Abstract
In the running of a genetic algorithm, the population is liable to be confined in the local optimum, that is the metastable state, making an equilibrium. It is known that, after a long time, the equilibrium is punctuated suddenly and the population transits into the better neighbor optimum. We adopt the formalization of Computational Ecosystems to show that the dynamics of the Simple Genetic Algorithm is represented by a differential equation focusing on the population mean of a phenotype. Referring to the studies of differential equations of this form, we show that the duration time of metastability is exponential in the population size and other parameters, on the one dimensional bistable fitness landscape which has one metastable and one stable state.
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References
H. A. Ceccatto and B. A. Huberman. Persistence of nonoptimal strategies. Proc. Natl. Acad. Sci. USA, 86:3443–3446, 1989.
A. Galves, E. Olivieri, and M. E. Vares. Metastability for a class of dynamical systems subject to small random perturbations. 15(4):1288–1305, 1987.
D. E. Goldberg. Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, 1989.
Tad Hogg and Bernardo A. Huberman. Controlling chaos in distributed systems. IEEE trans. on SMC, 21(6):1325–1332, 1991.
J. H. Holland. Adaptation in natural and artificial systems. Univ. of Michigan Press, 1975.
B. A. Huberman and T. Hogg. The behavior of computational ecologies. In B. A. Huberman, editor, The Ecology of Computation. North-Holland, 1988.
J. O. Kephart, T. Hogg, and B. A. Huberman. Dynamics of computational ecosystems. Phys. Rev. A, 40(1):404–421, 1989.
C. Kipnis and C. M. Newman. The metastable behavior of infrequently observed, weakly random, one-dimensional diffusion processes. SIAM J. Appl. Math., 45(6):972–982, 1985.
C. M. Newman, J. E. Cohen, and C. Kipnis. Neo-darwinian evolution implies punctuated equilibria. Nature, 315:400–401, May 30 1985.
A. Priigel-Bennett and Jonathan L. Shapiro. An analysis of genetic algorithms using statistical mechanics. Phys. Rev. Lett., 72:1305–1309, 1994.
R. L. Scheaffer and J. T. McClave. Probability and statistics for engineers. PWSKENT, 1990.
M. D. Vose. Punctuated equilibria in genetic search. Complex Systems, 5:31–44, 1991.
L. Darrell Whitley. Fundamental principles of deception in genetic search. In Gregory J. E. Rawlins, editor, FOGA. Morgan Kaufmann, 1991.
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© 1998 Springer-Verlag Berlin Heidelberg
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Oh, S., Yoon, H. (1998). An analysis of punctuated equilibria in simple genetic algorithms. In: Hao, JK., Lutton, E., Ronald, E., Schoenauer, M., Snyers, D. (eds) Artificial Evolution. AE 1997. Lecture Notes in Computer Science, vol 1363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0026601
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DOI: https://doi.org/10.1007/BFb0026601
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