A schema-based version of Geiringer's theorem for nonlinear genetic programming with homologous crossover

Lecture Notes in Computer Science

Volumn 3469, Issue , 2005, Pages 156-175

  Mitavskiy, Boris ^a   Rowe, Jonathan E ^a  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

GENETIC ALGORITHMS; LINEAR PROGRAMMING; MUTAGENESIS;

GEIRINGER'S THEOREM; LIMITING FREQUENCY; MUTATION;

THEOREM PROVING;

EID: 24944451592     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/11513575_9     Document Type: Conference Paper

References (17)

1. Booker, L. (1993). Recombination distributions for genetic algorithms. In L. Darrell Whitley, editor, Foundations of Genetic Algorithms 2, pages 29-44, Morgan Kaufmann.
2. Coffey, S. (1999) An Applied Probabilist's Guide to Genetic Algorithms. A Thesis Submitted to The University of Dublin for the degree of Master in Science.
3. Geiringer, H. (1944). On the probability of linkage in Mendelian heredity. Annals of Mathematical Statistics, 15:25-57.
4. Mitavskiy B. (2004). Crossover Invariant Subsets of the Search Space for Evolutionary Algorithms. Evolutionary Computation, 12(1): 19-46.
5. Mitavskiy B. (2003). Comparing Evolutionary Computation Techniques via Their Representation. In Eric Cantú-Paz et al. editor, Proceedings of the Genetic and Evolutionary Computation (GECCO) Conference, Vol. 1, pages 1196-1209, Springer-Verlag.
6. Mitavskiy B. (recently submitted). A Generalization of Geiringer Theorem for a wide class of evolutionary search algorithms. Evolutionary Computation. http://www.math.lsa.umich.edu/~bmitavsk/
7. Poli, R. (2000). Hyperschema Theory for GP with One-Point Crossover, Building Blocks, and Some New Results in GA Theory. In R. Poli, W. Banzhaf, and et al., editors, Genetic Programming, Proceedings of EuroGP'2000, Springer-Verlag
8. Poli, R. and Langdon, W. (1998). On the search Properties of Different Crossover Operators in Genetic Programming.
9. Poli, R., Stephens, C., Wright, A., Rowe, J. (2002). A Schema-Theory-Based Extension of Geiringer's Theorem for Linear GP and variable-length GAs under Homologous Crossover. FOGA 2002
10. Rabani, Y., Rabinovich, Y., Sinclair, A. (1995) A Computational View of Population Genetics. In Annual ACM Symposium on the Theory of Computing pages 83-92.
11. Rosenthal, Jeffrey (1995). Convergence Rates for Markov Chains. SIAM Review 37(3): 387-405.
12. Rowe, J., Vose, M., and Wright, A. (2002). Group properties of crossover and mutation. Evolutionary Computation, 10(2): 151-184.
13. Rowe, J., Vose, M., and Wright, A. (to appear) Structural Search Spaces and Genetic Operators. Evolutionary Computation.
14. Schmitt, L. (2001) "Theory of Genetic Algorithms." Theoretical Computer Science, 259: 1-61.
15. Schmitt, L. (2004) "Theory of Genetic Algorithms II: Models for Genetic Operators over the String-Tensor representation of Populations and Convergence to Global Optima for Arbitrary Fitness Function under Scaling." Theoretical Computer Science, 310: 181-231.
16. Spears, W. (2000) "The Equilibrium and Transient Behavior of Mutation and Recombination." Foundations of Genetic Algorithms 6 (FOGA-6).
17. Vose, M. (1999). The simple genetic algorithm: foundations and theory. MIT Press, Cambridge, Massachusetts.