Abstract: Large ships entering and leaving ports need tugboats to assist in berthing and unberthing. Because of the influence of their own ship length, draft, wind flow, and berth environment, they are unable to fully utilize their own control force for berthing and unberthing maneuvers. The tugboat is an important part of the port resources. Tugboat scheduling is one of the important planning items of the port. However, tugboats in ports are limited. In the face of a large number of ships entering and leaving the port during the tide period that requires the tugboat assistance, how to effectively dispatch tugboats and provide timely service to ships is the key to improving the port’s service level. At the same time, fuel consumption generated by various types of tugboats varies in different states. How to improve the utilization rate of tugboats and reduce the fuel consumption of tugboats during the scheduling process is also essential for reducing the operational costs of tugboat companies. Therefore, it is necessary to seek scientific and reasonable tugboat scheduling decisions. However, research literature on tugboat scheduling is still very limited. Most of the tugboat scheduling models in existing literature are single objective optimization. In fact, there are many factors to consider in tugboat scheduling decisions, and there is relatively little research on multi-objective optimization of tugboat scheduling. Therefore, it is necessary to conduct multi-objective optimization scheduling research on tugboats in this article.
Aiming at the problem of balancing completion time and fuel consumption in the process of tugboat scheduling to improve port service levels and reduce tugboat company operating costs, this paper aims at minimizing the maximum completion time of tugboats and the total fuel consumption of tugboats, and constructs a mixed integer programming tugboat multi-objective optimization scheduling model. The model takes into account the characteristics of a large number of ships entering and leaving the port in a tidal port during the tide, and calculates the fuel consumption of tugboats according to the different states in the tugboat scheduling process. To solve the model, the NSGA-II (Non-dominated Sorting Genetic Algorithm II) is used. NSGA-II has numerous advantages in solving multi-objective optimization problems and has been widely applied in solving various practical scheduling problems. The algorithm adopts one-dimensional real number coding, and the fitness function is set by the idea of event modeling. In combination with the characteristics of tugboat scheduling, the genetic operator is designed. The Pareto frontier solution obtained and the algorithm comparison show the effectiveness of the algorithm.
Finally, the actual operation data of Guangzhou Port is used as an example to verify the feasibility and effectiveness of the model, which provides a decision-making basis for the port tugboat scheduling plans. The instance shows the two objectives of this model cannot be minimized simultaneously, and the total fuel consumption of the tugboats in the Pareto frontier solution decreases with the increase of the maximum completion time of the tugboats. Port tugboat dispatchers can choose a suitable tugboat scheduling plan from Pareto frontier solutions based on actual needs. Different scheduling plans also indicate that in the case of limited tugboat resources within the same area, tugboats from other adjacent areas can come to assist in reducing ship waiting time. However, when tugboats sail across areas, non-speed limited navigation will consume more fuel, so reducing the number of cross area voyages can relatively reduce tugboats’ fuel consumption. In addition to considering the issues of balancing efficiency and energy conservation proposed in this article, the dynamic optimization of tugboat scheduling is also an important task for tugboat scheduling planners to adjust tugboat scheduling to cope with uncertain events, as many uncertain factors may occur during the actual tugboat berthing and unberthing process, resulting in the original tugboat scheduling plan not being able to proceed as usual. In addition, tugboats are a part of port resources, and it is worth considering how to combine them with other port resources to make port integrated operations more efficient. The above are all directions that this article will continue to study in the future.

Key words: tugboat scheduling, multi-objective optimization, NSGA-II, Pareto frontier solution

摘要： 进出港口的大型船舶需向港口申请拖轮协助以进行靠离泊作业。拖轮调度是港口重要的计划事项之一。针对拖轮调度过程中需要平衡完工时间和油耗量以提高港口服务水平和降低拖轮公司经营成本的问题,本文以最小化拖轮最大完工时间和最小化拖轮总油耗量为目标,构建了混合整数规划拖轮多目标优化调度模型。模型还考虑了潮汐港口大量船舶在潮水期间集中进出港的特点,并根据拖轮在调度过程中的不同状态分类计量其产生的油耗量,以使模型更接近实际状况。为求解模型,运用了带有精英策略的非支配排序遗传算法(NSGA-II),算法采用一维实数编码,以事件建模思想设置适应度函数,并结合拖轮调度特点设计了遗传算子,求得的Pareto前沿解和算法对比验证了该算法的有效性。最后,以广州港港口拖轮调度实际运作数据作为算例,验证了模型的可行性与有效性,为港口拖轮调度计划提供了决策依据。

关键词: 拖轮调度, 多目标优化, NSGA-II, Pareto前沿解