Advertisement

Control Law and Pseudo Neural Networks Synthesized by Evolutionary Symbolic Regression Technique

  • Zuzana Kominkova OplatkovaEmail author
  • Roman Senkerik
Chapter
Part of the Simulation Foundations, Methods and Applications book series (SFMA)

Abstract

This research deals with synthesis of final complex expressions by means of an evolutionary symbolic regression technique—analytic programming (AP)—for novel approach to classification and system control. In the first case, classification technique—pseudo neural network is synthesized, i.e. relation between inputs and outputs created. The inspiration came from classical artificial neural networks where such a relation between inputs and outputs is based on the mathematical transfer functions and optimized numerical weights. AP will synthesize a whole expression at once. The latter case, the AP will create chaotic controller that secures the stabilization of stable state and high periodic orbit—oscillations between several values of discrete chaotic system. Both cases will produce a mathematical relation with several inputs, the latter case uses several historical values from the time series. For experimentation, Differential Evolution (DE) for the main procedure and also for meta-evolution version of analytic programming (AP) was used.

Keywords

Analytic programming Differential evolution Control law Pseudo neural network 

Notes

Acknowledgement

This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme project No. LO1303 (MSMT-7778/2014) and also by the European Regional Development Fund under the project CEBIA-Tech No. CZ.1.05/2.1.00/03.0089, further it was supported by Grant Agency of the Czech Republic—GACR 588P103/15/06700S.

