A Pheromone-Rate-Based Analysis on the Convergence Time of ACO Algorithm

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Volumn 39, Issue 4, 2009, Pages 910-923

  Huang, Han ^a   Wu, Chun Guo ^b,c   Hao, Zhi Feng ^a,d  

^a SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

^b JILIN UNIVERSITY   (China)

^c INSTITUTE OF AUTOMATION   (China)

^d GUANGDONG UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Ant colony optimization (ACO); convergence time; nature inspired cybernetic mechanisms; pheromone rate; runtime analysis

Indexed keywords

PHEROMONE;

ALGORITHM; ANIMAL; ANT; ARTICLE; BIOLOGICAL MODEL; CYBERNETICS; METHODOLOGY; PHYSIOLOGY; PROBABILITY; STATISTICAL MODEL;

ALGORITHMS; ANIMALS; ANTS; CYBERNETICS; MARKOV CHAINS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; PHEROMONES;

EID: 70149121606     PISSN: 10834419     EISSN: 19410492     Source Type: Journal    
DOI: 10.1109/TSMCB.2009.2012867     Document Type: Article

References (37)

1. C. Q. Zhang and Y. C. Lu, “The improved ant colony algorithm based on immunity system genetic algorithm and application,” in Proc. 5th IEEE Int. Conf. Cognitive Inform., 2006, vol. 2, pp. 726–731.
2. Y. X. Wang and Y. Wang, “Cognitive informatics models of the brain,” IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 36, no. 2, pp. 203–207, Mar. 2006.
3. M. Dorigo, V. Maniezzo, and A. Colorni, “Ant system: Optimization by a colony of cooperating agents,” IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 26, no. 1, pp. 29–41, Feb. 1996.
4. M. Dorigo, G. D. Caro, and L. M. Gambardella, “Ant algorithms for discrete optimization,” Artif. Life, vol. 5, no. 2, pp. 137–172, Apr. 1999.
5. M. Dorigo and T. Stiitzle, Ant Colony Optimization. Cambridge, MA: MIT Press, 2004.
6. M. Dorigo and L. M. Gambardella, “Ant colony system: A cooperative learning approach to the traveling salesman problem,” IEEE Trans. Evol. Comput., vol. 1, no. 1, pp. 53–66, Apr. 1997.
7. T. Stützle and H. H. Hoos, “MAX-MIN ant system,” Future Gener. Comput. Syst., vol. 16, no. 8, pp. 889–914, 2000.
8. W. J. Gutjahr, “A generalized convergence result for the graph-based ant system metaheuristic,” Dept. Stat. Decis. Support Syst., Univ. Vienna, Vienna, Austria, 1999. Tech. Rep., pp. 99–109.
9. W. J. Gutjahr, “A graph-based ant system and its convergence,” Future Gener. Comput. Syst., vol. 16, no. 9, pp. 873–888, Jun. 2000.
10. W. J. Gutjahr, “ACO algorithms with guaranteed convergence to the optimal solution,” Inform. Process. Lett., vol. 82, no. 3, pp. 145–153, May 2002.
11. T. Stützle and M. Dorigo, “A short convergence proof for a class of ant colony optimization algorithms,” IEEE Trans. Evol. Comput., vol. 6, no. 4, pp. 358–365, Aug. 2002.
12. M. Dorigo and C. Blum, “Ant colony optimization theory: A survey,” Theor. Comput. Sci., vol. 344, no. 2/3, pp. 243–278, Nov. 2005.
13. A. Badr and A. Fahmy, “A proof of convergence for ant algorithms,” Inform. Sci., vol. 160, pp. 267–279, 2004.
14. F. Neumann and C. Witt, Runtime Analysis of a Simple Ant Colony Optimization Algorithm, vol. 4288. Berlin, Germany: Springer-Verlag, 2006, pp. 618–627.
15. Z. F. Hao and H. Huang, A Time Complexity Analysis of ACO for Linear Functions, vol. 4247. Berlin, Germany: Springer-Verlag, 2006, pp. 513–520.
16. H. Huang, Z. F. Hao, C. G. Wu, and Y. Qin, “The convergence speed of Ant Colony Optimization,” Chin. J. Comput., vol. 30, no. 8, pp. 1343–1353, 2007 (in Chinese).
17. G. Rudolph, “Convergence properties of canonical genetic algorithms,” IEEE Trans. Neural Netw., vol. 5, no. 1, pp. 96–101, Jan. 1994.
