1. Introduction
In the past, maritime transportation research focused on ship safety [
1,
2] as it is closely related to real-world events involving ship navigation, and meteorological and marine environments have a significant influence in this regard. Recent maritime accidents include the following: in April 2014, the Sewol ferry capsized in strong winds and waves, killing about 300 people; in December 2014, the Norman Atlantic ferry faced strong winds and waves in the Adriatic Sea, resulting in 11 deaths; in October 2015, the cargo ship El Faro went missing in a hurricane, killing all 33 crew members; in March 2021, strong winds pushed the Ever Given off course in Egypt’s Suez Canal and it ran aground; and in November 2020, a container ship stack collapse occurred after the ONE Apus encountered adverse weather and sea conditions in the North Pacific Ocean. Moreover, the loss rate of ships, of which bulk carriers account for the majority, is increasing amidst changes in wave patterns in recent years [
3]. Consequently, research on optimal route planning to help ships avoid dangerous regions is crucial for ship safety.
At present, route planning is the main topic of research in this field, but many studies have concentrated on weather and ocean conditions and have not quantitatively studied the risk-bearing capacity of ships when assessing risk values. For example, Ma et al. [
4] calculated the sailing cost associated with weather conditions by using weather data and terrain data for each section, but they did not factor in ship vulnerability. Absolute danger, hazard factors, and influential factors were used for risk contour mapping as the structure of their route planning technique [
5]. Pennino et al. [
6] provided a model to optimize routes with the maximum property values according to weather forecast maps and studied the effect of ship speed on these optimal routes. Ship information including the under keel clearance (UKC) and draft was calculated for safety contours that were used to assess the probability of ships running aground [
7]. Although these risk evaluation methods mentioned the ship parameters during navigation, they did not quantitatively analyze the ship vulnerability. Mamenko et al. [
8] only qualitatively constructed the risk field of ships needed to plan optimal routes, without calculating the risk values of sailing ships in depth. Therefore, this study proposes a multi-layer fuzzy comprehensive evaluation method to integrate the external environment of weather and marine factors with ship vulnerability. The multi-layer fuzzy comprehensive evaluation method can effectively synthesize different evaluation indicators from different criteria.
When sailing in harsh weather conditions, ships may encounter a variety of dangerous situations including wind-induced waves and heavy swells. To assist ship captains in handling such situations, the International Maritime Organization (IMO) [
9] set guidelines which apply to all types of ships. Weather routing has captured researchers’ attention in many studies, but only a few of them have taken the IMO guidelines into account. For example, a voyage optimization approach aimed to minimize fuel consumption and air emissions was tested in a harsh sea environment to prove that the approach was effective in avoiding storms [
10]. Gkerekos and Lazakis [
11] qualitatively used available weather forecast information when selecting the optimal routes via a data-driven decision support framework. Penalty costs were added to the fitness function of the algorithm for finding an optimal route with the minimum travel time and fuel consumption when the wave height was greater than the maximum acceptable wave height [
12]. As Wang et al. [
13] used a real-coded genetic algorithm to investigate how to plan minimum sailing time routes for ocean going vessels to avoid weather hazards such as wind and waves. if the wave height was significantly exceeded for the area. In a study on optimizing ship motion, Sotnikova and Veremey [
14] marked areas in harsh weather conditions, including strong winds or high waves, as the alarm area as dynamic constraints. While these studies were effective in finding routes that avoided storms or high waves, they did not quantitatively discuss the effect of wind and waves according to the IMO guidelines. In this study, dangerous situations that may lead to capsizing or severe roll motions causing damage to ships are quantificationally used as constraints to plan less risky routes.