References

  1. 1.
    Back T, Fogel DB, Michalewicz Z (1997) Handbook of evolutionary algorithms. Oxford University Press. ISBN: 0750303921Google Scholar
  2. 2.
    Deugo D, Ferguson D (2004) Evolution to the Xtreme: evolving evolutionary strategies using a meta-level approach. In: Proceedings of the 2004 IEEE congress on evolutionary computation. IEEE Press, Portland, Oregon, pp 31–38Google Scholar
  3. 3.
    Dioşan L, Oltean M (2009) Evolutionary design of evolutionary algorithms. Genet Program Evolvable Mach 10(3):263–306Google Scholar
  4. 4.
    Edmonds B (2001) Meta-genetic programming: co-evolving the operators of variation. Elektrik 9(1):13–29Google Scholar
  5. 5.
    Eiben AE, Michalewicz Z, Schoenauer M, Smith JE (2007) Parameter control in evolutionary algorithms. Springer, pp 19–46Google Scholar
  6. 6.
    Fausett LV (1993) Fundamentals of neural networks: architectures, algorithms and applications. Prentice Hall, ISBN: 9780133341867Google Scholar
  7. 7.
    Fekiac J, Zelinka I, Burguillo JC (2011) A review of methods for encoding neural network topologies in evolutionary computation. In: ECMS 2011, Krakow, Poland, ISBN: 978-0-9564944-3-6Google Scholar
  8. 8.
    Fisher RA (1936) The use of multiple measurements in taxonomic problems. Ann. Eugenics 7(2):179–188. doi: 10.1111/j.1469-1809.1936.tb02137.x Google Scholar
  9. 9.
    Gurney K (1997) An introduction to neural networks. CRC Press, ISBN: 1857285034Google Scholar
  10. 10.
    Hertz J, Kogh A, Palmer RG (1991) Introduction to the theory of neural computation. Addison-WesleyGoogle Scholar
  11. 11.
    Hilborn RC (2000) Chaos and nonlinear dynamics: an introduction for scientists and engineers. Oxford University Press, ISBN: 0-19-850723-2Google Scholar
  12. 12.
    Jones DF, Mirrazavi SK, Tamiz M (2002) Multi-objective meta-heuristics: an overview of the current state-of-the-art. Eur J Oper Res 137(1):1–9, ISSN: 0377-2217Google Scholar
  13. 13.
    Just W (1999) Principles of time delayed feedback control. In: Schuster HG (ed) Handbook of chaos control. Wiley-Vch, ISBN: 3-527-29436-8Google Scholar
  14. 14.
    Kalczynski PJ, Kamburowski J (2007) On the NEH heuristic for minimizing the makespan in permutation flow shops. Omega 35(1):53–60Google Scholar
  15. 15.
    Kordík P, Koutník J, Drchal J, Kovářík O, Čepek M, Šnorek M (2010) Meta-learning approach to neural network optimization. Neural Netw 23(4):568–582, ISSN: 0893-6080Google Scholar
  16. 16.
    Koza JR et al (1999) Genetic programming III; darwinian invention and problem solving. Morgan Kaufmann Publisher, ISBN: 1-55860-543-6Google Scholar
  17. 17.
    Koza JR (1998) Genetic programming. MIT Press, ISBN: 0-262-11189-6Google Scholar
  18. 18.
    Kwon OJ (1999) Targeting and stabilizing chaotic trajectories in the standard map. Phys Lett A 258:229–236Google Scholar
  19. 19.
    Lampinen J, Zelinka I (1999) New ideas in optimization—mechanical engineering design optimization by differential evolution, vol 1. McGraw-hill, London, 20p, ISBN: 007-709506-5Google Scholar
  20. 20.
    Machine learning repository with Iris data set http://archive.ics.uci.edu/ml/datasets/Iris
  21. 21.
    Murty KG (1983) Linear programming. Wiley, New York, ISBN: 0-471-09725-XGoogle Scholar
  22. 22.
    Murty KG (1988) Linear complementarity, linear and nonlinear programming, Sigma series in applied mathematics. Heldermann Verlag, Berlin, ISBN: 3-88538-403-5Google Scholar
  23. 23.
    O’Neill M, Ryan C (2003) Grammatical evolution. Evolutionary automatic programming in an arbitrary language. Kluwer Academic Publishers, ISBN: 1402074441Google Scholar
  24. 24.
    Oplatkova Z (2009) Metaevolution: synthesis of optimization algorithms by means of symbolic regression and evolutionary algorithms. Lambert Academic Publishing Saarbrücken, ISBN: 978-3-8383-1808-0Google Scholar
  25. 25.
    Oplatková Z, Zelinka I (2009) Investigation on evolutionary synthesis of movement commands, modelling and simulation in engineering, vol 2009, Article ID 845080, 12p. Hindawi Publishing Corporation, ISSN: 1687-559Google Scholar
  26. 26.
    Oplatkova Z, Senkerik R, Zelinka I, Holoska J (2010) Synthesis of control law for Chaotic Henon system—preliminary study, ECMS 2010, Kuala Lumpur, Malaysia, pp 277–282, ISBN: 978-0-9564944-0-5Google Scholar
  27. 27.
    Oplatkova Z, Senkerik R, Belaskova S, Zelinka I (2010) Synthesis of control rule for synthesized chaotic system by means of evolutionary techniques, Mendel 2010, Brno, Czech Republic, pp 91–98, ISBN: 978-80-214-4120-0Google Scholar
  28. 28.
    Ott E, Greboki C, Yorke JA (1990) Controlling chaos. Phys Rev Lett 64:1196–1199Google Scholar
  29. 29.
    Price K, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization, (Natural computing series), 1st edn. SpringerGoogle Scholar
  30. 30.
    Price K, Storn R (2001) Differential evolution homepage. http://www.icsi.berkeley.edu/~storn/code.html, [Accessed 29/02/2012]
  31. 31.
    Pyragas K (1992) Continuous control of chaos by self-controlling feedback. Phys Lett A 170:421–428Google Scholar
  32. 32.
    Pyragas K (1995) Control of chaos via extended delay feedback. Phys Lett A 206:323–330Google Scholar
  33. 33.
    Senkerik R, Zelinka I, Navratil E (2006) Optimization of feedback control of chaos by evolutionary algorithms. In: Proceedings 1st IFAC conference on analysis and control of chaotic systems, Reims, France, pp 97–102Google Scholar
  34. 34.
    Senkerik R, Zelinka I, Davendra D, Oplatkova Z (2009) Utilization of SOMA and differential evolution for robust stabilization of chaotic logistic equation. Comput Math Appl 60(4):1026–1037Google Scholar
  35. 35.
    Senkerik R, Oplatkova Z, Zelinka I, Davendra D, Jasek R (2010) Synthesis of feedback controller for chaotic systems by means of evolutionary techniques. In: Proceeding of fourth global conference on power control and optimization, Sarawak, Borneo (2010)Google Scholar
  36. 36.
    Smith J, Fogarty T (1997) Operator and parameter adaptation in genetic algorithms. Soft Comput 1(2):81–87Google Scholar
  37. 37.
    Voutsinas TG, Pappis CP (2010) A branch and bound algorithm for single machine scheduling with deteriorating values of jobs. Math Comput Model 52(1–2):55–61Google Scholar
  38. 38.
    Wasserman PD (1980) Neural computing: theory and practice. Coriolis Group, ISBN: 0442207433Google Scholar
  39. 39.
    Zelinka et al (2004) Analytical programming—a novel approach for evolutionary synthesis of symbolic structures, in Kita E.: evolutionary algorithms, InTech 2011, ISBN: 978-953-307-171-8Google Scholar
  40. 40.
    Varacha P, Zelinka I, Oplatkova Z (2006) Evolutionary synthesis of neural network, Mendel 2006—12th international conference on softcomputing, Brno, Czech Republic, 31 May–2 June 2006, pp 25–31, ISBN: 80-214-3195-4Google Scholar
  41. 41.
    Zelinka I,Oplatkova Z, Nolle L (2005) Boolean symmetry function synthesis by means of arbitrary evolutionary algorithms-comparative study. Int J Simul Syst Sci Technol 6(9):44–56, ISSN: 1473-8031Google Scholar
  42. 42.
    Zelinka I, Senkerik R, Navratil E (2009) Investigation on evolutionary optimization of chaos control. Chaos Solitons Fractals 40(1):111–129Google Scholar
  43. 43.
    Zelinka I, Guanrong Ch, Celikovsky S (2008) Chaos synthesis by means of evolutionary algorithms. Int J Bifurcat Chaos 18(4):911–942Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of Applied InformaticsTomas Bata University in ZlinZlinCzech Republic

Personalised recommendations