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Journal of Computer Science and Technology

, Volume 23, Issue 1, pp 2–18 | Cite as

Orthogonal Methods Based Ant Colony Search for Solving Continuous Optimization Problems

  • Xiao-Min Hu
  • Jun ZhangEmail author
  • Yun Li
Regular Paper

Abstract

Research into ant colony algorithms for solving continuous optimization problems forms one of the most significant and promising areas in swarm computation. Although traditional ant algorithms are designed for combinatorial optimization, they have shown great potential in solving a wide range of optimization problems, including continuous optimization. Aimed at solving continuous problems effectively, this paper develops a novel ant algorithm termed “continuous orthogonal ant colony” (COAC), whose pheromone deposit mechanisms would enable ants to search for solutions collaboratively and effectively. By using the orthogonal design method, ants in the feasible domain can explore their chosen regions rapidly and efficiently. By implementing an “adaptive regional radius” method, the proposed algorithm can reduce the probability of being trapped in local optima and therefore enhance the global search capability and accuracy. An elitist strategy is also employed to reserve the most valuable points. The performance of the COAC is compared with two other ant algorithms for continuous optimization — API and CACO by testing seventeen functions in the continuous domain. The results demonstrate that the proposed COAC algorithm outperforms the others.

Keywords

ant algorithm function optimization orthogonal design 

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Supplementary material

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References

  1. [1]
    Deneubourg J L, Aron S, Goss S, Pasteels J M. The self-organizing exploratory pattern of the Argentine ant. Journal of Insect Behavior, 1990, 3: 159–168.CrossRefGoogle Scholar
  2. [2]
    Goss S, Aron S, Deneubourg J L, Pasteels J M. Self-organized shortcuts in the Argentine ant. Naturwissenschaften, 1989, 76(12): 579–581.CrossRefGoogle Scholar
  3. [3]
    Dorigo M, Stützle T. Ant Colony Optimization. the MIT Press, 2003.Google Scholar
  4. [4]
    Dorigo M, Gambardella L M. Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE. Trans. Evol. Comput., 1997, 1(1): 53–66.CrossRefGoogle Scholar
  5. [5]
    Toth P, Vigo D. The Vehicle Routing Problem. SIAM Monographs on Discrete Mathematics and Applications, Philadelphia, Society for Industrial & Applied Mathematics, 2001.Google Scholar
  6. [6]
    Gambardella L M, Taillard É D, Agazzi G. MACS-VRPTW: A Multiple Ant Colony System for Vehicle Routing Problems with Time Windows. New Ideas in Optimization, Corne D, Dorigo M, Glover F (eds.), London, McGraw Hill, 1999, pp.63–76.Google Scholar
  7. [7]
    Zhang J, Hu X M, Tan X, Zhong J H, Huang Q. Implementation of an ant colony optimization technique for job shop scheduling problem. Transactions of the Institute of Measurement and Control, 2006, 28(1): 1–16.CrossRefGoogle Scholar
  8. [8]
    Zecchin A C, Simpson A R, Maier H R, Nixon J B. Parametric study for an ant algorithm applied to water distribution system optimization. IEEE Trans. Evol. Comput., 2005, 9: 175–191.CrossRefGoogle Scholar
  9. [9]
    Parpinelli R S, Lopes H S, Freitas A A. Data mining with an ant colony optimization algorithm. IEEE Trans. Evol. Comput., 2002, 4: 321–332.CrossRefGoogle Scholar
  10. [10]
    Sim K M, Sun W H. Ant colony optimization for routing and load-balancing: Survey and new directions. IEEE Trans. Systems, Man, and Cybernetics — Part A: System and Humans, 2003, 33: 560–572.CrossRefGoogle Scholar
  11. [11]
    Bilchev G, Parmee I C. The ant colony metaphor for searching continuous design spaces. In Proc. the AISB Workshop on Evolutionary Computation, University of Sheffield, UK, LNCS 933, Springer-Verlag, Berlin, Germany, 1995, pp.25–39.Google Scholar
  12. [12]
    Wodrich M, Bilchev G. Cooperative distributed search: The ant’s way. Control and Cybernetics, 1997, 3: 413–446.MathSciNetGoogle Scholar
  13. [13]
    Mathur M, Karale S B, Priye S, Jyaraman V K, Kulkarni B D. Ant colony approach to continuous function optimization. Ind. Eng. Chem. Res., 2000, 39: 3814–3822.CrossRefGoogle Scholar
  14. [14]
    Holland J H. Adaptation in Natural and Artificial Systems. Second Edition (First Edition, 1975), Cambridge: the MIT Press, MA, 1992.Google Scholar
  15. [15]
    Monmarché N, Venturini G, Slimane M. On how Pachycondyla apicalis ants suggest a new search algorithm. Future Generation Computer Systems, 2000, 16: 937–946.CrossRefGoogle Scholar
  16. [16]