Furthermore, the Dijkstra and A* algorithms are often applied to search for an optimal route which comprehensively considers the sailing time, risk, terrain, and other criteria with minimal influence. Zhu et al. [
15] improved the Dijkstra algorithm by adding the pheromone idea of the ant colony algorithm, thus reducing the moving cost of routes. Silveira et al. [
16] combined the information from an Automatic Identification System with the Dijkstra algorithm to plan a safe route. Ship navigation rules were added to the A* algorithm, forming the dynamic collision avoidance route planning algorithm under the circumstances of a complicated multi-ship encounter [
17]. Dong and Bian [
18] proposed an optimized A* algorithm based on a genetic algorithm to solve the problem of ship pipe route design. In terms of algorithm selection, the Dijkstra algorithm finds the optimal solution by searching all directions around the current node, while the A* algorithm, adding the heuristic function to change the direction of the search towards the target, is more efficient than the Dijkstra algorithm [
19]. However, the Dijkstra algorithm searches too many useless nodes, and the A* algorithm takes up too much space, both of which will affect the efficiency of finding the optimal route in the map with too large a size or too complex an environment [
20]. In recent years, the A* algorithm has been optimized; for example, the bidirectional A* algorithm [
21] can concurrently search from the start node to the end node and from the end node to the start node to reduce the number of nodes that need to be searched and improve the search efficiency. In view of the wide navigation range and long timespan of the ocean route, this study applies the bidirectional A* algorithm to solve our model.
Therefore, the main objectives of this study are as follows. First, the multi-layer fuzzy comprehensive evaluation method is applied to integrate the external environment of meteorological and marine factors with the vulnerability of ships so that the risk values are more accurate and comprehensive for the ships. Second, the dangerous situations which cause ships to capsize or suffer damage, as mentioned in the IMO guidelines, are quantificationally used as constraints in the algorithm. At the same time, the influence of wind, waves, and calm water on ship resistance is also considered. Then, a multi-objective nonlinear programming model is built, which comprehensively considers voyage time, voyage risk, fuel consumption, and constraints. Finally, the bidirectional A* algorithm is applied to solve the above model to obtain the optimal route. The remainder of this manuscript is organized as follows.
Section 2 presents the methods of this study. The case of the capsizing of Singapore barge CB100-01 is studied to demonstrate the validity of our model in
Section 3. Some discussions and conclusions are presented in
Section 4.
3. Case Study
3.1. Case Description and Datasets
The case selected in this study is the final investigation report of a maritime accident from the Transport Safety Investigation Bureau of Singapore (
https://www.mot.gov.sg, accessed on 28 June 2023), which classified it as a very serious maritime incident. The accident investigation report provides detailed records of the cause of the accident, information about and the status of the ship before and after the accident, and the planned route of navigation.
The ship in this accident was a barge, the CB100-01 (CB), with an overall length of 42.06 m, breadth of 15.24 m, depth of 3.05 m, and gross registered tonnage of 444 tons, and it was built in the PT ASL Shipyard, Indonesia, in 2016. The CB100-01, towed by the ASL Osprey (AO), departed the ASL Shipyard, Singapore, on 1 May 2022. The estimation from the AO’s captain was that the tug and tow would arrive at Djibouti on 3 June 2022, with an average towing speed of 5.5 knots. In addition, this voyage followed the planned route in the Towing Manual.
According to the investigation report, the planned route in the Towing Manual is divided into five parts: Singapore shipyard–North Sumatra–Sri Lanka–Mumbai, India–Salalah, and Oman–Djibouti. Due to the loss of the starboard side spud pole and the aft spud pole during the voyage to Sri Lanka around 12 May, arrangements were made for the maintenance, investigation, and fixation of the remaining port side spud pole after the tug and tow arrived in Colombo, Sri Lanka, on 18 May. One month later, two ships departed Colombo on 16 June and sailed along the original planned route. The tug and tow were expected to arrive in Djibouti on 7 July, with an average towing speed of five knots. On 2 July, due to a deviation from the planned route, the tug and tow entered an area with adverse weather, and ultimately, the CB capsized.
According to the average speed of the ships in the report and the planned route in the Towing Manual, the tug and tow could have reached Sri Lanka on the 12th day after departure and Djibouti on the 34th day after departure. Furthermore, according to the actual voyage, which was suspended in Colombo, Sri Lanka, for nearly a month, the original planned route, which is marked as TMroute in this manuscript, is divided into two sections to facilitate this study: the section from Singapore shipyard to Sri Lanka is recorded as Towing Manual route A (TMrouteA) from 1 to 12 May; and the section from Sri Lanka to Djibouti is recorded as Towing Manual route B (TMrouteB) from 16 June to 7 July, as shown in
Figure 3. Taking the CB100-01 as our research object, our route planning model integrating weather conditions, speed loss, terrain risks, and constraint conditions is established for planning analysis under the constraints of the IMO guidelines and the meteorological requirements in the Towing Manual.
