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Drift, Diffusion And Boltzmann Distribution In Simple Genetic Algorithm

This paper presents a general diffusion model of a simple genetic algorithm. Unlike the similar previous efforts made for modeling mutation based genetic search, this work includes the effect of crossover by considering the dynamics of spatially averaged observables, under the influence of deterministic and stochastic effects. The analysis shows a possibility of generating Boltzmann distribution in the population. A noise reduction mechanism by means of controlling the distributional bias of the population is conjectured based on observations made on the entropic structure of the representational space.