  The fitting of physical models is often done only using a single target
observable. However, when multiple targets are considered, the fitting
procedure becomes cumbersome, there being no easy way to quantify the
robustness of the model for all different observables. Here, we illustrate that
one can jointly search for the best model for each desired observable through
multi-objective optimization. To do so we construct the Pareto front to study
if there exists a set of parameters of the model that can jointly describe
multiple, or all, observables. To alleviate the computational cost, the
predicted error for each targeted objective is approximated with a Gaussian
process model, as it is commonly done in the Bayesian optimization framework.
We applied this methodology to improve three different models used in the
simulation of stationary state $cis-trans$ photoisomerization of retinal in
rhodopsin. Optimization was done with respect to different experimental
measurements, including emission spectra, peak absorption frequencies for the
$cis$ and $trans$ conformers, and the energy storage.
