Deep Q-network assisted variable neighborhood search algorithm for berth allocation considering berth shifting in dry bulk terminals

The expansion of global maritime trade, along with the surge in dry bulk vessel sizes, has intensified the shortage of deep-water berths. This work investigates a discrete berth allocation problem considering berth shifting in dry bulk terminals. It includes two shifting strategies: 1) load-reduction shifting, where large vessels first unload partial cargo at deep-water berths to lighten their draft, and then shift to shallow-water berths to complete operations; and 2) berth-releasing shifting, where small vessels shift from deep-water berths to shallow-water berths when a large vessel needs the space. A mixed-integer linear programming model is formulated to minimize the total vessel service time. A Deep Q-Network assisted Variable Neighborhood Search algorithm (DQN-VNS) is proposed to solve this problem. First, a Dynamic-priority-based Heuristic Initialization Strategy is proposed to generate high-quality initial solutions. Then, a Deep Q-Network is employed to guide the search by adaptively choosing the most promising neighborhood operator. Numerical experiments are conducted on real historical data from a dry bulk terminal. The results demonstrate that DQN-VNS can effectively improve search efficiency and solution quality, significantly reducing vessel service time in dry bulk terminals. This work can significantly enhance the operational efficiency of dry bulk terminals.