1.1. Background
Shipping is one of the most important modes of trade transport, accounting for more than 80% of international trade. However, with the development of maritime trade and the increase in ship tonnage, energy consumption and air pollution problems have become increasingly severe. The Fourth International Maritime Organization (IMO) GHG Study 2020 estimated that GHG emissions from shipping in 2018 accounted for some 2.89% of global anthropogenic GHG emissions and that such emissions could represent between 90% and 130% of 2008 emissions by 2050 [
1]. The 80th session of the IMO Marine Environment Protection Committee (MEPC 80) proposed that by 2030, the annual greenhouse gas emissions from international maritime trade should be reduced by at least 20%, with an aim to achieve a 30% reduction compared to 2008 levels [
2].
Strategies for energy saving and emission reduction in ships mainly include hull design optimization, operational optimization, and the application of new green energy. Hull design optimization involves optimizing the shape of the hull through hydrodynamic design before ship building to minimize resistance and improve seaworthiness [
3]. In addition to the optimization of the hull design, operational optimization is also a cost-effective and quick method, including speed optimization, route optimization, operational scheduling optimization, and trim optimization [
4].
Among various optimization strategies, including ship hull optimization, loading condition optimization, and sailing speed optimization, sailing speed optimization is the most direct and effective method. By reasonably adjusting the sailing speed, fuel consumption can be significantly reduced, and greenhouse gas emissions can be accordingly decreased. And speed optimization can further enhance the energy-saving and emission-reduction effects based on hull optimization. Greenhouse gas emissions are approximately proportional to fuel consumption, and fuel consumption per unit time increases with higher speeds. Studies have shown that the fuel consumption per unit time is approximately a cubic function of speed [
5]. Fuel costs account for more than 60% of total operating costs, greatly affecting the economic benefits and market competitiveness of shipping companies [
6]. Higher speeds enable faster arrival at ports, reducing inventory costs of goods in transit and increasing trade volume per unit of time. However, this also leads to increased fuel consumption and gas emissions [
7]. Therefore, considering the current competitive shipping market and rising fuel prices, shipowners or charterers often adopt slow steaming strategies. Nevertheless, extremely low speeds can lead to engine stalling, and ships must arrive at ports within stipulated times. Hence, the optimization of the sailing speed is a complex nonlinear optimization problem with multiple objectives and constraints.
The optimization of sailing speed during navigation depends on factors such as shipping mode, ship payload, fuel costs, inventory costs of goods, freight rates, and weather conditions [
8]. The Maersk Line conducted slow steaming trials with over 100 container ships, confirming that ships can operate normally with engine loads reduced to 10%, corresponding to about half of the design speed [
9]. Wen et al. developed a constrained programming model to solve multi-ship routing and speed optimization under time, cost, and environmental constraints but did not consider weather factors [
7]. Considering weather factors, meteorological ship route optimization mainly focuses on the impact of wind and waves on navigation, aiming to find the optimal route and speed to minimize operating costs, fuel consumption, and navigation risks [
10]. Moreover, speed optimization also needs to consider maritime regulations. IMO has established four emission control areas (ECAs), including the Baltic Sea, the North Sea, the English Channel and all European ports, the North American coast, and the US Caribbean coast. Within the areas of ECAs, ships must use more expensive fuels with a sulfur content of less than 1%, a standard reduced to 0.5% from 2020 onwards. The Chinese government has established the Yangtze River Delta ECA, stipulating that ships entering this control area must use fuel with a sulfur content of less than 0.1% after 1 January 2022. Many scholars have conducted speed optimization and route planning studies to mitigate the adverse effects of ECAs [
11,
12,
13]. Although inland ships and ocean-going ships both aim to reduce fuel consumption and operational costs, the factors influencing optimization are significantly different. The speed optimization of inland ships considers complex and variable environmental conditions such as fluctuating water depths, water flow, narrow waterways, and navigation rules specific to inland waterways. In contrast, the speed optimization of ocean-going ships focuses more on weather conditions, the impact of ECAs, and long-distance route planning. Overall, most current research on speed optimization concentrates on ocean-going ships, while research in the field of speed optimization for inland ships is relatively scarce.
In the context of the significant development of the shipping industry and the emphasis on energy saving and emission reduction, all-electric ships (AESs) represent the future trend. Currently, an increasing number of AES are being put into use. However, research on how to save electrical energy for inland AES is still insufficient. Studying the speed optimization for AESs in the complex inland waterway environment to reduce energy consumption is of great significance for lowering inland shipping costs and reducing environmental pollution.
