non-dominated sorting for evolutionary multi-objective optimization. IEEE Trans. Evol. Comput. 19(2), 201–213 (2015)CrossRefGoogle Scholar
  3. 3.
    Chen, Z.Q., Wang, R.L.: A new framework with FDPP-LX crossover for real-coded genetic algorithm. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E94.A(6), 1417–1425 (2011)CrossRefGoogle Scholar
  4. 4.
    Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)zbMATHGoogle Scholar
  5. 5.
    Socha, K., Dorigo, M.: Ant colony optimization for continuous domains. Eur. J. Oper. Res. 185(3), 1155–1173 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Tang, K., Yao, X., Suganthan, P.N., MacNish, C., Chen, Y.P., Chen, C.M., Yang, Z.: Benchmark Functions for the CEC’2008 Special Session and Competition on Large Scale Global Optimization. IEEE World Congress on Computational Intelligence (2008), Hong KongGoogle Scholar
  7. 7.
    Zhang, X., Tian, Y., Cheng, R., Jin, Y.: A decision variable clustering based evolutionary algorithm for large-scale many-objective optimization. IEEE Trans. Evol. Comput. (2016). doi: 10.1109/TEVC.2016.2600642
  8. 8.
    Zhang, X., Tian, Y., Jin, Y.: Approximate non-dominated sorting for evolutionary many-objective optimization. Inf. Sci. 369(10), 14–33 (2016)CrossRefGoogle Scholar
  9. 9.
    Dorigo, M., Maniezzo, V., Colorni, A.: The ant system: an autocatalytic optimizing process. Technical Report 91-016 Revised, Dipartimento di Elettronica, Politecnico di Milano, Italy, 1991Google Scholar
  10. 10.
    Dorigo, M., Maniezzo, V., Colorni, A.: Ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. B 26(1), 29–41 (1996)CrossRefGoogle Scholar
  11. 11.
    Bilchev, G., Parmee I.C.: The ant colony metaphor for searching continuous design spaces. Selected Papers from AISB Workshop on Evolutionary Computing, vol. 993, pp. 25–39 (1995)Google Scholar
  12. 12.
    Monmarche, N., Venturini, G., Slimane, M.: On how pachycondyla apicalis ants suggest a new search algorithm. Future Gener. Comput. Syst. 16(8), 937–946 (2000)CrossRefGoogle Scholar
  13. 13.
    Dreo, J., Siarry, P.: A new ant colony algorithm using the heterarchical concept aimed at optimization of multiminima continuous functions. Ant Algorithms 2463, 216–221 (2002)CrossRefGoogle Scholar
  14. 14.
    Dréo, J., Siarry, P.: Continuous interacting ant colony algorithm based on dense heterarchy. Future Gener. Comput. Syst. 20(5), 841–856 (2004)CrossRefGoogle Scholar
  15. 15.
    Hu, X.M., Zhang, J., Li, Y.: Orthogonal methods based ant colony search for solving continuous optimization problems. J. Comput. Sci. Technol. 23, 2–18 (2008)CrossRefGoogle Scholar
  16. 16.
    Hu, X.M., Zhang, J., Chung, H.S.H., Li, Y., Liu, O.: SamACO: variable sampling ant colony optimization algorithm for continuous optimization. IEEE Trans. Syst. Man Cybern. B Cybern. 40, 1555–1566 (2010)CrossRefGoogle Scholar
  17. 17.
    Liao, T., Stützle, T.: A unified ant colony optimization algorithm for continuous optimization. Eur. J. Oper. Res. 234, 597–609 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Eshelman, L.J., Schaffer, J.D.: Real-coded genetic algorithms and interval schemata. In: Whitley, D.L. (ed.) Foundation of Genetic Algorithms II, pp. 187–202. Morgan Kaufmann, San Mateo (1993)Google Scholar
  19. 19.
    Ono, I., Kobayashi, S.: A real-coded genetic algorithm for function optimization using unimodal normal distribution crossover. In: Back, T. (ed.) Proceedings of the Seventh International Conference on Genetic Algorithms, pp. 246–253. Morgan Kaufmann, San Mateo (1997)Google Scholar
  20. 20.
    Ballester, P.J., Carter, J.N.: An effective real-parameter genetic algorithm with parent centric normal crossover for multimodal optimization. In: Deb, K., et al. (eds.) Lecture Notes in Computer Science, vol. 3102, pp. 901–913. Springer, Berlin (2004)Google Scholar
  21. 21.
    Shang, Y.W., Qiu, Y.H.: A note on the extended rosenbrock function. Evol. Comput. 14, 119–126 (2006)CrossRefGoogle Scholar
  22. 22.
    Yao, X., Liu, Y., Lin, G.: Evolutionary programming made faster. IEEE Trans. Evol. Comput. 3(2), 82–102 (1999)CrossRefGoogle Scholar
  23. 23.
    Rosenbrock, H.H.: An automatic method for finding the greatest or least value of a function. Comput. J. 3(3), 175–184 (1960)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Ortiz-Boyer, D., Hervas-Martinez, C., Garcia-Pedrajas, N.: A crossover operator for evolutionary algorithms based on population features. J. Artif. Intell. Res. 24, 1–48 (2005)CrossRefzbMATHGoogle Scholar
  25. 25.
    Hansen, N.: The CMA Evolution Strategy: A Tutorial, 2010Google Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.National Research Base of Intelligent Manufacturing ServiceChongqing Technology and Business UniversityChongqingChina
  2. 2.Chongqing Engineering Laboratory for Detection Control and Integrated SystemChongqing Technology and Business UniversityChongqingChina
  3. 3.School of Computer Science and Information EngineeringChongqing Technology and Business UniversityChongqingChina
  4. 4.The Faculty of EngineeringUniversity of FukuiFukui-shiJapan

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