Abstract
This summer I found a beautiful paper titled The Equilibrium Genetic Algorithm and the Role of Crossover [1]. It's from Nov/1993 and is authored by Ari Juels, Shumeet Baluja, and Alistair Sinclair. To my best knowledge, this paper describes the first evolutionary algorithm that explicitly replaces the population by a probability vector. While reading the paper, one can recognize that the main goal of the authors is to come up with an abstraction of the basic genetic algorithm in order to better analyze it from a mathematical perspective. To that end, they develop the Equilibrium Genetic Algorithm (EGA), and, as a byproduct, are able to show that some of the mechanisms present in standard genetic algorithms are likely to be, in certain cases, unnecessarily complex.
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