Radial model of differential evolution dynamics

Despite extensive research into the state-of-the-art global optimization technique of Differential Evolution (DE) its theoretical foundations still need development. This paper provides a dynamics model of a population exploiting a radial (central-symmetric), unimodal function. Derivations are based on the analysis of moments of the population distribution and lead to formulae describing them in consecutive iterations. This allows for simulating the execution of DE for radial functions without running this algorithm. Analytical insights include an explicit, approximate formula linking the convergence speed of DE population with a generalized scaling factor, crossover probability and the search space dimension.