  A general procedure of average-case performance evaluation for population
dynamics such as genetic algorithms (GAs) is proposed and its validity is
numerically examined. We introduce a learning algorithm of Gibbs distributions
from training sets which are gene configurations (strings) generated by GA in
order to figure out the statistical properties of GA from the view point of
thermodynamics. The learning algorithm is constructed by means of minimization
of the Kullback-Leibler information between a parametric Gibbs distribution and
the empirical distribution of gene configurations. The formulation is applied
to the solvable probabilistic models having multi-valley energy landscapes,
namely, the spin glass chain and the Sherrington-Kirkpatrick model. By using
computer simulations, we discuss the asymptotic behaviour of the effective
temperature scheduling and the residual energy induced by the GA dynamics.
