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Solving Trigonometric Identities with Tree Adjunct Grammar Guided Genetic Programming

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Book cover Hybrid Information Systems

Part of the book series: Advances in Soft Computing ((AINSC,volume 14))

Abstract

Tree-adjunct grammar guided genetic programming (TAG3P) (Hoai and McKay 2001) is a grammar guided genetic programming system that uses context-free grammars along with tree-adjunct grammars as means to set language bias for the genetic programming system. In this paper, we show the result of TAG3P on the problem of discovering trigonometric identities, one of the benchmark problems in genetic programming (Koza 1992). The results show that although TAG3P did successfully discover all three popular trigonometric identities of the trigonometric function cos(2x), namely, sin(2x+π/2), sin(π/2-2x) and 1-2sin2(x), it had a tendency to converge towards the first two identities.

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References

  • Banzhaf W, Nordin P, Keller RE, Francone FD (1998) Genetic Programming: An Introduction. Morgan Kaufmann Pub, USA.

    Google Scholar 

  • Gruau F (1996) On Using Syntactic Constraints with Genetic Programming. In: Angeline P J Kinnear KE Jr (eds) Advances in Genetic Programming. The MIT Press, USA, pp 377–394.

    Google Scholar 

  • Hoai NX (2001) Solving The Symbolic Regression Problem with Tree-Adjunct Grammar Guided Genetic Programming: The Preliminary Results. (To appear in the Proceedings of The 5th Autraliasia-Japan Co-Joint Workshop on Evolutionary Computation, Nov 2001, Ontago New Zealand).

    Google Scholar 

  • Hoai NX, McKay RI (2001) A Framework for Tree Adjunct Grammar Guided Genetic Programming. In: Abbass HA, Barlow M (eds) Proceedings of the Post-graduate ADFA Conference on Computer Science (PACCS’01), pp 93–99.

    Google Scholar 

  • Joshi AK, Levy LS, Takahashi M (1975). Tree Adjunct Grammars. Journal of Computer and System Sciences, 10 (1): 136–163.

    Article  MathSciNet  MATH  Google Scholar 

  • Joshi AK, Schabes Y (1992) Tree-Adjoining Grammars and Lexicalized Grammars. In: Nivat M and Podelski A (eds) Tree Automata and Languages. Elsvier Science Publisher, pp 409–431.

    Google Scholar 

  • Joshi AK, Schabes Y (1997) Tree Adjoining Grammars. In: Rozenberg G, Saloma A (eds) Handbook of Formal Languages. Springer-Verlag, NY, USA, vol 3, pp 69–123.

    Google Scholar 

  • Koza J (1992) Genetic Programming. The MIT Press, USA.

    Google Scholar 

  • Montana DJ (1995) Strongly Typed Genetic Programming. Evolutionary Computation 3 (2): 199–230.

    Article  Google Scholar 

  • O’Neill M (1999) Automatic Programming with Grammatical Evolution. In: Proceedings of the Genetic and Evolutionary Computation Conference Workshop Program, July 13–17, Orlando, Florida USA.

    Google Scholar 

  • O’Neil M, Collin JJ (1998) Grammar Evolution: Solving Trigonometric Identities. In: Proceedings of Mendel ‘88, pp 111–119.

    Google Scholar 

  • O’Neill M, Ryan C (1998) Grammatical Evolution: A Steady State Approach. In: Proceedings of the Second International Workshop on Frontiers in Evolutionary Algorithms 1998, pp 419–423.

    Google Scholar 

  • O’Neil M, Ryan C (1999a) Under the Hood of Grammatical Evolution. In: Banzhaf W,.Daida J, Eiben AE, Garzon MH, Hovana V, Jakiela M, Smith RE (eds). GECCO99, Morgan Kaufmann Pub, USA.

    Google Scholar 

  • O’Neill M, Ryan C (1999b) Genetic Code Degeneracy: Implication for Grammatical Evolution and Beyond. In: Proceedings of the European Conference on Artificial Life.

    Google Scholar 

  • Ratle A, Sebag M (2000) Genetic Programming and Domain Knowledge: Beyond the Limitations of Grammar-Guided Machine Discovery. Ecole Polytechnique, France. (Available at: www.researchindex.com. Accessed: 30, May, 2001 ).

    Google Scholar 

  • Ryan C, Collin JJ, O’Neill M (1998) Grammatical Evolution: Evolving Programs for an Arbitrary Language. In: Lecture Note in Computer Science 1391, Proceedings of the First European Workshop on Genetic Programming, Springer-Verlag, pp 83–95.

    Google Scholar 

  • Whigham P (1995) Grammatically-based Genetic Programming. In: Proceedings of the Workshop on Genetic Programming: From Theory to Real-World Applications, pp 3341, Morgan Kaufmann Pub.

    Google Scholar 

  • Whigham P (1996) Search Bias, Language Bias and Genetic Programming. In Genetic Programming 1996, The MIT Press, USA, pp 230–237.

    Google Scholar 

  • Wong ML, Leung KS (1996) Evolving Recursive Functions for Even-Parity Problem Using Genetic Programming. In: Angeline PJ, Kinnear KE Jr (eds), Advances in Genetic Programming, The MIT Press, USA, pp 221–240.

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Computer Science, University College, The University of New South Wales, Australian Defence Force Academy, Canberra, ACT, 2600, Australia

    N. X. Hoai

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  1. N. X. Hoai
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Editor information

Editors and Affiliations

  1. School of Computing and Information Technology, Monash University, Gippsland Campus, 3842, Churchill, VIC, Australia

    Ajith Abraham

  2. Department of Pattern Recognition, Fraunhofer IPK Berlin, Pascalstraße 8-9, 10587, Berlin, Germany

    Mario Köppen

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© 2002 Springer-Verlag Berlin Heidelberg

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Hoai, N.X. (2002). Solving Trigonometric Identities with Tree Adjunct Grammar Guided Genetic Programming. In: Abraham, A., Köppen, M. (eds) Hybrid Information Systems. Advances in Soft Computing, vol 14. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1782-9_25

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  • DOI: https://doi.org/10.1007/978-3-7908-1782-9_25

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-1480-4

  • Online ISBN: 978-3-7908-1782-9

  • eBook Packages: Springer Book Archive

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