Simulated annealing for optimal ship routing

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.