Skip to main content
SpringerLink
Log in

On the Ability of the One-Point Crossover Operator to Search the Space in Genetic Algorithms

  • Conference paper
Artificial Intelligence and Soft Computing (ICAISC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9119))

Included in the following conference series:

Abstract

In this paper we study the search abilities of binary one-point crossover (1ptc) operator in a genetic algorithm (GA). We show, that under certain conditions, GA is capable of using only a 1ptc operator to explore the entire search space, fighting premature convergence. Further, we prove that to restore the entire space from any two binary chromosomes, each of length n, at least 2n − 1 − 1 one-point crossover operations is needed. This number can serve as a measure for comparing the search speed of the different algorithms. Moreover, we propose an algorithm spanning the search space in the minimal number of crossovers.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Bäck, T.: Evolutionary Algorithms in Theory and Practice. Oxford University Press, New York (1996)

    MATH  Google Scholar 

  2. Choubey, N.S., Kharat, M.U.: Approaches for Handling Premature Convergence in CFG Induction Using GA. Advances in Intelligent and Soft Computing 96, 55–66 (2011)

    Article  Google Scholar 

  3. Da Ronco, C.C., Benini, E.: GeDEA-II: A Simplex Crossover Based Evolutionary Algorithm Including the Genetic Diversity as Objective. Engineering Letters 21, 1 (2013)

    Google Scholar 

  4. Davis, L.: Adapting operator probabilities in genetic algorithms. In: International Conference on Genetic Algorithms 1989, pp. 61–69 (1989)

    Google Scholar 

  5. Davis, L.: Handbook of genetic algorithms. New York Van Nostrand Reinhold (1991)

    Google Scholar 

  6. De Jong, K.A., Spears, W.M.: A formal analysis of the role of multi-point crossover in genetic algorithms. Annals of Mathematics and Artificial Intelligence 5(1), 1–26 (1992)

    Article  MATH  Google Scholar 

  7. Dietzfelbinger, M., Naudts, B., Van Hoyweghen, C., Wegener, I.: The analysis of a recombinative hill-climber on H-IFF. IEEE Transactions on Evolutionary Computation 7(5), 417–423 (2003)

    Article  Google Scholar 

  8. Fischer, S., Wegener, I.: The one-dimensional Ising model: mutation versus recombination. Theoretical Computer Science 344(2-3), 208–225 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Fogel, D.B.: Evolving artificial intelligence. Doctoral dissertation University of California (1992)

    Google Scholar 

  10. Holland, J.H.: Adaptation in Natural and Artificial System. University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  11. Jones, T.: Crossover, macromutation and population-based search. In: Proceedings of the Sixth International Conference on Genetic Algorithms, pp. 73–80 (1995)

    Google Scholar 

  12. Kötzing, T., Sudholt, D., Theile, M.: How crossover helps in pseudo-boolean optimization. In: Proceedings of the 13th Annual Genetic and Evolutionary Computation Conference (GECCO 2011), Dublin, Ireland, pp. 989–996 (2011)

    Google Scholar 

  13. Ochoa, G., Verel, S., Daolio, F., Tomassini, M.: Local Optima Networks: A New Model of Combinatorial Fitness Landscapes. In: Recent Advances in the Theory and Application of Fitness Landscapes, pp. 233–262. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  14. McGinley, B.: Maintaining Healthy Population Diversity Using Adaptive Crossover, Mutation, and Selection. IEEE Transactions on Evolutionary Computation 15, 692–714 (2011)

    Article  Google Scholar 

  15. Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer (1996)

    Google Scholar 

  16. Neumann, F., Theile, M.: How crossover speeds up evolutionary algorithms for the multicriteria all-pairs-shortest-path problem. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6238, pp. 667–676. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  17. Neumann, F., Oliveto, P.S., Rudolph, G., Sudholt, D.: On the effectiveness of crossover for migration in parallel evolutionary algorithms. In: Proceedings of the 13th ACM Conference on Genetic and Evolutionary Computation (GECCO 2011), Dublin, Ireland, pp. 1587–1594 (2011)

    Google Scholar 

  18. Oliveto, P., He, J., Yao, X.: Analysis of population-based evolutionary algorithms for the vertex cover problem. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2008), Hong Kong, China, pp. 1563–1570 (2008)

