About the convergence rates of a class of gene expression programming
This paper studies the convergence rates of gene expression programming based on maintaining elitist (ME-GEP) by means of Markov chain and spectrum analysis. We obtain the following results: (1) ME-GEP algorithm converges to the global optimum in probability. (2) The convergence rates of ME-GEP algorithm depend on the revised spectral radius of transition matrix of Markov chain corresponding to the algorithm. (3) The upper bounds of revised spectral radius are estimated, which are determined by the parameters of ME-GEP algorithm. (4) As an application of the theoretical results acquired in the paper, the convergence rates of ME-GEP for the polynomial function modeling problem are also analyzed, which verifies the relations between the convergence rates and the algorithm parameters.
convergence rates me-gep markov chain revised spectral radius gep