Dynamic speed optimization and berth reallocation for autonomous vessels under sailing time disturbances

Abstract

Autonomous vessels (AVs) have attracted growing attention due to their potential advantages in operational efficiency and navigational safety. However, their voyages may be affected by stochastic disturbances, which can lead to delayed arrivals at ports and the unavailability of pre-assigned berths. This paper first proposes a dynamic optimization approach for AV speed optimization and berth reallocation to mitigate the impacts of stochastic disturbances. Specifically, the sailing speeds of AVs are dynamically adjusted if stochastic disturbances affect their expected arrival times. Meanwhile, the real-time berth reallocation for AVs is performed when their originally allocated berths become unavailable. To meet real-time operational requirements, a rolling horizon framework is employed, which supports dynamic and adaptive adjustments to sailing speeds and berth reallocation based on the latest information on stochastic disturbances and berth occupancy. In each decision period, the problem is formulated as a mixed integer nonlinear programming model to minimize the total cost. To solve the proposed model efficiently, a tailored branch-and-cut algorithm incorporating an outer approximation method is developed. To evaluate the performance and effectiveness of the proposed model and solution method, extensive numerical experiments based on the operational data of a maritime logistics company were conducted. The results demonstrate that the proposed algorithm significantly outperforms both the Gurobi solver and a 'first-come-first-served' greedy algorithm in terms of solution quality. Sensitivity analyses revealed that greater sailing time disturbances and lower penalty costs for arrival delays tend to reduce the punctuality of AVs at ports. Moreover, higher fuel prices prompt AVs to adopt lower sailing speeds to reduce energy costs.