Browse > Article

The Duration of Punctuated Equilibria in Simple Genetic Algorithms  

Oh, Sang-Yeop (금오공과대학교 컴퓨터공학과)
Publication Information
Journal of KIISE:Software and Applications / v.32, no.11, 2005 , pp. 1059-1070 More about this Journal
Abstract
For genetic algorithms, the population may get stuck in a local optimum. The population can escape from this after a long duration. This phenomenon is called punctuated equilibrium. The punctuated equilibria observed in nature and computational ecosystems are known to be well described by diffusion equations. In this paper, simple genetic algorithms are theoretically analyzed to show that they can also be described by a diffusion equation. When fitness is the function of unitation, this analysis can be further refined to make the parameters of genetic algorithms appear in this equation. Using theoretical results on the diffusion equation, the duration of equilibrium is shown to be exponential of such parameters as population size, 1/(mutation probability), and potential barrier. This is corroborated by simulation results for bistable potential landscapes with one local optimum and one global optimum.
Keywords
genetic algorithms; punctuated equilibria;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Prugel-Bennett, A. and. Shapiro, J. L., 'The dynamics of a genetic algorithm for simple random ising systems,' Physica D, Vol.104, No.1, pp. 75？114, 1997   DOI   ScienceOn
2 Rattray, M., 'The dynamics of a genetic algorithm under stabilizing selection,' Complex Systems, Vol.6, No.3, pp. 213-234, 1995
3 Jansen, T. and Wegener, I., 'On the analysis of evolutionary algorithms - a proof that crossover really can help,' in Proceedings of the 7th Annual European Symposium on Algorithms (ESA'99) edited by Nesetril, J., Springer, Berlin, 1999
4 Rogers, A. and Prugel-Bennett, A., 'The dynamics of a genetic algorithm on a model hard optimization problem,' Complex Systems, Vol.11, No.6, pp. 437-464, 2000
5 Prugel-Bennett, A. and Shapiro, J. L., 'An analysis of genetic algorithms using statistical mechanics,' Physical Review Letters, Vol.72, No.9, pp. 1305？1309, 1994
6 Kipnis, C. and Newman, C. M. 'The metastable behavior of infrequently observed, weakly random, one-dimensional diffusion processes,' SIAM Journal on Applied Mathematics, Vol.45, No.6, pp. 972-982, 1985   DOI   ScienceOn
7 Nimwegen, E. van, Crutchfield, J. P. and Mitchell, M., 'Statistical dynamics of the royal road genetic algorithm,' Santa Fe Institute Working Paper 97-04-035, 1997
8 Newman, C. M., Cohen, J. E. and Kipnis, C., 'Neo-darwinian evolution implies punctuated equilibria,' Nature, pp. 400？401, May 1985   DOI
9 Vose, M. D. and Liepins, G. E., 'Punctuated equilibria in genetic search,' Complex Systems, Vol.5, No.1, pp. 31-44, 1991
10 Ceccatto, H. A. and Huberman, B. A., 'Persistence of nonoptimal strategies,' Proceedings of the National Academy of Sciences of the United States of America, pp. 3443？3446, 1989   DOI   ScienceOn
11 Holland, J. H., Adaptation in natural and artificial systems, The MIT Press, Cambridge, MA, 2nd Ed., 1992
12 Goldberg, D. E.,
13 Shapiro, J. and Prugel-Bennett, A., 'Genetic algorithm dynamics in a two-well potential,' in FOGA4 edited by Belew, R. K. and Vose, M. D., Morgan Kaufmann, San Francisco, 1997
14 Goldberg, D. E., Genetic algorithms in search, optimization, and machine learning, Addison-Wesley, New York, 1989
15 Kephart, J. O., Hogg, T. and Huberman, B. A., 'Dynamics of computational ecosystems,' Physical Review A, Vol.40, No.1, pp. 404？421, 1989
16 Aarts, E. and Corst, J., Simulated Annealing and Boltzmann Machines, John Wiley & Sons, New York, 1989
17 Hogg, T. and Huberman, B. A., 'Controlling chaos in distributed systems,' IEEE transactions on Systems, Man, and Cybernetics, Vol.21, No.6, pp. 1325-1332, 1991   DOI   ScienceOn
18 Kampen, N. V., Stochastic processes in physics and chemistry, Elsevier Science, Amsterdam, 1981
19 Galves, A., Olivieri, E. and Vares, M. E., 'Metastability for a class of dynamical systems subject to small random perturbations,' The Annals of Probability, Vol.15, No.4, pp. 1288-1305, 1987   DOI   ScienceOn
20 Scheaffer, R. L. and McClave, J. T., Probability and statistics for engineers, PWS-KENT, Boston, 1990
21 Srinivas, M. and Patnaik, L. M., 'On modeling genetic algorithms for functions of unitation,' IEEE transactions on Systems, Man, and Cybernetics, Vol.26, No.6, pp. 809-821, 1996   DOI
22 Huberman, B. A. and Hogg, T., 'The behavior of computational ecologies.,' in The Ecology of Computation edited by Huberman, B. A., North-Holland, Amsterdam, 1988