Skip to main content
SpringerLink
Log in

Chaos Powered Selected Evolutionary Algorithms

  • Conference paper
Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 210))

Abstract

It is well known that the evolution algorithms use pseudo-random numbers generators for example to generate random individuals in the space of possible solutions, crossing etc. In this paper we are dealing with the effect of different pseudo-random numbers generators on the course of evolution and the speed of their convergence to the global minimum. From evolution algorithms the differential evolution and self organizing migrating algorithm have been chosen because they have different strategies. As the random generators Mersenne Twister and chaotic system - logistic map have been used.

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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. Zelinka, I., et al.: Evolutionary Algorithms and Chaotic Systems. SCI. Springer (2010) ISBN-10: 3642107060, ISBN-13: 978-364210706

    Google Scholar 

  2. Zelinka, I.: On evolutionary synthesis of chaotic systems. In: Zelinka, I., Snasel, V., Rössler, O.E., Abraham, A., Corchado, E.S. (eds.) Nostradamus: Mod. Meth. of Prediction, Modeling. AISC, vol. 192, pp. 29–34. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  3. Brandejsky, T., Zelinka, I.: Specific behaviour of GPA-ES evolutionary system observed in deterministic chaos regression. In: Zelinka, I., Snasel, V., Rössler, O.E., Abraham, A., Corchado, E.S. (eds.) Nostradamus: Mod. Meth. of Prediction, Modeling. AISC, vol. 192, pp. 73–81. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  4. Pluhacek, M., Senkerik, R., Zelinka, I.: Impact of various chaotic maps on the performance of chaos enhanced PSO algorithm with inertia weight – an initial study. In: Zelinka, I., Snasel, V., Rössler, O.E., Abraham, A., Corchado, E.S. (eds.) Nostradamus: Mod. Meth. of Prediction, Modeling. AISC, vol. 192, pp. 153–166. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  5. Tien, J.P., Li, T.H.S.: Hybrid Taguchi-chaos of multilevel immune and the artificial bee colony algorithm for parameter identification of chaotic systems. Computer & Mathematics with Applications 64, 1108–1119 (2012)

    Article  Google Scholar 

  6. Manal, K.K., et al.: Emission Constrained Economic Dispatch Using Logistic Map Adaptive Differential Evolution. In: Proceedings of the International Conference on Information Systems Design and Intelligent Applications 2012, vol. 132, pp. 387–394 (2012)

    Google Scholar 

  7. Mandal, K.K., Bhattacharya, B., Tudu, B., Chakraborty, N.: Logistic Map Adaptive Differential Evolution for Optimal Capacitor Placement and Sizing. In: Panigrahi, B.K., Suganthan, P.N., Das, S., Satapathy, S.C. (eds.) SEMCCO 2011, Part I. LNCS, vol. 7076, pp. 68–76. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  8. Senkerik, R., et al.: Utilization of SOMA and differential evolution for robust stabilization of chaotic Logistic equation. 3rd Global Conference on Power Control Optimization. Computers & Mathematics with Applications 60, 1026–1037 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hu, H.P., et al.: Pseudorandom sequence generator based on the Chen chaotic system. Computer Physicics Communications 184, 765–768 (2013)

    Article  Google Scholar 

  10. Wang, X.Y., Qin, X.: A new pseudo-random number generator based on CML and chaotic iteration. Nonlinear Dynamics 70, 1589–1592 (2012)

    Article  MathSciNet  Google Scholar 

  11. Song, H.L.: New Pseudorandom Number Generator Artin-Schreier Tower for p=5. China Communications 9, 60–67 (2012)

    Google Scholar 

  12. Marquardt, P., et al.: Pseudorandom number generators based on random covers for finite groups. Designs Codes and Cryptography 64, 209–220 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Karimi, H., et al.: On the combination of self-organized systems to generate pseudo-random numbers. Information Science 221, 371–388 (2013)

