On the Dynamics of Genetic Algorithms (and Other Evolving Systems)

		/vol02/gozl2/	© Copyright 1995
		Volume 02	Received: Accepted:	---- ----

On the Dynamics of Genetic Algorithms (and Other Evolving Systems) Ben Goertzel, Malwane Ananda and Matthew Ikl?/h3>
Abstract
	The genetic algorithm is approximated by a deterministic iteration on , called the "iterated mean path" and obtained by repeatedly iterating the function which takes a population into its expected value after one step of the GA. This is a "no genetic drift" approximation which becomes increasingly accurate as population size increases. It is shown that the optimum of the fitness function is usually not an attractor for the iterated mean path; a result which reflects the empirical phenomenon of "dithering". Also, a surprisingly simple formula for the Jacobian determinant of is presented, which states that under appropriate conditions, this determinant is inversely proportional to a positive power of the average fitness of the population. These results, it is argued, suggest the possibility of two general principles of evolutionary dynamics, extending beyond the context of the GA: a law of diversity generation and a law of fitness-driven focussing.

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