Skip to main content
SpringerLink
Log in

Runtime Analysis of (1+1) Evolutionary Algorithm for a TSP Instance

  • Conference paper
Swarm, Evolutionary, and Memetic Computing (SEMCCO 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6466))

Included in the following conference series:

Abstract

Evolutionary Algorithms (EAs) have been used widely and successfully in solving a famous classical combinatorial optimization problem-the traveling salesman problem (TSP). There are lots of experimental results concerning the TSP. However, relatively few theoretical results on the runtime analysis of EAs on the TSP are available. This paper conducts a runtime analysis of a simple Evolutionary Algorithm called (1+1) EA on a TSP instance. We represent a tour as a string of integer, and randomly choose 2-opt and 3-opt operator as the mutation operator at each iteration. The expected runtime of (1+1) EA on this TSP instance is proved to be O(n 4), which is tighter than O(n 6 + (1/ρ)nln n) of (1+1) MMAA (Max-Min ant algorithms). It is also shown that the selection of mutation operator is very important in (1+1) EA.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  2. Schwefel, H.-P.: Evolution and Optimum Seeking. Wiley, New York( (1995)

    MATH  Google Scholar 

  3. Fogel, D.B.: Evolutionary Computation: Toward a New Philosophy of Machine Intelligence. IEEE Press, Piscataway (1995)

    MATH  Google Scholar 

  4. Karakoca, M., Kavakb, A.: Genetic Approach for Dynamic OVSF Code Allocation in 3G Wireless Networks. Applied Soft Computing 9(1), 348–361 (2009)

    Article  Google Scholar 

  5. Liang, K.-H., Yao, X., Newton, C., Hoffman, D.: A New Evolutionary Approach to Cutting Stock Problems with and without Contiguity. Computers & Operations Research 29(12), 1641–1659 (2002)

    Article  MathSciNet  Google Scholar 

  6. Beligiannis, G.N., Moschopoulos, C.N., Kaperonisa, G.P., et al.: Applying Evolutionary Computation to the School Timetabling Problem: The Greek Case. Computers & Operations Research 35, 1265–1280 (2008)

    Article  MATH  Google Scholar 

  7. Rudolph, G.: Convergence Analysis of Canonical Genetic Algorithms. IEEE Transactions on Neural Networks 5(1), 96–101 (1994)

    Article  Google Scholar 

  8. Rudolph, G.: Convergence of Non-elitist Strategies. In: The First IEEE Conference on Evolutionary Computation, vol. 1, pp. 63–66. IEEE Press, Orlando (1994)

    Google Scholar 

  9. Rudolph, G.: Convergence Properties of Evolutionary Algorithms. Ph.D. Thesis. Verlag Dr. Kovac, Hamburg (1997)

    Google Scholar 

  10. Droste, S., Jansen, T., Wegener, I.: A Rigorous Complexity Analysis of the (1+1) Evolutionary Algorithm for Linear Functions with Boolean Inputs. In: IEEE International Conference on Evolutionary Computation, pp. 499–504. IEEE Press, NJ (1998)

    Google Scholar 

  11. Droste, S., Jansen, T., Wegener, I.: On the Analysis of the (1+1)Evolutionary Algorithm. Theoretical Computer Science 276, 51–81 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Witt, C.: Worst-case and Average-case Approximations by Simple Randomized Search Heuristic. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 44–56. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Sudholt, D.: Crossover is Provably Essential for the Ising Model on Trees. In: Genetic and Evolutionary Computation Conference, Washington, DC, pp. 1161–1167 (2005)

    Google Scholar 

  14. Zhou, Y.R.: Runtime Analysis of Ant Colony Optimization Algorithm for TSP Instances. IEEE Transaction on Evolutionary Computation 13(5), 1083–1092 (2009)

    Article  Google Scholar 

  15. Wegener, I.: Methods for the Analysis of Evolutionary Algorithms on Pseudo-boolean Functions. In: Sarker, R., Mohammadian, M., Yao, X. (eds.) Evolutionary Optimization. Kluwer Academic Publishers, Boston (2001)

    Google Scholar 

  16. Gutjahr, W.J.: Mathematical Runtime Analysis of ACO Algorithms: Survey on an Emerging Issue. Swarm Intelligence 1(1), 59–79 (2007)

    Article  Google Scholar 

  17. Oliveto, P.S., He, J., Yao, X.: Analysis of the (1+1)-EA for Finding Approximate Solutions to Vertex Cover Problems. IEEE Transactions on Evolutionary Computation 13(5), 1006–1029 (2009)

    Article  Google Scholar 

  18. Chen, T., He, J., Sun, G., et al.: A New Approach for Analyzing Average Time Complexity of Population-based Evolutionary Algorithms on Unimodal Problems. IEEE Transactions on Systems, Man and Cybernetics, Part B 39(5), 1092–1106 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics & Computational Science, Guangdong University of Business Studies, Guangzhou, 510320, P.R. China

    Yu Shan Zhang

  2. School of Computer Science & Engineering, South China University of Technology, Guangzhou, 510006, P.R. China

    Yu Shan Zhang & Zhi Feng Hao

  3. Faculty of Computer, Guangdong University of Technology, Guangzhou, 510006, P.R. China

    Zhi Feng Hao

Authors
  1. Yu Shan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhi Feng Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology, New Delhi, India

    Bijaya Ketan Panigrahi

  2. Department of Electronics and Communication Engineering, Jadavpur University, 700032, Kolkata, West Bengal, India

    Swagatam Das

  3. School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore

    Ponnuthurai Nagaratnam Suganthan

  4. Department of Electrical and Electronics Engineering, SRM University, Chennai, Tamil Nadu, India

    Subhransu Sekhar Dash

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zhang, Y.S., Hao, Z.F. (2010). Runtime Analysis of (1+1) Evolutionary Algorithm for a TSP Instance. In: Panigrahi, B.K., Das, S., Suganthan, P.N., Dash, S.S. (eds) Swarm, Evolutionary, and Memetic Computing. SEMCCO 2010. Lecture Notes in Computer Science, vol 6466. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17563-3_36

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-17563-3_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17562-6

  • Online ISBN: 978-3-642-17563-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation