Exact schema theory and Markov chain models for genetic programming and variable-length genetic algorithms with homologous crossover

Genetic Programming and Evolvable Machines

Volumn 5, Issue 1, 2004, Pages 31-70

  Poli, Riccardo ^a   McPhee, Nicholas Freitag ^b   Rowe, Jonathan E ^c  

^a UNIVERSITY OF ESSEX   (United Kingdom)

^b UNIVERSITY OF MINNESOTA   (United States)

^c UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Genetic programming; Markov chain; Mixing matrices; Schema theory; Variable length genetic algorithms; Vose model

Indexed keywords

MARKOV PROCESSES; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; POPULATION STATISTICS; TREES (MATHEMATICS);

GENETIC PROGRAMMING; MIXING MATRICES; SCHEMA THEORY; VARIABLE-LENGTH GENETIC ALGORITHMS; VOSE MODELS;

GENETIC ALGORITHMS;

EID: 3543080914     PISSN: 13892576     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:GENP.0000017010.41337.a7     Document Type: Article

References (46)

1. L. Altenberg, "Emergent phenomena in genetic programming," in Evolutionary Programming - Proceedings of the Third Annual Conference, A. V. Sebald and L. J. Fogel (eds.), World Scientific Publishing: San Diego, CA, USA, 24-26 Feb. 1994, pp. 233-241.
2. L. Altenberg, "The schema theorem and price's Theorem," in Foundations of Genetic Algorithms 3, L. D. Whitley and M. D. Vose (eds.), Morgan Kaufmann: San Francisco, CA, USA, 1995, pp. 23-49.
3. L. B. Booker, "Recombination distributions for genetic algorithms," in Foundations of Genetic Algorithms 2, L. D. Whitley (ed.), Morgan Kaufmann: San Francisco, CA, 1993, pp. 29-44.
4. T. E. Davis and J. C. Principe, "A Markov chain framework for the simple genetic algorithm," Evolutionary Comp., vol. 1, no. 3, pp. 269-288, 1993.
5. H. Geiringer, "On the probability theory of linkage in Mendelian heredity," Annals of Mathematical Statistics, vol. 15, no. 1, pp. 25-57, 1944.
6. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley: Reading, Massachusetts, 1989.
7. J. Holland, Adaptation in Natural and Artificial Systems, University of Michigan Press: Ann Arbor, USA, 1975.
8. J. R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press: Cambridge, MA, USA, 1992.
9. W. B. Langdon, "Size fair and homologous tree genetic programming crossovers," Genetic Programming and Evolvable Machines, vol. 1, no. 1/2, pp. 95-119, 2000.
10. W. B. Langdon and R. Poli, Foundations of Genetic Programming, Springer-Verlag, 2002.
11. N. F. McPhee, R. Poli, and J. E. Rowe, "A schema theory analysis of mutation size biases in genetic programming with linear representations," in Proceedings of the 2001 Congress on Evolutionary Computation CEC2001, COEX, World Trade Center, 159 Samseong-dong, Gangnam-gu, Seoul, Korea, 27-30 May 2001, IEEE Press, 2001, pp. 1078-1085.
12. M. Mitchell, An introduction to genetic algorithms, MIT Press: Cambridge, MA, 1996.
13. D. J. Montana, "Strongly typed genetic programming," Evolutionary Compu., vol. 3, no. 2, pp. 199-230, 1995.
14. A. E. Nix and M. D. Vose, "Modeling genetic algorithms with Markov chains," Annals of Mathematics and Artificial Intelligence, vol. 5, pp. 79-88, 1992.
15. U.-M. O'Reilly and F. Oppacher, "The troubling aspects of a building block hypothesis for genetic programming," in Foundations of Genetic Algorithms 3, L. D. Whitley and M. D. Vose (eds.), Morgan Kaufmann: San Francisco, CA, 1995, pp. 73-88.
16. R. Poli, "Exact schema theory for genetic programming and variable-length genetic algorithms with one-point crossover," Genetic Programming and Evolvable Machines, vol. 2, no. 2, pp. 123-163, June 2001.
17. 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, USA, 22-25 July 1998, 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: University of Wisconsin, Madison, Wisconsin, USA, 22-25 July 1998, pp. 293-301.
18. R. Poli and W. B. Langdon, "Schema theory for genetic programming with one-point crossover and point mutation," Evolutionary Computation, vol. 6, no. 3, pp. 231-252, 1998.
19. R. Poli and N. F. McPhee, "Exact GP schema theory for headless chicken crossover and subtree mutation," in Proceedings of the 2001 Congress on Evolutionary Computation CEC2001, IEEE Press: COEX, World Trade Center, 159 Samseong-dong, Gangnam-gu, Seoul, Korea, 27-30 May 2001, pp. 1062-1069.
20. R. Poli and N. F. McPhee, "Exact schema theory for GP and variable-length GAs with homologous crossover," in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), San Francisco, California, USA, 7-11 July 2001, L. Spector, E. D. Goodman, A. Wu, W. B. Langdon, H.-M. Voigt, M. Gen, S. Sen, M. Dorigo, S. Pezeshk, M. H. Garzon, and E. Burke (eds.), Morgan Kaufmann: San Francisco, California, USA, 7-11 July 2001, pp. 104-111.
21. R. Poli and N. F. McPhee, "General schema theory for genetic programming with subtree-swapping crossover: Part I," Evolutionary Comp., vol. 11, no. 1, pp. 53-66, 2003.
22. R. Poli and N. F. McPhee, "General schema theory for genetic programming with subtree-swapping crossover: Part II," Evolutionary Comp., vol. 11, no. 2, pp. 169-206, 2003.
23. R. Poli, J. E. Rowe, and N. F. McPhee, "Markov chain models for GP and variable-length GAs with homologous crossover," in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), L. Spector, E. D. Goodman, A. Wu, W. B. Langdon, H.-M. Voigt, M. Gen, S. Sen, M. Dorigo, S. Pezeshk, M. H. Garzon, and E. Burke (eds.), Morgan Kaufmann: San Francisco, California, USA, 7-11 July 2001, pp. 112-119.
24. R. Poli, C. R. Stephens, A. H. Wright, and J. E. Rowe, "On the search biases of homologuous crossover in linear genetic programming and variable-length genetic algorithms," in GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, W. B. Langdon, E. Cantú-Paz, K. Mathias, R. Roy, D. Davis, R. Poli, K. Balakrishnan, V. Honavar, G. Rudolph, J. Wegener, L. Bull, M. A. Potter, A. C. Schultz, J. F. Miller, E. Burke, and N. Jonoska (eds.), Morgan Kaufmann Publishers, New York, 9-13 July 2002, pp. 868-876.
25. R. Poli, C. R. Stephens, A. H. Wright, and A. H. Rowe, "A schema-theory-based extension of Geiringer's theorem for linear GP and variable-length GAs under homologous crossover," in Foundations of Genetic Algorithm 7, K. D. Jong, R. Poli, and J. Rowe (eds.), Morgan Kaufmann: San Francisco, CA, 2003, pp. 45-62.
26. A. Prügel-Bennett and J. L. Shapiro, "An analysis of genetic algorithms using statistical mechanics," Physical Review Letters, vol. 72, pp. 1305-1309, 1994.
27. N. J. Radcliffe, "Schema processing," Handbook of Evolutionary Computation, T. Baeck, D. B. Fogel, and Z. Michalewicz (eds.), Oxford University Press, 1997, pp. B2.5-1-B2.5-10.
28. C. Reeves and J. Rowe, "Genetic algorithms: principles and perspectives," Kluwer Academic Press, 2003.
29. J. P. Rosca, "Analysis of complexity drift in genetic programming," in Genetic Programming 1997: Proceedings of the Second Annual Conference, Stanford University, J. R. Koza, K. Deb, M. Dorigo, D. B. Fogel, M. Garzon, H. Iba, and R. L. Riolo (eds.), Morgan Kaufmann: CA, USA, 13-16 July 1997, pp. 286-294.
30. J. E. Rowe, "Population fixed-points for functions of unitation," in Foundations of Genetic Algorithms 5, W. Banzhaf and C. Reeves (eds.), Morgan Kaufmann: San Francisco, CA, 1999, pp. 69-84.
31. J. E. Rowe, M. D. Vose, and A. H. Wright, "Group properties of crossover and mutation," Evolutionary Comp., vol. 10, no. 2, pp. 151-184, 2002.
32. G. Rudolph, "Convergence analysis of canonical genetic algorithm," IEEE Transactions on Neural Networks, vol. 5, no. 1, pp. 96-101, 1994.
33. G. Rudolph, "Genetic algorithms," in Handbook of Evolutionary Computation, T. Baeck, D. B. Fogel, and Z. Michalewicz (eds.), Oxford University Press, 1997, pp. B2.4-20-B2.4-27.
34. G. Rudolph, "Models of stochastic convergence," in Handbook of Evolutionary Computation, T. Baeck, D. B. Fogel, and Z. Michalewicz (eds.), Oxford University Press, 1997, pp. B2.3-1-B2.3-3.
35. G. Rudolph, "Stochastic processes," in Handbook of Evolutionary Computation, T. Baeck, D. B. Fogel, and Z. Michalewicz (eds.), Oxford University Press, 1997, pp. B2.2-1-B2.2-8.
36. W. M. Spears, "Aggregating models of evolutionary algorithms," in Proceedings of the Congress on Evolutionary Computation, P. J. Angeline, Z. Michalewicz, M. Schoenauer, X. Yao, and A. Zalzala (eds.), Mayflower Hotel, Washington D.C., USA, 6-9 July 1999, IEEE Press, vol. 1, 1999, pp. 631-638.
37. W. M. Spears, "The equilibrium and transiente behaviour of mutation and recombination," in Foundations of Genetic Algorithms Workshop 6, W. M. Spears and W. Martin (eds.), Morgan Kaufmann: San Francisco, CA, 2001, pp. 241-260.
38. M. R. Spiegel, Probability and Statistics, McGraw-Hill: New York, 1975.
39. C. R. Stephens, "Some exact results from a coarse grained formulation of genetic dynamics," in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), L. Spector, E. D. Goodman, A. Wu, W. B. Langdon, H.-M, Voigt, M. Gen, S. Sen, M. Dorigo, S. Pezeshk, M. H. Garzon, and E. Burke (eds.), Morgan Kaufmann: San Francisco, California, USA, 7-11 July 2001, pp. 631-638.
40. C. R. Stephens and H. Waelbroeck, "Effective degrees of freedom in genetic algorithms and the block hypothesis," in Proceedings of the Seventh International Conference on Genetic Algorithms (ICGA97), T. Bäck (ed.), Morgan Kaufmann: East Lansing, 1997, pp. 34-40.
41. C. R. Stephens and H. Waelbroeck, "Schemata evolution and building blocks," Evolutionary Comp., vol. 7, no. 2, pp. 109-124, 1999.
42. M. D. Vose, The Simple Genetic Algorithm: Foundations and Theory, MIT Press: Cambridge, MA, 1999.
43. M. D. Vose and G. E. Liepins, "Punctuated equilibria in genetic search," Complex Systems, vol. 5, no. 1, pp. 31-44, 1991.
44. P. A. Whigham, "A schema theorem for context-free grammars," in 1995 IEEE Conference on Evolutionary Computation, Perth, Australia, 29 Nov-1Dec. 1995, IEEE Press, vol. 1, 1995, pp. 178-181.
45. P. A. Whigham, "Grammatical Bias for Evolutionary Learning, 14 Oct. 1996," PhD thesis, School of Computer Science, University College, University of New South Wales, Australian Defence Force Academy, Canberra, Australia.
46. D. Whitley, "A genetic algorithm tutorial," Technical Report CS-93-103, Department of Computer Science, Colorado State University, Aug. 1993.