## 8 Conclusions  
This paper proposes an improved crayfish algorithm based on multi-strategy fusion (JLSCOA) for optimizing the parameters of the terminal sliding mode controller in ship dynamic positioning systems. To address issues with the traditional crayfish algorithm, such as susceptibility to local optima, slow convergence in later iterations, and insufficient optimization accuracy, improvements have been made by incorporating subtraction averaging strategies, Levy Flight strategies, and sparrow search position update strategies.  
Comparative tests with COA, WOA, and SSA optimization algorithms show that JLSCOA outperforms the others with an 83% advantage in finding the optimal value, an  
Figure 14: Comparison of lateral control force variations.  
Figure 13: Comparison of longitudinal control force variations.  
Figure 15: Comparison of pitch control torque variations.  
83% advantage in average performance, and a 75% advantage in standard deviation, indicating stronger optimization capability and robustness. JLSCOA demonstrates significant advantages in optimization accuracy, convergence performance, and stability.  
The application of JLSCOA to optimize the parameters of the terminal sliding mode controller has been verified through simulations on the \"Xin Hongzhaun\" ship from Dalian Maritime University. The simulation results indicate that the terminal sliding mode controller optimized by JLSCOA significantly outperforms the traditional un-optimized controller in terms of disturbance resistance, response speed, and system stability. The average time for three-degree-of-freedom position changes is over 300 s faster compared to the given parameter set, and control force and velocity oscillations are nearly eliminated. JLSCOA not only enhances the performance of the terminal sliding mode controller but also reduces parameter tuning difficulty, improving the robustness and reliability of the control system. This provides new insights and methods for the design and optimization of practical ship dynamic positioning systems.  
In summary, the application of the multi-strategy fusion improved crayfish algorithm in optimizing the parameters of the terminal sliding mode controller for ship dynamic positioning systems shows significant effects, demonstrating its practicality and superiority in complex environments, and providing important reference value for future research and practical applications.  
Conceptualization, Z.W.; Funding acquisition, Z.H.; Investigation, F.Y.; Methodology, Z.W.; Project administration, Z.W.; Software, Z.W.; Validation, B.S.; Writing--original draft, Z.W.; Writing--review and editing, Z.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Innovation Project of the Offshore LNG Equipment Industry Chain: CBG3N21-2-7; the High-technology Ship Research Program: CBG3N21-3-3; and new technology equipment for rapid and green elimination of COVID-19 hydroxyl radicals in cold chain logistics: 62127806.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
The authors extend their appreciation to the anonymous reviewers for their valuable feedback.  
The authors declare no conflicts of interest.