1.2. Related Works
Scholars have conducted many studies to optimize sailing speed, reduce ships’ operating costs, and lower emissions. Wang and Meng develop a mixed-integer nonlinear programming model to study speed optimization in the container shipping network, taking routes into account [
14]. Du et al. established an artificial neural network model based on ships’ navigation report data, which minimizes fuel consumption by adjusting the ship’s speed and trim [
15]. Norstad et al. consider speed as an input to study the scheduling and speed optimization of tramp shipping, significantly improving the profitability of shipping companies [
16]. Lashgari et al. developed a stochastic linear integer programming model to jointly optimize route decisions, speed optimization, and refueling strategies in liner shipping, aiming to reduce total costs [
17]. These studies demonstrate the effectiveness of various optimization models and techniques in improving fuel efficiency and operational costs for maritime transportation.
Other scholars have considered the impact of ECA regulations on costs and emissions in their speed optimization studies. By analyzing actual ship route data, Fagerholt et al. find that ship operators often choose to detour longer routes to avoid ECA. Additionally, ships tend to sail at reduced speeds within ECA and at higher speeds outside ECA [
18]. Ma et al. optimize both ship routes and speeds while considering the impact of ECA, finding that reducing emissions within ECA might increase total voyage emissions [
19]. Zhen et al. develop a dual-objective model to minimize total fuel costs and SO
2 emissions, optimizing routes and speeds both inside and outside ECAs [
20]. These studies indicate that while it is possible to reduce emissions within ECAs through various methods, they may lead to higher overall emissions and operational costs. Other studies have focused on speed optimization based on weather conditions and Estimated Time of Arrival (ETA). ETA is determined according to the navigation plan, and within the allowable range of ETA, the ship’s route planning needs to meet the requirements of low energy consumption and short navigation time as much as possible [
21]. To address the issue of decreased accuracy in long-term weather forecasting, Tzortzis and Sakalis propose a method that divides the total time of a fixed route into several smaller time intervals to dynamically determine the speed for each segment [
22]. Du et al. thoroughly consider meteorological conditions, ship main engine power, and navigation safety constraints, analyzing the differences in speed, ETA, energy consumption, and emissions on multiple pre-set routes, and providing different optimal routes based on navigation objectives [
23]. These studies have contributed to speed optimization through model construction, combining relevant maritime regulations and ship operations. However, their focus and scenarios are mainly on ocean-going ships, and there is currently little research on speed optimization for inland ships.
Unlike ocean navigation, inland waterways are narrow, with significant variations in water depth and flow speed, presenting a more complex navigation environment. Some scholars have conducted research on ship energy efficiency and speed optimization by considering the characteristics of inland waterways. Wang et al. consider the time-varying nature of inland environmental factors (wind, water flow, water depth, etc.), use a Model Predictive Control (MPC) method to design an optimized controller, testing the optimal speed under time-varying environmental factors with different time steps. This approach significantly improves ship energy efficiency and reduces fuel consumption and CO
2 emissions compared to traditional static optimization methods [
6]. Yan et al. consider the effects of wind speed, wind direction, water depth, and flow speed, employing a distributed parallel K-means algorithm to achieve finer segmentation of inland navigation segments and determine the optimal engine speed for each segment, ultimately improving ship energy efficiency [
24]. Fan et al. use speed as a decision variable and construct a multi-stage speed optimization model considering environmental factors, showing that flow speed and direction are key factors affecting the navigation speed of ships on the Yangtze River [
25]. Yuan et al. use a density-based spatial clustering method to cluster environmental information such as wind speed, wind direction, water level, and water flow on the Yangtze River trunk line, segmenting the Yangtze River waterway to reduce the impact of the highly variable inland navigation environment on speed optimization [
26].
With the increasing density and performance of large-capacity lithium-ion batteries, the application of electric propulsion ships has become possible. Although fully electric ships cannot currently meet the energy demands of ocean navigation, they can be used for port-to-port transportation and berthing tasks in shorter inland voyages with the advent of high-capacity marine batteries and the increase in the number of charging stations along inland waterways [
27]. Fan et al. analyze the green decarbonization needs of China’s inland ships and the characteristics of new power systems, proposing a solution to replace traditional power systems with electric propulsion [
28]. Zhang et al. consider environmental factors such as cargo load, flow speed, and water depth, constructing an energy-consumption model based on the energy transfer process of electric ships and optimizing the speed and energy under battery swapping mode, reducing battery replacement costs [
29]. Sun et al. consider the dynamic changes in electricity prices and the complex navigation environment of inland waterways to establish a speed and energy optimization model, minimizing ship operating costs. They conducted a case study on AES in inland navigation, providing a reference for the operation and management of inland electric propulsion ships [
30]. These scholars’ studies have contributed to the development of inland AES, but overall, the application of and research on inland AES ships are still relatively limited. More comprehensive and in-depth research on AES for inland navigation needs to be conducted on green, low-carbon, and efficient development of inland shipping.