  We implement for the first time the simulated annealing method (SAM) to the
problem of searching for the global minimum in the hyper-surface of the
chi-square function which depends on the values of the parameters of a Skyrme
type effective nucleon-nucleon interaction. We undertake a realistic case of
fitting the values of the Skyrme parameters to an extensive set of experimental
data on the ground state properties of many nuclei ranging from normal to
exotic ones. The set of experimental data used in our fitting procedure
includes the radii for the valence $1d_{5/2}$ and $1f_{7/2}$ neutron orbits in
the $^{17}$O and $^{41}$Ca nuclei, respectively, and the breathing mode
energies for several nuclei, in addition to the typically used data on binding
energy, charge radii and spin-orbit splitting. We also include in the fit the
critical density $\rho_{cr}$ and further constrain the values of the Skyrme
parameters by requiring that (i) the quantity $P = 3\rho \frac{dS}{d\rho}$,
directly related to the slope of the symmetry energy $S$, must be positive for
densities up to $3\rho_0$ (ii) the enhancement factor $\kappa$, associated with
the isovector giant dipole resonance, should lie in the range of $0.1 - 0.5$
and (iii) the Landau parameter $G_0^\prime$ is positive at $\rho = \rho_0$. We
provide simple but consistent schemes to account for the center of mass
corrections to the binding energy and charge radii.
