  A simulated annealing based algorithm is presented for the determination of
optimal ship routes through the minimization of a cost function. This cost
function is a weighted sum of the time of voyage and the voyage comfort (safety
is taken into account too). The latter is dependent on both the wind speed and
direction and the wave height and direction. The algorithm first discretizes an
initial route and optimizes it by considering small deviations which are
accepted by utilizing the simulated annealing technique. Using calculus of
variations we prove a key theorem which dramatically accelerates the
convergence of the algorithm. Finally both simulated and real experiments are
presented.
