Abstract
A new mathematical description of the dynamics of a simple genetic algorithm is presented. This formulation is based on ideas from statistical physics. Rather than trying to predict what happens to each individual member of the population, methods of statistical mechanics are used to describe the evolution of statistical properties of the population. We present equations which predict these properties at one generation in terms of those at the previous generation. The effect of the selection operator is shown to depend only on the distribution of fitnesses within the population, and is otherwise problem independent. We predict an optimal form of selection scaling and compare it with linear scaling. Crossover and mutation are problem-dependent, and are discussed in terms of a test problem — the search for the low energy states of a random spin chain. The theory is shown to be in good agreement with simulations.
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© 1994 Springer-Verlag Berlin Heidelberg
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Shapiro, J., Prügel-Bennett, A., Rattray, M. (1994). A statistical mechanical formulation of the dynamics of genetic algorithms. In: Fogarty, T.C. (eds) Evolutionary Computing. AISB EC 1994. Lecture Notes in Computer Science, vol 865. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58483-8_2
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DOI: https://doi.org/10.1007/3-540-58483-8_2
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