Fourier Analysis of Genetic Algorithms

We propose a general framework for Fourier analysis in the field of genetic algorithms. We introduce special functions, analogous to sine and cosine for real numbers, that have nice properties with respect to genetic operations such as mutation and crossover. The special functions we introduce are generalizations of bit products and Walsh products. As applications, we trace (both analytically and numerically) the behavior of genetic algorithms, and obtain results on the fitness of schemata.

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