The range of the meteorological and marine environmental data used in this study is 5° S–25° N, 40° E–110° E, and the time ranges of the two routes are from 1 May 2022 to 18 May 2022 and from 16 June 2022 to 7 July 2022. The selected wind field ten meters above the sea surface is represented as three-dimensional grid data from the Copernicus Atmospheric Monitoring Service (CAMS). The wind field includes the two aspects of wind direction and wind speed, and the spatial resolution of the grid is 1/12 × 1/12. The selected sea surface wave data and sea surface temperature data are three-dimensional grid data from the Copernicus Marine Environmental Monitoring Service (CMEMS). The wave data include the effective wave height, average period, and wave direction, and the grid spatial resolution is 1/4 × 1/4. Due to the different sources of data, the spatial resolution of all data is consistent with the wave data. The type, size, flag, age, average speed, and other data of the ship are obtained from the maritime investigation report by the Transport Safety Investigation Bureau of Singapore.
3.2. Results and Analysis
3.2.1. Risk Assessment Results
Construction of Membership Function
According to the data of each indicator in the set of evaluation factors, the parameters of the sigmoidal membership function are fit to obtain the sigmoidal membership function and images of the indicators. We selected three indicators, namely, wave height, visibility, and vessel age, and their images are shown in
Figure 4,
Figure 5 and
Figure 6.
The fitted parameters of the sigmoidal membership function and weights of risk indicators obtained via the analytic hierarchy process are shown in
Table 3,
Table 4 and
Table 5.
Risk Zoning Results
Following our risk assessment model in
Section 2.1, the results of the risk assessments of the two sections in this case are shown in
Figure 7 and
Figure 8.
From
Figure 7, during the time of the first section of the ship’s route, from 1 May to 12 May, the overall risk in the navigation area is low, and the level of safety of the sailing ship is mostly high.
From
Figure 8, during the time of the second section of the ship’s route, from 16 June to 7 July, the risk of sailing in the navigation area gradually increased from 29 June, and the scope of the high-risk area gradually increased. According to an investigation report, the sea area entered a seasonal monsoon period at this time, which is consistent with the risk change in the results in
Figure 8. We can see that the risk assessment based on the assessment model in this study is accurate.
3.2.2. Route Planning Results
The routes of the two sections are planned using our route planning model in
Section 2.2. The route from the Singapore shipyard to Sri Lanka is recorded as IBA*routeA, and the route from Sri Lanka to Djibouti is recorded as IBA*routeB. The whole route from the Singapore shipyard to Djibouti is recorded as IBA*route. The route planning results are shown in
Figure 9 and
Figure 10.
According to the result in
Figure 9, IBA*routeA basically coincides with TMrouteA. The average risk of TMrouteA is 0.3499, while the average risk of IBA*routeA is only 0.3388, which shows that IBA*routeA can avoid risk more effectively than TMrouteA.
According to the result in
Figure 10, IBA*routeB coincides with TMrouteB for the most part, but it is better at avoiding high risks in the open sea than TMrouteB. The average risk of TMrouteB is 0.4424, while the average risk of IBA*routeB is only 0.3929, which shows that IBA*routeB can avoid risk more effectively overall.
3.2.3. Comparison and Verification of Routes
When there is little difference between the two planned routes visually, the similarity between TMroute and IBA*route can be compared using the goodness of fit
[
38], and the calculation formula of
is shown in Equation (39).
The average relative error
of TMroute and IBA*route is calculated as follows:
where
are the latitude grid values corresponding to the
th longitude grid value of TMroute and IBA*route, respectively, and
are the maximum latitude grid value and the minimum latitude grid value of TMroute, respectively.
TMrouteA and TMrouteB are compared with IBA*routeA and IBA*routeB, respectively. The goodness of fit and the average relative error are calculated, as shown in
Table 6.
In
Table 6, the goodness-of-fit values of IBA*routeA and IBA*routeB separately compared with TMrouteA and TMrouteB are both higher than 95%, and their average relative errors are lower than 5%, indicating that IBA*route and TMroute are highly similar.
According to the investigation report, the ship deviated from the TMroute between 19 June and 2 July and entered an area of increasingly severe weather conditions, as shown in
Figure 11.