    Article  MathSciNet  Google Scholar 

  14. Zhou, Y., Li, X., Gao, L.: A differential evolution algorithm with intersect mutation operator. Applied Soft Computing 13, 390–401 (2013)

    Article  Google Scholar 

  15. Nolle, L., Zelinka, I., Hopgood, A.A., Goodyear, A.: Comparison of an self-organizing migration algorithm with simulated annealing and differential evolution for automated waveform tuning

    Google Scholar 

  16. Matsumoto, M., Nishimura, T.: Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator. ACM Transactions on Modeling and Computer Simulation 8, 3–30 (1998)

    Article  MATH  Google Scholar 

  17. Bonato, V., et al.: A Mersenne Twister Hardware Implementation for the Monte Carlo Localization Algorithm. Journal of Signal Processing Systemsfor Signal, Image, and Video Technology (formerly the Journal of VLSI Signal Processing Systems for Signal, Image, and Video Technology) (2012)

    Google Scholar 

  18. Manssen, M., et al.: Random number generators for massively parallel simulations on GPU. The European Physical Journal Special Topics, EDP Sciences, 53–71 (2012)

    Google Scholar 

  19. Leiserson, et al.: Deterministic Parallel Random-Number Generation for Dynamic-Multithreading Platforms. In: 17th ACM SIGPLAN symposium on Principles and Practice of Parallel Programming, pp. 193–204. ACM, New York (2012)

    Google Scholar 

  20. Maucher, M., Schning, U., Kestler, H.A.: Search heuristics and the influence of non-perfect randomness: examining Genetic Algorithms and Simulated Annealing. Springer (2011)

    Google Scholar 

  21. Wiese, K.C., et al.: P-RnaPredict - A parallel evolutionary algorithm for RNA folding: Effects of pseudorandom number quality. IEEE Transactions on Nanobioscience 4, 219–227 (2005)

    Article  Google Scholar 

  22. Igarashi, J., Sonoh, S., Koga, T.: Particle Swarm Optimization with SIMD-Oriented Fast Mersenne Twister on the Cell Broadband Engine. In: Köppen, M., Kasabov, N., Coghill, G. (eds.) ICONIP 2008, Part II. LNCS, vol. 5507, pp. 1065–1071. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  23. http://msdn.microsoft.com/en-us/library/system.random.aspx

  24. Hegazi, A.S., et al.: On chaos control and synchronization of the commensurate fractional order Liu system. Communications in Nonlinear Science and Numerical Simulation 18, 1193–1202 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  25. Senkerik, R.: On the Evolutionary Optimization of Chaos Control - A Brief Survey. Nostradamus: Modern Methods of Prediction, Modeling and Analysis of Nonlinear Systems 192, 35–48 (2013)

    Article  Google Scholar 

  26. Senkerik, R., Davendra, D., Zelinka, I., Oplatkova, Z., Pluhacek, M.: Optimization of the batch reactor by means of chaos driven differential evolution. In: Snasel, V., Abraham, A., Corchado, E.S. (eds.) SOCO Models in Industrial & Environmental Appl. AISC, vol. 188, pp. 93–102. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  27. Chen, D.Y., et al.: Control and synchronization of chaos in an induction motor system. International Journal of Innovative Computing Information and Control 8, 7237–7248 (2012)

    Google Scholar 

  28. Schuster, H.G., Just, W.: Deterministic Chaos An Introduction. Wiley-VCH Verlag GmbH & Co., KGaA, Weinheim (2005)

    Book  MATH  Google Scholar 

  29. Nagatani, T., Sugiyama, N.: Vehicular traffic flow through a series of signals with cycle time generated by a logistic map. Physica A: Statistical Mechanics and its Applications 392, 851–856 (2013)

    Article  Google Scholar 

  30. Hussain, I., et al.: An efficient approach for the construction of LFT S-boxes using chaotic logistic map. Nonlinear Dynamics 71, 133–140 (2013)

