## 3 Case Study  
### 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](https://www.mot.gov.sg)]([https://www.mot.gov.sg](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 Djibout 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  
Figure 2: The arithmetic process of bidirectional A\({}^{*}\) algorithm. 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 12 th day after departure and Djibouti on the 34 th 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\({}^{\circ}\) S-25\({}^{\circ}\) N, 40\({}^{\circ}\) E-110\({}^{\circ}\) 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 \(1/12^{\circ}\times 1/12^{\circ}\). 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 \(1/4^{\circ}\times 1/4^{\circ}\). Due to the different sources of data, the spatial resolution of all data is consistent with the wave data.