This paper deals with a dual-axis sun tracking system for a photovoltaic system. Its trajectories are determined by an optimization procedure. The optimization goal is the maximization of the electrical energy production within a photovoltaic system, by considering the tracking system consumption. The procedure used for determining the tilt angle and azimuth angle trajectories is described as a nonlinear and bounded optimization problem. Since an explicit form of the objective function is unavailable, a stochastic search algorithm called Differential Evolution is applied as the optimization tool. In order to evaluate the objective function, models for calculating the available solar radiation and tracking system consumption are applied together with the efficiencies of solar cells, a DC/DC converter and inverter. A new algorithm is introduced for the time dependent prediction of available solar radiation. It is based on the length of a sunbeam's path through the atmosphere and the statistical data of a pyranometer measured total and diffuse solar radiation at a given location on the Earth. The optimization bounds are given in the form of angular speed, lower and upper bounds for both angles and angle quantization. The results presented in this paper show, that the optimal trajectories can help to increase the electrical energy production within photovoltaic systems by sun tracking. (C) 2011 Elsevier Ltd. All rights reserved.