    Google Scholar 

  19. Pandey, H.M., Chaudhary, A., Mehrotra, D.: A comparative review of approaches to prevent premature convergence in GA. Applied Soft Computing 24, 1047–1077 (2014)

    Article  Google Scholar 

  20. Pliszka, Z., Unold, O.: Metric Properties of Populations in Artificial Immune Systems. In: Proceedings of the International Multiconference on Computer Science and Information Technology (AAIA 2010), Wisla, Poland, pp. 113–119 (2010)

    Google Scholar 

  21. Pliszka, Z., Unold, O.: How to predict future in a world of antibody-antigen chromosomes. In: Ganzha, M., Maciaszek, L., Paprzycki, M. (eds.) Proceedings of the Federated Conference on Computer Science and Information Systems, pp. 91–96. IEEE (2011)

    Google Scholar 

  22. Pliszka, Z., Unold, O.: Efficient crossover and mutation operator in genetic algorithm. Elektronika (LII), 166–170 (2011) (in Polish)

    Google Scholar 

  23. Pliszka, Z., Unold, O.: On some properties of binary chromosomes and states of artificial immune systems. Int. J. of Data Analysis Techniques and Strategies 4(3), 277–291 (2012)

    Article  Google Scholar 

  24. Pliszka, Z., Unold, O.: On multi-individual crossing over in evolutionary algorithms. Elektronika (LV) (9/2014), 140–141 (in Polish)

    Google Scholar 

  25. Prasanth, N., Kirti Vaishnavi, M., Sekar, K.: An algorithm to find all palindromic sequences in proteins. Journal of Biosciences 38(1), 173–177 (2013)

    Article  Google Scholar 

  26. Richter, J.N., Wright, A., Paxton, J.: Ignoble trails-where crossover is provably harmful. In: Rudolph, G., Jansen, T., Lucas, S., Poloni, C., Beume, N. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 92–101. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  27. Qian, C., Yu, Y., Zhou, Z.-H.: An analysis on recombination in multi-objective evolutionary optimization. In: Proceedings of the 13th ACM Conference on Genetic and Evolutionary Computation (GECCO 2011), Dublin, Ireland, pp. 2051–2058 (2011)

    Google Scholar 

  28. Schweitzer, J.A., Martinsen, G.D., Whitham, T.G.: Cottonwood hybrids gain fitness traits of both parents: a mechanism for their long-term persistence? American Journal of Botany 89(6), 981–990 (2002)

    Article  Google Scholar 

  29. Spears, W.M.: Crossover or mutation? In: FOGA, pp. 221–237 (1992)

    Google Scholar 

  30. Syswerda, G.: Uniform crossover in genetic algorithms. In: Schaffer, J.D. (ed.) Proceedings of the International Conference on Genetic Algorithms, pp. 2–9. Morgan Kaufmann Publishers, San Mateo (1989)

    Google Scholar 

  31. Uy, N.Q., Hoai, N.X., O’Neill, M., McKay, R.I., Phong, D.N.: On the roles of semantic locality of crossover in genetic programming. Information Sciences 235, 195–213 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  32. Verel, S., Ochoa, G., Tomassini, M.: Local optima networks of NK landscapes with neutrality. IEEE Transactions on Evolutionary Computation 15(6), 783–797 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Wroclaw Public Library, Sztabowa 95, 53-310, Wroclaw, Poland

    Zbigniew Pliszka

  2. Department of Computer Engineering, Faculty of Electronics, Wroclaw University of Technology, Wyb. Wyspianskiego 27, 50-370, Wroclaw, Poland

    Olgierd Unold

Authors
  1. Zbigniew Pliszka
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Olgierd Unold
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Częstochowa, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Częstochowa, Poland

    Marcin Korytkowski

  3. Częstochowa University of Technology, Częstochowa, Poland

    Rafal Scherer

  4. AGH University of Science and Technology, Krakow, Poland

    Ryszard Tadeusiewicz

  5. University of California, Berkeley, California, USA

    Lotfi A. Zadeh

  6. University of Louisville, Louisville, Kentucky, USA

    Jacek M. Zurada

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Pliszka, Z., Unold, O. (2015). On the Ability of the One-Point Crossover Operator to Search the Space in Genetic Algorithms. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2015. Lecture Notes in Computer Science(), vol 9119. Springer, Cham. https://doi.org/10.1007/978-3-319-19324-3_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-19324-3_33

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19323-6

  • Online ISBN: 978-3-319-19324-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation