Floating macro-marine debris becomes a global environmental problem when emitted into the ocean. It damages the marine ecosystem, threatens human health, and also causes incalculable economic losses. Due to the impacts of ocean currents and winds, marine debris has been transported to different locations over time and time window cannot be ignored to navigate the locations of marine debris. To effectively mitigate the risk, we propose the vessel routing optimization with a time window to collect and remove marine debris. Ocean currents and winds also affect the velocity and direction of the collecting vessel. We first employ GNOME software to determine the debris trajectory and set a time window for each debris location. A mixed-integer nonlinear programming model considering vessel velocity is proposed to minimize the total debris collection cost. We propose two customized solution approaches: Branch-and-Cut (B&C) algorithm and two-stage Adaptive Large Neighborhood Search (ALNS) based heuristic algorithm to solve the proposed mathematical model in a reasonable timeframe. A computational study in waters off Boston is used to validate the proposed model and the solution algorithms. The result indicates that the average optimality gap for GUROBI and B&C algorithm is 17.53% and 10.52%, respectively, while this gap is only 3.44% for the ALNS algorithm. Moreover, the average computing time of the ALNS algorithm is roughly 24 and 17 times faster than that of the GUROBI and the B&C algorithm, respectively. The experimental results show that distance from debris location to the harbor is positively related to the collection cost and negatively related to the average usage of vessels’ capacity, and the dispersion of debris is also positively related to the fuel consumption of vessels.

漂浮的大型海洋垃圾在排放到海洋中时成为一个全球性的环境问题。它破坏海洋生态系统，威胁人类健康，也造成不可估量的经济损失。 由于洋流和风的影响，海洋垃圾随着时间的推移被运送到不同的位置，不能忽略时间窗口来导航海洋垃圾的位置。为了有效降低风险，我们提出了带有时间窗口的船舶航线优化，以收集和清除海洋垃圾。洋流和风也会影响收集船的速度和方向。我们首先使用 GNOME 软件来确定碎片轨迹并为每个碎片位置设置一个时间窗口。提出了一种考虑容器速度的混合整数非线性规划模型，以最小化总碎片收集成本。我们提出了两种定制的解决方案方法：Branch-and-Cut (B& C) 算法和基于两阶段自适应大邻域搜索 (ALNS) 的启发式算法，以在合理的时间范围内求解所提出的数学模型。在波士顿附近水域进行的计算研究用于验证所提出的模型和求解算法。结果表明，GUROBI和B&C算法的平均最优性差距分别为17.53%和10.52%，而ALNS算法的这一差距仅为3.44%。此外，ALNS 算法的平均计算时间分别比 GUROBI 和 B&C 算法快 24 倍和 17 倍。实验结果表明，碎片位置到港口的距离与收集成本呈正相关，与船舶运力的平均使用率呈负相关，