18. J. Gamier, L. Kallel, and M. Schoenauer, “Rigorous hitting times for binary mutations,” Evol. Comput., vol. 7, no. 2, pp. 167–203, 1999.
19. S. Droste, T. Jansen, and I. Wegener, “A rigorous complexity analysis of the (1 + 1) evolutionary algorithm for linear functions with Boolean inputs,” Evol. Comput., vol. 6, no. 2, pp. 185–196, 1998.
20. S. Droste, T. Jansen, and I. Wegener, “On the analysis of the (1 + 1) evolutionary algorithms,” Theor. Comput. Sci., vol. 276, no. 1/2, pp. 51–81, Apr. 2002.
21. J. Gamier and L. Kallel, “Statistical distribution of the convergence time of evolutionary algorithms for long path problems,” IEEE Trans. Evol. Comput., vol. 4, no. 1, pp. 16–30, Apr. 2000.
22. G. Rudolph, “How mutation and selection solve long-path problems in polynomial expected time,” Evol. Comput., vol. 4, no. 2, pp. 194–205, 1996.
23. J. He and X. Yao, “From an individual to a population: An analysis of the first hitting time of population-based evolutionary algorithms,” IEEE Trans. Evol. Comput., vol. 6, no. 5, pp. 495–511, Oct. 2002.
24. J. He, H. Huang, and L. Kang, “The computational time of genetic algorithms for fully deceptive problem,” Chin. J. Comput., vol. 21, no. 9, pp. 999–1003, 1999.
25. J. He and X. Yao, “A study of drift analysis for estimating computation time of evolutionary algorithms,” Nat. Comput., vol. 3, no. 1, pp. 21–35, Mar. 2004.
26. J. He, X. Yao, and J. Lin, “A comparative study of three evolutionary algorithms incorporating different amounts of domain knowledge for node covering problem,” IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 35, no. 2, pp. 266–271, May 2005.
27. J. He, C. Reeves, C. Witt, and X. Yao, “A note on problem difficulty measures in black-box optimization: Classification, realizations and predictability,” Evol. Comput., vol. 15, no. 4, pp. 435–443, 2007.
28. Y. R. Zhou and J. He, “A runtime analysis of evolutionary algorithms for constrained optimization problems,” IEEE Trans. Evol. Comput., vol. 11, no. 5, pp. 608–619, Oct. 2007.
29. C. Witt, “Runtime analysis of the (u + 1)EA on the simple pseudo-Boolean functions,” in Proc. 8th Annu. Conf. Genetic Evol. Comput., Seattle, WA, 2006, pp. 651–658.
30. C. Witt, “Population size vs. runtime of a simple EA,” in Proc. Congr. Evol. Comput., Canberra, Australia, 2003, pp. 1996–2003.
31. C. Witt, “Worse-case and average-case approximations by simple randomized search heuristics,” in Proc. 22nd Annu. Symp. Theor. Aspects Comput. Sci., Stuttgart, Germany: Springer-Verlag, 2005, vol. 3404, pp. 44–56.
32. F. Neumann, “Expected run-times of evolutionary algorithms for the Eulerian cycle problem,” in Proc. Congr. Evol. Comput., 2004, pp. 904–910.
33. F. Neumann and I. Wegener, “Minimum spanning trees made easier via multi-objective models,” Nat. Comput., vol. 5, no. 3, pp. 305–319, Sep. 2006.
34. F. Neumann and I. Wegener, “Randomized local search, evolutionary algorithms and the minimum spanning tree problem,” in Proc. Genetic Evol. Comput. Conf. Seattle, WA: Springer-Verlag, 2004, vol. 3102, pp. 713–724.
35. Y. Yu and Z. H. Zhou, “A new approach to estimating the expected first hitting time of evolutionary algorithms,” in Proc. 21st Nat. Conf. Artif. Intell. AAAI, Boston, MA, 2006, pp. 555–556.
36. G. Reinelt, “TSPLIB—A traveling salesman problem library,” ORSA J. Comput., vol. 3, no. 4, pp. 376–384, 1991.
37. H. Huang, “A relation-and-ordering-based analysis for convergence and convergence time of evolutionary algorithm,” Ph.D. dissertation, South China Univ. Technol., Guangzhou, China, 2008. Unpublished (in Chinese).