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Asia-Pacific Conference on Simulated Evolution and Learning

SEAL 2006: Simulated Evolution and Learning pp 513–520Cite as

A Time Complexity Analysis of ACO for Linear Functions

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4247))

Abstract

The time complexity analysis of ant colony optimization (ACO) is one of the open problems in ACO research. There has been little proposed work on this topic recently. In the present paper, two ACO algorithms (ACO I and ACO II) for linear functions with Boolean input are indicated, and their time complexity is estimated based on drift analysis which is a mathematical tool for analyzing evolutionary algorithms. It is proved that the algorithm ACO II can find the optimal solution with a polynomial time complexity. It is a preliminary work about estimating the time complexity of ACO, which should be improved in the future study.

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References

  1. Dorigo, M., Caro, G.D., Gambardella, L.M.: Ant algorithms for Discrete Optimization. Massachusetts Institute of Technology, Artificial Life 5, 137–172 (1999)

    Article  Google Scholar 

  2. Dorigo, M., Gambardella, L.M.: Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem. IEEE Transactions on Evolutionary Computation 1(1), 53–66 (1997)

    Article  Google Scholar 

  3. Stützle, T., Hoos, H.H.: MAX-MIN ant system. Future Gener. Comput. Syst. 16(8), 889–914 (2000)

    Article  Google Scholar 

  4. Gutjahr, W.J.: Ageneralized convergence result for the graph-based ant system metaheuristic. Tech. Report 99-09, Department of Statistics and Decision Support Systems, University of Vienna, Austria (1999)

    Google Scholar 

  5. Gutjahr, W.J.: Agraph-based ant system and its convergence. Future Gen. Comput. Systems 16(9), 873–888 (2000)

    Article  Google Scholar 

  6. Gutjahr, W.J.: ACO algorithms with guaranteed convergence to the optimal solution. Information Processing Letters 82, 145–153 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  7. Stützle, T., Dorigo, M.: A Short Convergence Proof for a Class of Ant Colony Optimization Algorithms. IEEE Transactions on Evolutionary Computation 6(4), 358–365 (2002)

    Article  Google Scholar 

  8. Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  9. Dorigo, M., Blum, C.: Ant colony optimization theory: A survey. Theoretical Computer Science 344, 243–278 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Badr, A., Fahmy, A.: A proof of convergence for Ant algorithms. Information Sciences 160, 267–279 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. Fidanova, S.: ACO Algorithm with Additional Reinforcement. In: Dorigo, M., Di Caro, G.A., Sampels, M. (eds.) Ant Algorithms 2002. LNCS, vol. 2463, pp. 292–293. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  12. Fidanova, S.: Convergence Proof for a Monte Carlo Method for Combinatorial Optimization Problems. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2004. LNCS, vol. 3039, pp. 523–530. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Droste, S., Jansen, T., Wegener, I.: A rigorous complexity analysis of the (1+1)-evolutionary algorithms. Evolutionary Computation 6(2), 185–196 (1998)

    Article  Google Scholar 

  14. Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1)-evolutionary algorithms. Theoretical Computer Science 276(1-2), 51–81 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  15. He, J., Yao, X.: A study of drift analysis for estimating computation time of evolutionary algorithms. Natural Computing 3, 21–35 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  16. He, J., Yao, X.: From an individual to a population: An analysis of the first hitting time of population-based evolutionary algorithms. IEEE Transactions on Evolutionary Computation 6(5), 495–511 (2002)

    Article  Google Scholar 

  17. He, J., Yao, X.: Erratum to: Drift analysis and average time complexity of evolutionary algorithms. Artificial Intelligence 127, 57–85 (2001), Artificial Intelligence 140(1), 245–248 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  18. He, J., Huang, H.: The computational time analysis of genetic algorithms. In: Proc. Fifth Chinese Joint Conference on Artificial Intelligence, pp. 440–443. Xi’an Jiaotong University Press, Xi’an (1998)

    Google Scholar 

  19. He, J., Huang, H., Kang, L.: The computational time of genetic algorithms for fully deceptive problem. Chinese J. Comput. 21(9), 999–1003 (1999)

    MathSciNet  Google Scholar 

  20. He, J., Yao, X., Li, J.: A Comparative Study of Three Evolutionary Algorithms Incorporating Different Amounts of Domain Knowledge for Node Covering Problem. IEEE Transactions on systems, man, and cybernetics—Part C: Applications and Reviews 35(2) (May 2005)

    Google Scholar 

  21. He, J., Yao, X.: Towards an analytic framework for analyzing the computation time of evolutionary algorithms. Artificial Intelligence 145(1-2), 59–97 (2003)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. College of Mathematical Science, South China University of Technology, Guangzhou, 510640, P.R. China

    Zhifeng Hao, Xili Zhang & Kun Tu

  2. Nation Mobile Communications Research Laboratory Southeast University, Nanjing, 210096, China

    Zhifeng Hao

  3. College of Computer Science and Engineering, South China University of Technology, Guangzhou, 510640, P.R. China

    Han Huang

Authors
  1. Zhifeng Hao
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  2. Han Huang
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  3. Xili Zhang
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  4. Kun Tu
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Editor information

Editors and Affiliations

  1. Department of Industrial Engineering and Management, Cheng Shiu University, Kaohsiung County Taiwan, ROC

    Tzai-Der Wang

  2. School of Computer Science and information Technology, RMIT University, VIC 3001, Melbourne, Australia

    Xiaodong Li

  3. AI-ECON Research Center, Department of Economics, National Chengchi University, 11623, Taipei, Taiwan

    Shu-Heng Chen

  4. Department of Computer Science and Technology, University of Sci. & Tech. of China, 230026, Hefei, Anhui, P.R. China

    Xufa Wang

  5. School of Information Technology and Electrical Engineering, University of New South Wales, Australian Defence Force Academy, Canberra, Australia

    Hussein Abbass

  6. The Univertity of Tokyo, Japan

    Hitoshi Iba

  7. Department of Computer, University of Science and Technology of China, 230027, Hefei, China

    Guo-Liang Chen

  8. University of Birmingham, Birmingham, UK

    Xin Yao

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© 2006 Springer-Verlag Berlin Heidelberg

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Cite this paper

Hao, Z., Huang, H., Zhang, X., Tu, K. (2006). A Time Complexity Analysis of ACO for Linear Functions. In: Wang, TD., et al. Simulated Evolution and Learning. SEAL 2006. Lecture Notes in Computer Science, vol 4247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11903697_65

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  • DOI: https://doi.org/10.1007/11903697_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-47331-2

  • Online ISBN: 978-3-540-47332-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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