  The throughout knowledge of a X-ray beam spectrum is mandatory to assess the
quality of its source device. Since the techniques to directly measurement such
spectra are expensive and laborious, the X-ray spectrum reconstruction using
attenuation data has been a promising alternative. However, such reconstruction
corresponds mathematically to an inverse, nonlinear and ill-posed problem.
Therefore, to solve it the use of powerful optimization algorithms and good
regularization functions is required. Here, we present a generalized simulated
annealing algorithm combined with a suitable smoothing regularization function
to solve the X-ray spectrum reconstruction inverse problem. We also propose an
approach to set the initial acceptance and visitation temperatures and a
standardization of the objective function terms to automatize the algorithm to
address with different spectra range. Numerical tests considering three
different reference spectra with its attenuation curve are presented. Results
show that the algorithm provides good accuracy to retrieve the reference
spectra shapes corroborating the central importance of our regularization
function and the performance improvement of the generalized simulated annealing
compared to its classical version.