    Article  Google Scholar 

  31. Akhshani, A., et al.: An image encryption scheme based on quantum logistic map. Communications in Nonlinear Science and Numerical Simulation 17, 4653–4661 (2012)

    Article  MathSciNet  Google Scholar 

  32. He, Y.Y., et al.: A fuzzy clustering iterative model using chaotic differential evolution algorithm for evaluating flood disaster. Expert Systems with Applications 38, 10060–10065 (2011)

    Article  Google Scholar 

  33. Wu, X., Zhu, P.: Chaos in a class of non-autonomous discrete systems. Applied Mathematics Letters 26, 431–436 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  34. Kuznetsov, N.V., Leonov, G.A.: On stability by the first approximation for discrete systems. In: Proceedings of International Conference on Physics and Control, PhysCon 2005, vol. 2005, pp. 596–599 (2005)

    Google Scholar 

  35. Leonov, G.A., Kuznetsov, N.V.: Time-Varying Linearization and the Perron effects. International Journal of Bifurcation and Chaos 17, 1079–1107 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  36. Kaclek, J., Mca, I.: Nelinern analza a predikce stovho provozu Elektrorevue (2009) ISSN 1213 – 1539

    Google Scholar 

  37. Pluhacek, M., et al.: On the Behaviour and Performance of Chaos Driven PSO Algorithm with Inertia Weight. Computers & Mathematics with Applications (2012) (accepted for publication) ISSN 0898-1221

    Google Scholar 

  38. Pluhacek, M., Budikova, V., Senkerik, R., Oplatkova, Z., Zelinka, I.: Extended initial study on the performance of enhanced PSO algorithm with lozi chaotic map. In: Zelinka, I., Snasel, V., Rössler, O.E., Abraham, A., Corchado, E.S. (eds.) Nostradamus: Mod. Meth. of Prediction, Modeling. AISC, vol. 192, pp. 167–177. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  39. Pluhacek, M., Senkerik, R., Zelinka, I.: Impact of various chaotic maps on the performance of chaos enhanced PSO algorithm with inertia weight – an initial study. In: Zelinka, I., Snasel, V., Rössler, O.E., Abraham, A., Corchado, E.S. (eds.) Nostradamus: Mod. Meth. of Prediction, Modeling. AISC, vol. 192, pp. 153–166. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  40. Pluhacek, M., Senkerik, R., Davendra, D., Zelinka, I.: Designing PID controller for DC motor by means of enhanced PSO algorithm with dissipative chaotic map. In: Snasel, V., Abraham, A., Corchado, E.S. (eds.) SOCO Models in Industrial & Environmental Appl. AISC, vol. 188, pp. 475–483. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  41. Pluhacek, M., et al.: PID Controller Design For 4th Order system By Means Of Enhanced PSO algorithm With Lozi Chaotic Map. In: Proceedings of 18th International Conference on Soft Computing, MENDEL 2012, pp. 35–39 (2012) ISBN 978-80-214-4540-6

    Google Scholar 

  42. Pluhacek, M., et al.: On The Performance Of Enhanced PSO algorithm With Lozi Chaotic Map –An Initial Study. In: Proceedings of 18th International Conference on Soft Computing, MENDEL 2012, pp. 40–45 (2012) ISBN 978-80-214-4540-6

    Google Scholar 

  43. Pluhacek, M., et al.: Designing PID Controller For DC Motor System By Means Of Enhanced PSO Algorithm With Discrete Chaotic Lozi Map. In: Proceedings of 26th European Conference on Modelling and Simulation, ECMS 2012, pp. 405–409 (2012) ISBN 978-0-9564944-4-3

    Google Scholar 

  44. Pluhacek, M., et al.: Designing PID Controller for 4th Order System By Means of Enhanced PSO Algorithm with Discrete Chaotic Dissipative Standard Map. In: Proceedings of 24th European Modeling & Simulation Symposium, EMSS 2012, pp. 396–401 (2012) ISBN 978-88-97999-09-6