    Dréo J, Siarry P. Continuous interacting ant colony algorithm based on dense heterarchy. Future Generation Computer Systems, 2004, 20: 841–856.CrossRefGoogle Scholar
  17. [17]
    Dréo J, Siarry P. A new ant colony algorithm using the heterarchical concept aimed at optimization of multiminima continuous functions. In Proc. ANTS 2002, Brussels, Belgium, LNCS 2463, 2002, pp.216–221.Google Scholar
  18. [18]
    Socha K. ACO for continuous and mixed-variable optimization. In Proc. ANTS 2004, Brussels, Belgium, LNCS 3172, 2004, pp.25–36.Google Scholar
  19. [19]
    Socha K, Dorigo M. Ant colony optimization for continuous domains. Eur. J. Oper. Res., 2008, 185(3): 1155–1173.zbMATHCrossRefGoogle Scholar
  20. [20]
    Pourtakdoust S H, Nobahari H. An extension of ant colony system to continuous optimization problems. In Proc. ANTS 2004, Brussels, Belgium, LNCS 3172, 2004, pp.294–301.Google Scholar
  21. [21]
    Kong M, Tian P. A binary ant colony optimization for the unconstrained function optimization problem. In Proc. International Conference on Computational Intelligence and Security (CIS'05), Xi’an, China, LNAI 3801, 2005, pp.682–687.Google Scholar
  22. [22]
    Kong M, Tian P. A direct application of ant colony optimization to function optimization problem in continuous domain. In Proc. ANTS 2006, Brussels, Belgium, LNCS 4150, 2006, pp.324–331.Google Scholar
  23. [23]
    Chen L, Shen J, Qin L, Chen H J. An improved ant colony algorithm in continuous optimization. Journal of Systems Science and Systems Engineering, 2003, 12(2): 224–235.CrossRefGoogle Scholar
  24. [24]
    Dréo J, Siarry P. An ant colony algorithm aimed at dynamic continuous optimization. Appl. Math. Comput., 2006, 181: 457–467.CrossRefMathSciNetGoogle Scholar
  25. [25]
    Feng Y J, Feng Z R. An immunity-based ant system for continuous space multi-modal function optimization. In Proc. the Third International Conference on Machine Learning and Cybernetics, Shanghai, August 26–29, 2004, pp.1050–1054.Google Scholar
  26. [26]
    Shelokar P S, Siarry P, Jayaraman V K, Kulkarni B D. Particle swarm and ant colony algorithms hybridized for improved continuous optimization. Appl. Math. Comput., 2006, doi: 10.1016/j.amc.2006.09.098.
  27. [27]
    Rao C R. Factorial experiments derivable from combinatorial arrangements of arrays. J. Royal Statist. Soc., 1947, 9(Suppl.): 128–139.Google Scholar
  28. [28]
    Bush K A. Orthogonal arrays [Dissertation]. University of North Carolina, Chapel Hill, 1950.Google Scholar
  29. [29]
    Math Stat Res Group, Chinese Acad Sci. Orthogonal Design. Bejing: People Education Pub., 1975. (in Chinese)Google Scholar
  30. [30]
    Fang K T, Wang Y. Number-Theoretic Methods in Statistics. New York: Chapman & Hall, 1994.zbMATHGoogle Scholar
  31. [31]
    Hedayat A S, Sloane N J A, Stufken J. Orthogonal Arrays: Theory and Applications. New York: Springer-Verlag, 1999.zbMATHGoogle Scholar
  32. [32]
    Nathanson M B. Elementary Methods in Number Theory. New York: Springer-Verlag, 2000.zbMATHGoogle Scholar
  33. [33]
    Zhang Q, Leung Y W. An orthogonal genetic algorithm for multimedia multicast routing. IEEE Trans. Evolutionary Computation, 1999, 3(1): 53–62.CrossRefGoogle Scholar
  34. [34]
    Leung Y W, Wang W. An orthogonal genetic algorithm with quantization for global numerical optimization. IEEE Trans. Evol. Comput., 2001, 5(1): 41–53.CrossRefGoogle Scholar
  35. [35]
    Ho S Y, Chen J H. A genetic-based systematic reasoning approach for solving traveling salesman problems using an orthogonal array crossover. In Proc. the Fourth Internal Conference/Exhibition on High Performance Computing in the Asia-Pacific Region, May 2000, 2: 659–663.Google Scholar
  36. [36]
    Liang X B. Orthogonal designs with maximal rates. IEEE Trans. Information Theory, 2003, 49(10): 2468–2503.CrossRefGoogle Scholar
  37. [37]
    Tanaka H. Simple genetic algorithm started by orthogonal design of experiments. In Proc. SICE Annual Conference in Sapporp, August 2004, pp.1075–1078.Google Scholar
  38. [38]
    Salomon R. Reevaluating genetic algorithm performance under coordinate rotation of benchmark functions. BioSystems, 1996, 39: 263–278.CrossRefGoogle Scholar

Copyright information

© Science Press, Beijing, China and Springer Science + Business Media, LLC, USA 2008

Authors and Affiliations

  1. 1.Department of Computer ScienceSun Yat-Sen UniversityGuangzhouChina
  2. 2.Key Laboratory of Digital Life(Sun Yat-Sen University), Ministry of EducationGuangzhouChina
  3. 3.Department of Electronics and Electrical EngineeringUniversity of GlasgowGlasgowUK

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