Solving iterated functions using genetic programming

Proceedings of the 11th Annual Genetic and Evolutionary Computation Conference, GECCO-2009

Volumn 2009-January, Issue , 2009, Pages 2149-2153

  Schmidt, Michael Douglas ^a   Lipson, Hod ^a  

^a Cornell University ^*  (United States)

Author keywords

iterated functions; symbolic regression

Indexed keywords

DYNAMICAL SYSTEMS; FRACTALS; GENETIC ALGORITHMS;

ANALYSIS TECHNIQUES; FINDING SOLUTIONS; FRACTAL THEORY; ITERATED FUNCTIONS; SYMBOLIC REGRESSION;

GENETIC PROGRAMMING;

EID: 84864644978     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1570256.1570292     Document Type: Conference Paper

References (19)

1. R. Brown, "On Solving Nonlinear Functional, Finite Difference, Composition, and Iterated Equations," Fractals, vol. 7, pp. 277-282, 1999.
2. B. A. Brown, A. R. Brown, and M. F. Shlesinger, "Solutions of Doubly and Higher Order Iterated Equations," Journal of Statistical Physics, vol. 110, pp. 1087-1097, 2003.
3. "Mathvn journal problems," in Mathvn. vol. 01/2009 mathvn.org, 2009.
4. B. Andrzej and S. Barbara, "Finding an iterated function systems based representation for complex visual structures using an evolutionary algorithm," MG&V, vol. 16, pp. 171-189, 2007.
5. A. Bielecki and B. Strug, "An Evolutionary Algorithm for Solving the Inverse Problem for Iterated Function Systems for a Two Dimensional Image," in Computer Recognition Systems, 2005, pp. 347-354.
6. J. R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection. Cambridge, MA, USA: MIT Press, 1992.
7. M. Ben, J. W. Mark, and W. B. Geoffrey, "Using a Tree Structured Genetic Algorithm to Perform Symbolic Regression," in First International Conference on Genetic Algorithms in Engineering Systems: Innovations and Applications, GALESIA. vol. 414, 1995, pp. 487-492.
8. D. Edwin and B. P. Jordan, "Multi-Objective Methods for Tree Size Control," in Genetic Programming and Evolvable Machines. vol. 4, 2003, pp. 211-233.
9. M. Schmidt and H. Lipson, "Comparison of tree and graph encodings as function of problem complexity," in Proceedings of the Genetic and Evolutionary Computation Conference, London, 2007, pp. 1674-1679.
10. X. H. Nguyen, R. I. McKay, and D. L. Essam, "Solving the Symbolic Regression Problem with Tree-Adjunct Grammar Guided Genetic Programming: The Comparative Results," in The Australian Journal of Intelligent Information Processing Systems. vol. 7, 2001, pp. 114-121.
11. J. Bongard and H. Lipson, "Automated reverse engineering of nonlinear dynamical systems," Proceedings of the National Academy of Sciences, vol. 104, pp. 9943-9948, 2007.
12. M. Schmidt and H. Lipson, "Distilling Free-Form Natural Laws from Experimental Data," Science, vol. 324, pp. 81-85, 2009.
13. W. Stein, "Sage Mathematics Software (Version 3.4)," The Sage Development Team, http://www.sagemath.org/, 2009.
14. M. D. Schmidt and H. Lipson, "Coevolution of Fitness Maximizers and Fitness Predictors," in Proceedings of the Genetic and Evolutionary Computation Conference, Late Breaking Paper, 2005.
15. M. D. Schmidt and H. Lipson, "Co-evolving Fitness Predictors for Accelerating and Reducing Evaluations," in Genetic Programming Theory and Practice IV. vol. 5, 2006, pp. 113-130.
16. M. D. Schmidt and H. Lipson, "Coevolution of Fitness Predictors," IEEE Transactions on Evolutionary Computation, vol. 12, pp. 736-749, Dec 2008.
17. S. W. Mahfoud, "Niching methods for genetic algorithms," University of Illinois at Urbana-Champaign, 1995.
18. F. Francisco, S. Giandomenico, T. Marco, and V. Leonardo, "Parallel Genetic Programming," in Parallel Metaheuristics, 2005, pp. 127-153.
19. G. Christian, P. Marc, and D. Marc, "A Robust Master-Slave Distribution Architecture for Evolutionary Computations," in Genetic and Evolutionary Computation Conference Late Breaking Papers, 2003, pp. 80-87.