    Google Scholar 

  45. Pluhacek, M., et al.: On the Performance of Enhanced PSO Algorithm with Lozi Chaotic Map. In: Application of Modern Methods of Prediction, Modeling and Analysis of Nonlinear Systems. SCI, vol. 1, p. 18. Springer (November 2012) (accepted for publication) ISSN: 1860-949X

    Google Scholar 

  46. Glover, F., Laguna, M., Mart, R.: Scatter Search. In: Ghosh, A., Tsutsui, S. (eds.) Advances in Evolutionary Computation: Theory and Applications, pp. 519–537. Springer, New York (2003)

    Google Scholar 

  47. Beyer, H.-G.: Theory of Evolution Strategies. Springer, New York (2001)

    Book  Google Scholar 

  48. Holland, J.H.: Genetic Algorithms. Scientific American, 44–50 (July 1992)

    Google Scholar 

  49. Clerc, M.: Particle Swarm Optimization. ISTE Publishing Company (2006) ISBN 1905209045

    Google Scholar 

  50. Matousek, R.: HC12: The Principle of CUDA Implementation. In: Matousek (ed.) 16th International Conference on Soft Computing, MENDEL 2010, Brno, pp. 303–308 (2010)

    Google Scholar 

  51. Matousek, R., Zampachova, E.: Promising GAHC and HC12 algorithms in global optimization tasks. Journal Optimization Methods & Software 26(3), 405–419 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  52. Matousek, R.: GAHC: Improved Genetic Algorithm. In: Krasnogor, N., Nicosia, G., Pavone, M., Pelta, D. (eds.) Nature Inspired Cooperative Strategies for Optimization (NICSO 2007). SCI, vol. 129, pp. 507–520. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  53. Zelinka, I., Davendra, D., Senkerik, R., Jasek, R., Oplatkova, Z.: Analytical Programming - a Novel Approach for Evolutionary Synthesis of Symbolic Structures. In: Kita, E. (ed.) Evolutionary Algorithms. InTech (2011) ISBN: 978-953-307-171-8, http://www.intechopen.com/books/evolutionary-algorithms/analytical-programming-a-novel-approach-for-evolutionary-synthesis-of-symbolic-structures , doi:10.5772/16166

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, VSB-Technical university Ostrava, 17. listopadu 15, 708 33, Ostrava-Poruba, Czech Republic

    Lenka Skanderova, Ivan Zelinka & Petr Šaloun

Authors
  1. Lenka Skanderova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ivan Zelinka
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Petr Šaloun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lenka Skanderova .

Editor information

Editors and Affiliations

  1. Faculty of Electrical Eng. & Comp. Sci, Department of Computer Science, VŠB-TUO, 17. listopadu 15, Ostrava-Poruba, 708 33, Czech Republic

    Ivan Zelinka

  2. , Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, China, People's Republic

    Guanrong Chen

  3. , Institute of Physical, University of Tuebingen, Auf der Morgenstelle 8, Tuebingen, 72076, Germany

    Otto E. Rössler

  4. Faculty of Electrical Eng. & Comp. Sci., Department of Computer Science, VŠB-TUO, 17. listopadu 15, Ostrava-Poruba, 708 33, Czech Republic

    Vaclav Snasel

  5. (MIR Labs), Scientific Network for Innovation, Machine Intelligence Research Labs, Auburn, 98071, Washington, USA

    Ajith Abraham

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this paper

Cite this paper

Skanderova, L., Zelinka, I., Šaloun, P. (2013). Chaos Powered Selected Evolutionary Algorithms. In: Zelinka, I., Chen, G., Rössler, O., Snasel, V., Abraham, A. (eds) Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems. Advances in Intelligent Systems and Computing, vol 210. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00542-3_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-00542-3_12

  • Publisher Name: Springer, Heidelberg

  • Print ISBN: 978-3-319-00541-6

  • Online ISBN: 978-3-319-00542-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation