Statistical Dynamics of the Royal Road Genetic Algorithm

Theoretical Computer Science

Volumn 229, Issue 1-2, 1999, Pages 41-102

  Van Nimwegen, Erik ^a   Crutchfield, James P ^a,b   Mitchell, Melanie ^a  

^a SANTA FE INSTITUTE   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Epochal evolution; Genetic algorithm; Metastability; Neutral evolution; Statistical dynamics

Indexed keywords

EID: 0001938575     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(99)00119-X     Document Type: Article

References (48)

1. R. Baserga, (Ed.), Cell Proliferation, Cancer, and Cancer Therapy, Ann. New York Acad. Sci., vol. 397, 1982.
2. R.K. Belew, L.B. Booker (Eds.), Proc. 4th Internat. Conf. on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA, 1991.
3. A. Bergman, M.W. Feldman, Question marks about the period of punctuation, Santa Fe Institute Working paper 96-02-006, 1996.
4. T.D. Brock, Biology of Microorganisms, Ch. 23, Prentice-Hall, Englewood Cliffs, NJ, 1997, pp. 942-943.
5. T.D. Brock, Biology of Microorganisms, Ch. 23, Prentice-Hall, Englewood Cliffs, NJ, 1997, pp. 956-957.
6. J.P. Crutchfield, Subbasins, portals, and mazes: transients in high dimensions, J. Nucl. Phys. B 5A (1988) 287-293.
7. J.P. Crutchfield, The calculi of emergence: computation, dynamics, and induction, Physica D 75 (1994) 11-54.
8. J.P. Crutchfield, M. Mitchell, The evolution of emergent computation, Proc. Natl. Acad. Sci. U.S.A. 92 (1995) 10742-10746.
9. R. Das, J.P. Crutchfield, M. Mitchell, J.E. Hanson, Evolving globally synchronized cellular automata, in: L.J. Eshelman (Ed.), Proc. 6th Internat. Conf. on Genetic Algorithms, Morgan Kaufmann, San Francisco, CA, 1995, pp. 336-343.
10. L.D. Davis (Ed.), The Handbook of Genetic Algorithms, Van Nostrand Reinhold, New York, 1991.
11. M. Eigen, Naturwissenschaften 58 (1971) 465-522.
12. M. Eigen, J. McCaskill, P. Schuster, The molecular quasispecies, Adv. Chem. Phys. 75 (1989) 149-263.
13. M. Eigen, P. Schuster, Naturwissenschaften 64 (1977) 541-565.
14. M. Eigen, P. Schuster, The Hypercycle, Springer, Berlin, 1979.
15. S.F. Elena, V.S. Cooper, R.E. Lenski, Punctuated evolution caused by selection of rare beneficial mutations, Science 272 (1996) 1802-1804.
16. L. Eshelman (Ed.), Proc. 6th Internat. Conf. on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA, 1995.
17. W. Feller, An Introduction to Probability Theory and its Applications, 3rd revised ed., Wiley, New York, 1970.
18. R.A. Fisher, The Genetical Theory of Natural Selection, The Clarendon Press, Oxford, 1930.
19. A.D. Fokker, Ann. Phys. (Leipzig) 43 (310) (1915).
20. S. Forrest (Ed.), Proc. 5th Internat. Conf. on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA, 1993.
21. C.W. Gardiner, Handbook of Stochastic Methods, Springer, Berlin, 1985.
22. J.H. Gillespie, in: M.W. Feldman (Ed.), Mathematical Evolutionary Theory, Ch. 4, Princeton University Press, Princeton, NJ, 1989.
23. S.J. Gould, N. Eldredge, Punctuated equilibria: the tempo and mode of evolution reconsidered, Paleobiology 3 (1977) 115-251.
24. R. Haygood, The structure of royal road fitness epochs, Evolutionary Computation, submitted, ftp://ftp.itd.ucdavis.edu/pub/people/rch/StrucRoyRdFitEp.ps.gz, 1997.
25. M. Huynen, P.F. Stadler, W. Fontana, Smoothness within ruggedness: the role of neutrality in adaptation, Proc. Natl. Acad. Sci. 93 (1996) 397-401.
26. M. Kimura, On the probability of fixation of mutant genes in a population, Genetics 47 (1962) 713-719.
27. M. Kimura, Diffusion models in population genetics, J. Appl. Prob. 1 (1964) 177-232.
28. M. Kimura, The Neutral Theory of Molecular Evolution, Cambridge University Press, Cambridge, 1983.
29. M. Kimura, T. Ohta, The average number of generations until fixation of a mutant gene in a finite population, Genetics 61 (1969) 763-771.
30. A.N. Kolmogorov, Math. Ann. 104 (1931) 415-418.
31. K. Lindgren, Evolutionary phenomena in simple dynamics, in: C.G. Langton, C. Taylor, J.D. Farmer, S. Rasmussen (Eds.), Artificial Life II, Addison-Wesley, Reading, MA, 1992, pp. 295-312.
32. J.S. McCaskill, A stochastic theory of macromolecular evolution, Biol. Cybernet. 50 (1984) 63-73.
33. M. Mitchell, J.P. Crutchfield, P.T. Hraber, Evolving cellular automata to perform computations: Mechanisms and impediments, Physica D 75 (1994) 361-391.
34. M. Mitchell, J.H. Holland, S. Forrest, When will a genetic algorithm outperform hill climbing? in: J.D. Cowan, G. Tesauro, J. Alspector (Eds.), Advances in Neural Information Processing Systems 6, Morgan Kaufmann, San Mateo, CA.
35. A.E. Nix, M.D. Vose, Modeling genetic algorithms with Markov chains, Ann. Math. Artif. Intell. 5 (1991).
36. A.S. Perelson, S.A. Kauffman (Eds.), Molecular Evolution on Rugged Landscapes: Proteins, RNA and the Immune System, Santa Fe Institute Studies in the Science of Complexity, vol. IX, 1989.
37. M. Planck, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 325 (1917).
38. A. Prug̈el-Bennett, J.L. Shapiro, Analysis of genetic algorithms using statistical mechanics, Phys. Rev. Lett. 72(9) (1994) 1305-1309.
39. A. Prügel-Bennett, J.L. Shapiro, The dynamics of a genetic algorithm in simple random Ising systems, Physica D 104(1) (1977) 75-114.
40. M. Rattray, J.L. Shapiro, The dynamics of a genetic algorithm for a simple learning problem, J. Phys. A 29(23) (1996) 7451-7473.
41. T.S. Ray, An approach to the synthesis of life, in: C.G. Langton, C. Taylor, J.D. Farmer, S. Rasmussen (Eds.), Artificial Life II, Addison-Wesley, Reading, MA, 1992, pp. 371-408.
42. J. Swetina, P. Schuster, Self replicating with error, a model for polynucleotide replication, Biophys. Chem. 16 (1982) 329-340.
43. N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, 1992.
44. E. van Nimwegen, J.P. Crutchfield, M. Mitchell, Finite populations induce metastability in evolutionary search, Phys. Lett. A 229 (1997) 144-150.
45. E. van Nimwegen, J.P. Crutchfield, Optimizing Epochal Evolutionary Search: Population-Size Independent theory. Computer Methods in Applied Mechanics and Engineering, Special issue on Evolutionary and Genetic Algorithms in Computational Mechanics and Engineering. D. Goldberg and K. Deb, editors (1999, in press).
46. E. van Nimwegen, J.P. Crutchfield, Optimizing Epochal Evolutionary Search: Population-Size Dependent theory, Machine Learning Journal (1999, accepted for publication).
47. M.D. Vose, G.E. Liepins, Punctuated equilibria in genetic search, Complex Systems 5 (1991).
48. S. Wright, The roles of mutation, inbreeding, crossbreeding and selection in evolution, in: Proc. 6th Internat. Congress of Genetics, vol. 1, 1932, pp. 356-366.