Analysis of the effects of lifetime learning on population fitness using vose model

Vose's dynamical systems model of the simple genetic algorithm (SGA) is an exact model that uses mathematical operations to capture the dynamical behavior of genetic algorithms. The original model was defined for a simple genetic algorithm. This paper suggests how to extend the model and incorporate two kinds of learning, Darwinian and Lamarckian, into the framework of the Vose model. The extension provides a new theoretical framework to examine the effects of lifetime learning on the fitness of a population. We analyze the asymptotic behavior of different hybrid algorithms on an infinite population vector and compare it to the behavior of the classical genetic algorithm on various population sizes. Our experiments show that Lamarckianlike inheritance - direct transfer of lifetime learning results to offsprings - allows quicker genetic adaptation. However, functions exist where the simple genetic algorithms without learning, as well as Lamarckian evolution, converge to the same local optimum, while genetic search based on Darwinian inheritance converges to the global optimum.