Skip to main content

Advertisement

SpringerLink
Log in

On the influence of different number generators on results of the symbolic regression

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

This paper deals with mutual comparison of different pseudorandom number generators and its impact on the performance of selected algorithms of the symbolic regression. In this paper we discuss the use of genetic programming (GP) with use of chaotic systems as well as its main attributes and universal features. It is also explained why deterministic chaos is used and compared here with standard pseudorandom number generators. Based on the characterization of deterministic chaos, universal features of that kind of behavior are explained. In the second part of the paper we discuss selected examples of GP powered by deterministic chaos and classical pseudorandom number generators and its results.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Arnold V (1991) The theory of singularities and its applications. Accademia Nazionale Dei Lincei, Pisa

    MATH  Google Scholar 

  • Drazin P, Kind G (eds) (1992) Interpretation of time series from nonlinear systems. Special Issue Physica D 58

  • Fang H, Ross P, Corne D (1994) Genetic algorithms for timetabling and scheduling. http://www.asap.cs.nott.ac.uk/ASAP/ttg/resources.html. Accessed Feb 2013

  • Gilmore R (1993) Catastrophe theory for scientists and engineers. John Wiley and Sons, London

  • Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Longman Publishing, Boston

  • Group K (2012) Opencl—the open standard for parallel programming of heterogeneous systems, OpenCL 1.2. http://www.khronos.org/opencl/. Accessed Nov 2013

  • Haken H (2004) Synergetics: introduction and advanced topics. Springer, New York

  • Huang C, Li G, Xu Z, Yu A, Chang L (2012) Design of optimal digital lattice filter structures based on genetic algorithm. Signal Process 92(4):989–998

    Article  Google Scholar 

  • Ishibuchi H, Nakashima Y, Nojima Y (2011) Performance evaluation of evolutionary multiobjective optimization algorithms for multiobjective fuzzy genetics-based machine learning. Soft Comput 15(12):2415–2434

    Article  Google Scholar 

  • Johnson C (2004) Artificial immune systems programming for symbolic regression. In: Ryan C, Soule T, Keijzer M, Tsang E, Poliand R, Costa E (eds) Lecture notes in computer science. Springer-Verlag, Berlin, pp 345–353

  • Juzoji H, Nakajima I, Kitano T (2011) A development of network topology of wireless packet communications for disaster situation with genetic algorithms or with dijkstra’s. In: ICC, pp 1–5

  • Koza J (1990) Genetic programming: a paradigm for genetically breeding populations of computer programs to solve problems. In: Technical report, STAN-CS-90-1314. Stanford University, Stanford

  • Koza J (1998) Genetic programming. MIT Press, Cambridge

  • Koza J, Bennet F, Andre D, Keane M (1999) Genetic programming III. Morgan Kaufmann, New York

  • Koza J, Keane M, Streeter M (2003) Evolving inventions. Scientific American, pp 40–47

  • Matsumoto M, Nishimura T (1998) Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans Model Comput Simul 8(1):3–30. doi:10.1145/272991.272995

    Google Scholar 

  • Mitchell M (1999) An introduction to genetic algorithms. A Bradford book. MIT-Press, Cambridge

  • Mitchell M, Forrest S (1994) Genetic algorithms and artificial life. Artificial Life 1(3):267–289. doi:10.1162/artl.1994.1.267

    Google Scholar 

  • O’Neill M, Brabazon A (2006) Grammatical differential evolution. In: Proceedings of international conference on artificial intelligence. CSEA Press, California, pp 231–236

  • Oplatkova Z, Zelinka I (2006) Investigation on artificial ant using analytic programming. IN: Proceedings of genetic and evolutionary computation conference, Seattle, pp 949–950

  • Packard N, Crutchfield J, Farmer D, Shaw R (1980) Geometry from a time series. Phys Rev Lett 45:712

    Article  Google Scholar 

  • Pan ST (2010) A canonic-signed-digit coded genetic algorithm for designing finite impulse response digital filter. Digital Signal Process 20(2):314–327

    Article  Google Scholar 

  • Park BJ, Choi HR (2006) A genetic algorithm for integration of process planning and scheduling in a job shop. In: Australian conference on artificial intelligence, pp 647–657

  • Poston T, Stewart I (1977) Catastrophe theory and its applications. Pitman, IEEE Press, New York, pp 842–844

  • Price K (1999) An introduction to differential evolution. In: Corne D, Dorigo M, Glover F (eds) New ideas in optimization. McGraw-Hill, London, pp 79–108

  • Ryan C, Collins J, O’Neill M (1998) Grammatical evolution: evolving programs for an arbitrary language. In: Lecture notes in computer science, First European workshop on genetic programming

  • Sedighi KH, Manikas TW, Ashenayi K, Wainwright RL (2009) A genetic algorithm for autonomous navigation using variable-monotone paths I. J Robotics Autom 24(4)

  • Takens F (1981) Detecting strange attractors in turbulence. In: Lecture notes in mathematics, vol 898.