In
Figure 11, the route that the CB actually sailed, which is marked as Realroute in this manuscript, entered the high-risk area around 2 July after deviating from TMroute, while according to the ship’s planned arrival time in the investigation report, it can be calculated that TMrouteB had already left the open sea area on 30 June. IBA*routeB bypassed the high-risk area on 28 June and also left the open sea on 30 June.
To study the risks of Realroute, TMrouteB, and IBA*routeB during the period of the accident, the average risks of the three routes during the period from Colombo, Sri Lanka to Salalah were calculated, respectively, as shown in
Table 7, and the box plots of the three routes are shown in
Figure 12.
In
Table 7, Realroute is larger than TMrouteB and IBA*routeB in terms of the average risk, maximum risk, and minimum risk values. Moreover, the average risk value of IBA*routeB is only 0.3929, the maximum risk value is only 0.6592, and the minimum risk value is only 0.1252, all of which are the minimum values in the three routes, so it can be seen that IBA*routeB exhibits the minimum overall risk.
In
Figure 12, IBA*routeB has the smallest maximum, lower quartile, and upper quartile values of risk, which indicates that our planning model has a strong risk avoidance ability.
3.3. Validation
To verify the validity of this model on other ship types, CELSIUSBRICKE, a container ship from the Marshall Islands, was selected for a voyage of 24 days in the Maritime Silk Sea (Hainan–Indian Ocean). The ship is 246.87 m long, 32.2 m wide, and 19.3 m deep, with a displacement of 61,521 tons, a draft of 9.8 m, and a maximum speed of 23.0 knots. The route starts in Mombasa (4°4.490 S/39°41.172 E) and ends in Shanghai, China (31°14.442 N/122°2.208 E). The voyage lasted 24 days, from 2 May 2023 to 25 May 2023, covering a total distance of 6476 nautical miles at an average speed of 13.32 knots. On May 13, 14, 21, and 24, ships slowly circled or stopped sailing in place in the sea area, so the simulated ships did not sail on these four days during the planning process. All information about the voyage comes from the Hifleet website (
https://www.hifleet.com/, accessed on 30 May 2023). The actual route and planned route are shown in
Figure 13.
The planned route is a red line segment, while the actual route is a yellow line segment. It can be seen from the figure that the distance between the planned route result and the actual result is relatively small. The calculation results of the three comparison models show that the average relative error is 1.62%, the goodness of fit is 98.71%, and the risk is 4.27% lower than the actual route. According to the actual sailing situation, this voyage is safer, and the route planned by the track planning model is thus safer.
3.4. Sensitivity Analysis
In this section, we perform a sensitivity analysis on several parameters to analyze the results of the impact of different parameters on the planning avoidance risk of the model. We show how different propulsion efficiencies and the roughness allowance factors accounting for the roughness of the hull surface differ in the average risk of a planned route to be analyzed.
To analyze the effect of the ship’s propulsion efficiency on the risk caused by bad weather and the sea state during the ship’s voyage planning route, we applied the proposed model under different propulsion efficiency scenarios and calculated the average risk for the whole planned route.
Figure 14 shows that the average risk value of the navigation will decrease with the increase in propulsion efficiency under the planned route. This means that the new model can avoid high risk in the route and further help the ship to better cope with the dangers of bad weather and the sea state in the ocean.
Second, we analyzed the average risk of the planned route under different roughness allowance factor scenarios.
Figure 15 shows that the value of the navigational risk will increase with the increase in the roughness allowance factor under the planned route. This implies that the roughness subsidy coefficient of different hulls has an impact on the navigational risk.
4. Discussion
Meteorological and marine environment factors directly or indirectly cause damage to ships or the loss of ships [
39]. In the field of maritime transport, in which cargo transport accounts for more than 90% of world trade [
40], the relationship between ship safety and meteorological and marine environment factors has been broadly investigated. Recently, many researchers have studied the optimization of route planning to improve the safety of sailing ships [
41,
42,
43,
44]. However, these planning models do not consider the constraints of the IMO guidelines, and there are few studies on the impact of ship vulnerability on vessel safety.
