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Solving High-Order Boolean Parity Problems with Smooth Uniform Crossover, Sub-Machine Code GP and Demes

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Abstract

We propose and study new search operators and a novel node representation that can make GP fitness landscapes smoother. Together with a tree evaluation method known as sub-machine-code GP and the use of demes, these make up a recipe for solving very large parity problems using GP. We tested this recipe on parity problems with up to 22 input variables, solving them with a very high success probability.

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References

  1. R. Aler, “Immediate transference of global improvements to all individuals in a population in genetic programming compared to automatically defined functions for the even-5 parity problem,” in Proceedings of the First European Workshop on Genetic Programming, Paris, W. Banzhaf, R. Poli, M. Schoenauer, and T. C. Fogarty (eds.), Springer-Verlag, 14-15 Apr. 1998, vol. 1391 of LNCS, pp. 60-70.

  2. D. Andre and J. R. Koza, “Parallel genetic programming: A scalable implementation using the transputer network architecture,” in Advances in Genetic Programming 2, P. J. Angeline and K. E. Kinnear, Jr. (eds.), MIT Press, Cambridge, MA, 1996, chap. 16, pp. 317-338.

    Google Scholar 

  3. W. Banzhaf, P. Nordin, R. E. Keller, and F. D. Francone, Genetic Programming—An Introduction; On the Automatic Evolution of Computer Programs and its Applications, dpunkt.verlag, Morgan Kaufmann, Jan. 1998.

  4. K. Chellapilla, “A preliminary investigation into evolving modular programs without subtree crossover,” in Genetic Programming 1998: Proceedings of the Third Annual Conference, University of Wisconsin, Madison, Wisconsin, J. R. Koza, W. Banzhaf, K. Chellapilla, K. Deb, M. Dorigo, D. B. Fogel, M. H. Garzon, D. E. Goldberg, H. Iba, and R. Riolo (eds.), Morgan Kaufmann, 2225 July1998, pp. 23-31.

    Google Scholar 

  5. C. Gathercole and P. Ross, “Tackling the Boolean even N parity problem with genetic programming and limited-error fitness,” in Genetic Programming 1997: Proceedings of the Second Annual Conference, Stanford University, CA, J. R. Koza, K. Deb, M. Dorigo, D. B. Fogel, M. Garzon, H. Iba, and R. L. Riolo (eds.), Morgan Kaufmann, 1316 July 1997, pp. 119-127.

    Google Scholar 

  6. J. R. Koza, Genetic Programming: On the Programming of Computers by Natural Selection, MIT Press: Cambridge, MA, 1992.

    Google Scholar 

  7. J. R. Koza, Genetic Programming II: Automatic Discovery of Reusable Programs, MIT Press: Cambridge, MA, May 1994.

    Google Scholar 

  8. W. B. Langdon, “Size fair and homologous tree genetic programming crossovers,” in GECCO-99: Proceedings of the Genetic and Evolutionary Computation Conference, Orlando, FL, W. Banzhaf, J. Daida, A. E. Eiben, M. H. Garzon, V. Honavar, M. Jakiela, and R. E. Smith (eds.), Morgan Kaufmann, 13-17 July 1999.

  9. W. B. Langdon and R. Poli, “Why building blocks don't work on parity problems,” University of Birmingham, School of Computer Science, Technical Report CSRP-98-17, vol. 13, July 1998.

  10. W. B. Langdon, T. Soule, R. Poli, and J. A. Foster, “The evolution of size and shape,” in Advances in Genetic Programming 3, J. Spector, W. B. Langdon, U.-M. O'Reilly, and P. J. Angeline (eds.), MIT Press, Cambridge, MA, June 1999, chap. 8, pp. 163-190.

    Google Scholar 

  11. B. McKay, M. J. Willis, and G. W. Barton, “Using a tree structured genetic algorithm to perform symbolic regression,” in First International Conference on Genetic Algorithms in Engineering Systems: Innovations and Applications, GALESIA, A. M. S. Zalzala (ed.), IEE, Sheffield, UK, 12-14 Sept. 1995, vol. 414, pp. 487-492.

    Google Scholar 

  12. P. Nordin, “A compiling genetic programming system that directly manipulates the machine code,” in Advances in Genetic Programming, K. E. Kinnear, Jr. (ed.), MIT Press, 1994, chap. 14, pp.311-331.

  13. P. Nordin, “Evolutionary Program Induction of Binary Machine Code and its Applications,” Fachbereich Informatik, Universitaet Dortmund, PhD thesis, 1997.

  14. P. Nordin, “AIMGP: A formal description,” in Late Breaking Papers of the Genetic Programming 1998 Conference, J. R. Koza (ed.), Stanford University Bookstore, University of Wisconsin, Madison, Wisconsin, 22-25 July 1998.

