Sharp asymptotic results for simplified mutation-selection algorithms

Annals of Applied Probability

Volumn 13, Issue 4, 2003, Pages 1534-1568

  Berard J ^a   Bienvenue A ^b,c  

^a UNIVERSITÉ LYON 1   (France)

^b INP Grenoble ENSIMAG   (France)

^c IMAG CNRS   (France)

Author keywords

Genetic algorithm; Interacting particle systems; Invariance principle; Large deviations; Population dynamics; Random walks

Indexed keywords

EID: 0347544145     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1069786510     Document Type: Article

References (15)

1. BÉRARD, J. and BIENVENÜE, A. (2000). Convergence of a genetic algorithm with finite population. In Mathematics and Computer Science: Algorithms, Trees, Combinatorics and Probabilities 155-163. Birkhäuser, Basel.
2. BÉRARD, J. and BIENVENÜE, A. (2000). Un principe d'invariance pour un algorithme génétique en population finie. C. R. Acad. Sci. Paris Sér. I Math. 331 469-474.
3. BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York.
4. BONNAZ, D. (1998). Modèles stochastiques de dynamique des populations. Ph.D. dissertation, Univ. Lausanne.
5. CERF, R. (1998). Asymptotic convergence of genetic algorithms. Adv. in Appl. Probab. 30 521-550.
6. DEMBO, A. and ZEITOUNI, O. (1998). Large Deviations Techniques and Applications, 2nd ed. Springer, New York.
7. DURRETT, R. (1996). Probability: Theory and Examples, 2nd ed. Duxbury, Belmont, CA.
8. GRADSHTEYN, I. S. and RYZHIK, I. M. (1996). Table of Integrals, Series, and Products, 5th ed. Academic, San Diego.
9. HOLLAND, J. H. (1975). Adaptation in Natural and Artificial Systems. Univ. Michigan Press, Ann Arbor.
10. KESSLER, D., LEVINE, H., RIDGWAY, D. and TSIMRING, L. (1997). Evolution on a smooth landscape. J. Statist. Phys. 87 519-544.
11. MATSUMOTO, M. and NISHIMURA, T. (1998). Mersenne twister a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Modeling Comput. Simulation 8 3-30.
12. MAZZA, C. and PIAU, D. (2001). On the effect of selection in genetic algorithms. Random Structures Algorithms 18 185-200.
13. RABINOVICH, Y. and WIGDERSON, A. (1999). Techniques for bounding the convergence rate of genetic algorithms. Random Structures Algorithms 14 111-138.
14. REVUZ, D. and YOR, M. (1991). Continuous Martingales and Brownian Motion. Springer, Berlin.
15. TSIMRING, L. S., LEVINE, H. and KESSLER, D. A. (1996). RNA virus evolution via a fitness-space model. Phys. Rev. Lett. 76 4440.