The purpose of the revised IMO guidelines is to provide a basis for ship captains to make decisions about ship operations in bad weather and sea conditions, thereby helping them avoid the dangerous phenomena they may encounter in such conditions, including surf-riding and broaching-to phenomena, a reduction in intact stability when riding a wave crest amidships, synchronous rolling motion, parametric roll motions, and successive high-wave attacks. The empirical equation of the IMO guidelines is not sufficient and can only avoid most of the common risks to ships. Moreover, the sudden change in a ship’s state while sailing at sea is a highly chaotic nonlinear system, and the unfavorable combination of ocean parameters and the ship’s state may lead to dangerous situations. In this study, we take the empirical formula of the IMO guidelines as the basis of the principle of avoiding danger, while for dead ship conditions, excessive accelerations, and other situations that cause ship instability and damage, further research into and the prediction of these nonlinear dangerous situations are significant for the optimization of the weather route model. Therefore, based on this study, we can continue to study the influence of ship stability under dynamic constraints from the perspective of ship dynamics and add these constraints into the multi-objective programming model.
In this study, meteorological and marine environment factors and the vulnerability of ships are integrated by a multi-layer fuzzy comprehensive evaluation to obtain a risk assessment value. Meanwhile, the IMO guidelines are taken as hard constraints, and the bidirectional A* algorithm is used for route planning. If risk and the IMO guidelines are not considered during the voyage from Colombo, Sri Lanka to Djibouti, the bidirectional A* algorithm is used for route planning, the route of which is marked as WrouteB, compared with IBA*routeB, and the result is shown in
Figure 16.
In
Figure 16, when risk and the IMO guidelines are not considered, WrouteB enters the high-risk area around 27 June, while IBA*routeB bypasses the high-risk area. It can be understood that the consideration of risk and the IMO regulations is therefore very important for the safety of sailing ships.
In previous studies, common algorithms to solve the pathfinding problem have included the Dijkstra and A* algorithms. Compared with Dijkstra, the A* algorithm not only considers the distance from the start node to the current node, but also considers the estimated cost from the current node to the end node. However, the area involved in the ocean route is large and the timespan is long, so more efficient algorithms are needed for route planning. The bidirectional A* algorithm, an improvement on the A* algorithm, searches the intersection points from the start node and the end node at the same time, thus reducing the number of nodes to search and improving the search efficiency. We compare the running time of the Dijkstra, A*, and bidirectional A* algorithms when planning routes for the case chosen in this study, as shown in
Table 8.
In
Table 8, the Dijkstra algorithm has the longest running time of 31.739 s, which is much longer than the A* and bidirectional A* algorithms, and the bidirectional A* algorithm has the shortest running time of 4.187 s. It can thus be concluded that the operation efficiency of the bidirectional A* algorithm is greater than that of the Dijkstra and A* algorithms.
5. Conclusions
In view of the few studies involving quantitative considerations of ship vulnerability and IMO guidelines in ocean route planning models, this study proposes a multi-objective nonlinear programming model which integrates ship vulnerability and meteorological and marine environment factors to obtain a comprehensive risk assessment, and it implements the IMO guidelines as hard constraints to solve the model using the bidirectional A* algorithm. Firstly, this study uses the multi-layer fuzzy comprehensive evaluation model, which comprehensively assesses the risk of sailing ships by evaluating ship vulnerability and meteorological and marine environment factors. Secondly, the multi-objective nonlinear programming model is constructed by adding IMO constraints and comprehensively considering the navigation risk, sailing time, and fuel consumption in this study. This study then uses the bidirectional A* algorithm to solve the route planning model. Finally, an accident case in the Singapore Maritime Investigation Report was studied, and the experimental results show that the model planning route in this study is similar to the original route in the Towing Manual, with an average fit of 98.22%, and the average risk is 11.19% lower than that of the original route. Comparing algorithms, the bidirectional A* algorithm is 86.81% faster than the Dijkstra algorithm and 49.16% faster than the A* algorithm. In summary, our model realizes two goals: a safer ocean route and more efficient computing. In future works, the algorithms for ocean ship route planning can be improved, which will greatly improve search efficiency and further approach an optimal solution. Finally, we will continue studying the influence of ship stability under dynamic constraints from the perspective of ship dynamics, and these constraints will be added into the proposed multi-objective programming model.