  • Tsang EPK, Warwick T (1990) Applying genetic algorithms to constraints satisfaction optimization problems. In: Aiello LC (ed) Proceeding of the 9th European conference on AI

  • Wainwright RL (1993) Introduction to genetic algorithms theory and applications. In: 7th Oklahoma symposium on artificial intelligence

  • Weisser R, Osmera P (2010) Two-level transplant evolution for optimization of general controllers. New trends in technologies. Sciyo, Austria

    Google Scholar 

  • Weisser R, Osmera P (2010) Two-level tranpslant evolution, 17th Zittau fuzzy colloquium. Zittau, Germany

    Google Scholar 

  • Weisser R, Osmera P, Matousek R (2010) Transplant evolution with modified schema of differential evolution: optimization structure of controllers. In: International conference on soft computing MENDEL, Brno

  • Zelinka I (2004) SOMA—self organizing migrating algorithm. In: Babu BV, Onwubolu G (eds) New optimization techniques in engineering. Springer-Verlag, New York, pp 167–218

  • Zelinka I, Oplatkova Z (2003) Analytic programming—comparative study. In: Proceedings of 2nd international conference on computational intelligence, robotics, and autonomous systems, Singapore

  • Zelinka I, Oplatkova Z, Nolle L (2005) Analytic programming—symbolic regression by means of arbitrary evolutionary algorithms. Int J Simul Syst Sci Technol 6(9):44–56

    Google Scholar 

  • Zelinka I, Chen G, Celikovsky S (2008) Chaos synthesis by means of evolutionary algorithms. Int J Bifurcation Chaos 18(4):911–942 (ISSN 0218-1274)

    Google Scholar 

  • Zelinka I, Chen G, Celikovsky S (eds) (2010) Evolutionary Algorithms and Chaotic Systems. Springer, Germany

    MATH  Google Scholar 

  • Zelinka I, Davendra D, Senkerik R, Jasek R, Oplatkova Z (2011) Analytical programming—a novel approach for evolutionary synthesis of symbolic structures, evolutionary algorithms. In: Kita E (ed) InTech doi:10.5772/16166. http://www.intechopen.com/books/evolutionary-algorithms/analytical-programming-a-novel-approach-for-evolutionary-synthesis-of-symbolic-structures. ISBN 978-953-307-171-8. Accessed Nov 2013

  • Zelinka I, Chadli M, Davendra D, Senkerik R, Pluhacek M, Lampinen J (2013a) Do evolutionary algorithms indeed require random numbers? Extended study. In: Proceedings of Nostradamus 2013: international conference prediction, modeling and analysis of complex systems. Springer series: advances in intelligent systems and computing, vol 210, pp 61–75

  • Zelinka I, Skanderova L, Saloun P, Senkerik R, Pluhacek M (2013b) Chaos powered symbolic regression in be stars spectra modeling. In: International symposium of complex systems, Prague

  • Zelinka I, Chadli M, Davendra D, Senkerik R, Pluhacek M, Lampinen J (2013c) Hidden periodicity—chaos dependance on numerical precision. In: Proceedings of Nostradamus 2013: international conference prediction, modeling and analysis of complex systems. Springer series: advances in intelligent systems and computing vol 210, pp 47–59

  • Zelinka I, Senkerik R, Pluhacek M (2013d) Do evolutionary algorithms indeed require randomness? In: IEEE congress on evolutionary computation, Cancun, pp 2283–2289

Download references

Acknowledgments

This article has been elaborated in the framework of the IT4Innovations Centre of Excellence project, Reg. No. CZ.1.05/1.1.00/02.0070 funded by Structural Funds of the European Union and state budget of the Czech Republic. Next, following two grants are acknowledged for the financial support provided for this research: Grant Agency of the Czech Republic—GACR P103/13/08195S, by the Development of human resources in research and development of latest soft computing methods and their application in practice project, Reg. No. CZ.1.07/2.3.00/20.0072 funded by Operational Programme Education for Competitiveness, co-financed by ESF and state budget of the Czech Republic, partially supported by Grant of SGS No. SP2013/114, VŠB—Technical University of Ostrava, Czech Republic.

Author information

Authors and Affiliations

  1. Department of Computer Science, VŠB, Technical University of Ostrava, 17. Listopadu 15, Ostrava, Czech Republic

    Petr Gajdoš & Ivan Zelinka

Authors
  1. Petr Gajdoš
    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

Corresponding author

Correspondence to Petr Gajdoš.

Additional information

Communicated by I. Zelinka.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gajdoš, P., Zelinka, I. On the influence of different number generators on results of the symbolic regression. Soft Comput 18, 641–650 (2014). https://doi.org/10.1007/s00500-013-1172-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-013-1172-x

Keywords

Search

Navigation