    Google Scholar 

  15. P. Nordin and W. Banzhaf, “Evolving Turing-complete programs for a register machine with self-modifying code,” in Genetic Algorithms: Proceedings of the Sixth International Conference (ICGA95), Pittsburgh, PA, L. Eshelman (ed.), Morgan Kaufmann, 1519 July 1995, pp. 318-325.

  16. J. Page, R. Poli, and W. B. Langdon, “Smooth uniform crossover with smooth point mutation in genetic programming: A preliminary study,” in Proceedings of the Second European Workshop on Genetic Programming—EuroGP'99, Goteborg, R. Poli, P. Nordin, W. B. Langdon, and T. Fogarty (eds.), Springer-Verlag, May 1999.

  17. R. Poli,''Is crossover a local search operator?” Position paper at the Workshop on Evolutionary Computation with Variable Size Representation at ICGA-97, 20 July 1997.

  18. R. Poli, “Sub-machine-code GP: New results and extensions,” in Genetic Programming, Proceedings of EuroGP'99, LNCS, Goteborg, Sweden, R. Poli, P. Nordin, W. B. Langdon, and T. C. Fogarty (eds.), Springer-Verlag, 2627 May 1999.

  19. R. Poli and W. B. Langdon, “Genetic programming with one-point crossover,” in Second On-line World Conference on Soft Computing in Engineering Design and Manufacturing, London, P. K. Chawdhry, R. Roy, and R. K. Pant (eds.), Springer-Verlag, 2327 June 1997.

  20. R. Poli and W. B. Langdon, “On the search properties of different crossover operators in genetic programming,” in Genetic Programming 1998: Proceedings of the Third Annual Conference, University of Wisconsin, Madison, Wisconsin, J. R. Koza, W. Banzhaf, K. Chellapilla, K. Deb, M. Dorigo, D. B. Fogel, M. H. Garzon, D. E. Goldberg, H. Iba, and R. Riolo (eds.), Morgan Kaufmann, 22-25 July 1998, pp. 293-301.

    Google Scholar 

  21. R. Poli and W. B. Langdon, “Sub-machine-code genetic programming,” in Advances in Genetic Programming 3, L. Spector, W. B. Langdon, U.-M. O'Reilly, and P. J. Angeline (eds.), MIT Press, Cambridge, MA, 1999, chap. 13.

    Google Scholar 

  22. W. F. Punch, “How effective are multiple populations in genetic programming,” in Genetic Programming 1998: Proceedings of the Third Annual Conference, University of Wisconsin, Madison, Wisconsin, J. R. Koza, W. Banzhaf, K. Chellapilla, K. Deb, M. Dorigo, D. B. Fogel, M. H. Garzon, D. E. Goldberg, H. Iba, and R. Riolo (eds.), Morgan Kaufmann, 2225 July 1998, pp. 308-313.

    Google Scholar 

  23. J. P. Rosca, “Hierarchical Learning with Procedural Abstraction Mechanisms,” University of Rochester, Rochester, NY, PhD thesis, Feb. 1997.

    Google Scholar 

  24. T. Soule and J. A. Foster, “Code size and depth flows in genetic programming,” in Genetic Programming 1997: Proceedings of the Second Annual Conference, Stanford University, CA, J. R. Koza, K. Deb, M. Dorigo, D. B. Fogel, M. Garzon, H. Iba, and R. L. Riolo (eds.), Morgan Kaufmann, 1316 July 1997, pp. 313-320.

  25. G. Syswerda, “Uniform crossover in genetic algorithms,” in Proceedings of the Third International Conference on Genetic Algorithms, J. Schaffer (ed.), Morgan Kaufmann, 1989.

  26. M. L. Wong and K. S. Leung, “Evolving recursive functions for the even-parity problem using genetic programming,” in Advances in Genetic Programming 2, P. J. Angeline and K. E. Kinnear, Jr. (eds.), MIT Press, Cambridge, MA, 1996, chap. 11, pp. 221-240.

    Google Scholar 

  27. T. Yu and C. Clark, “Recursion, lambda-abstractions and genetic programming,” in Late Breaking Papers at EuroGP'98: the First European Workshop on Genetic Programming, Paris, France, R. Poli, W. B. Langdon, M. Schoenauer, T. Fogarty, and W. Banzhaf (eds.), The University of Birmingham, UK, 1415 Apr. 1998, pp. 26-30.

    Google Scholar 

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Poli, R., Page, J. Solving High-Order Boolean Parity Problems with Smooth Uniform Crossover, Sub-Machine Code GP and Demes. Genetic Programming and Evolvable Machines 1, 37–56 (2000). https://doi.org/10.1023/A:1010068314282

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