Information theoretic justification of Boltzmann selection and its generalization to Tsallis case

Abstract

A generalized evolutionary algorithm based on Tsallis statistics is proposed. The algorithm uses Tsallis generalized canonical distribution, which is one parameter generalization of Boltzmann distribution, to weigh the configurations in the selection mechanism. This generalization is motivated by the recently proposed generalized simulated annealing algorithm based on Tsallis statistics. We also present an information theoretic justification to use Boltzmann distribution in the selection mechanism, since these 'canonical' distributions have deep roots in information theory. Our simulation results show that for an appropriate choice of non-extensive index that is offered by Tsallis statistics, evolutionary algorithms based on this generalization outperform algorithms based on Boltzmann distribution.