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An approach to address the berth allocation problem is presented that is based on the receding horizon paradigm. In more detail, berthing decisions are computed by solving an optimization problem at each time step aimed at minimizing the waiting times of vessels, exploiting predictions on the ship arrivals and berth occupancy over a moving window starting from the current time instant. A discrete time dynamic model is devised to forecast the state of the terminal in the forward window, and a computationally-efficient approximate solution method based on random search is proposed. The considered framework can be used either for real time planning or scheduling in advance. Simulation results are reported to show the effectiveness of the method in different terminal configurations, forward horizons, and traffic intensities, in comparison with state-of-the-art approaches.

The goal of this work is the optimal control of level sets generated by the normal flow equation. The problem consists in finding the normal velocity that minimizes a given performance index expressed by means of a cost functional. In this perspective, a sufficient condition of optimality requiring the solution of a system of partial differential equations is derived. As in general it is difficult to solve such a system, an approximation scheme based on the extended Ritz method is proposed to find suboptimal solutions. The control law is forced to take on a fixed structure depending nonlinearly on a finite number of parameters to be suitably chosen. The selection of the parameters is accomplished by using a gradient-based technique. To this end, the adjoint equation is derived to compute the gradient of the cost functional with respect to the parameters of the control law. The effectiveness of the proposed approach is shown by means of simulations.