  Aima. To determine to what extent the problem of forward fitting visibilities
measured by the Spectrometer/Telescope Imaging X-rays (STIX) on-board Solar
Orbiter is more challenging with respect to the same problem in the case of
previous hard X-ray solar imaging missions; to identify an effective
optimization scheme for parametric imaging for STIX. Methods. This paper
introduces a Particle Swarm Optimization (PSO) algorithm for forward fitting
STIX visibilities and compares its effectiveness with respect to the standard
simplex-based optimization algorithm used so far for the analysis of
visibilities measured by the Reuven Ramaty High Energy Solar Spectroscopic
Imager (RHESSI). This comparison is made by considering experimental
visibilities measured by both RHESSI and STIX, and synthetic visibilities
generated by accounting for the STIX signal formation model. Results. We found
out that the parametric imaging approach based on PSO is as reliable as the one
based on the simplex method in the case of RHESSI visibilities. However, PSO is
significantly more robust when applied to STIX simulated and experimental
visibilities. Conclusions. Standard deterministic optimization is not effective
enough for forward-fitting the few visibilities sampled by STIX in the angular
frequency plane. Therefore a more sofisticated optimization scheme must be
introduced for parametric imaging in the case of the Solar Orbiter X-ray
telescope. The forward-fitting routine based on PSO we introduced in this paper
proved to be significantly robust and reliable, and could be considered as an
effective candidate tool for parametric imaging in the STIX context.
