## 5 Simulation Analysis
### Method Application  
To verify the feasibility and effectiveness of the decision support method, a case study of multiple vessels encountered in the port is selected. The vessel (OS) is 290.5 m in length (\(L\)) and 50 m in breadth (\(B\)), has a deadweight weight of 202,000 tons, a heading of \(C_{0}\) = 330\({}^{\circ}\), a speed of \(v_{0}\) = 13 knots, and a minimum speed of \(v_{\text{se}}\) = 2 knots to maintain rudder effectiveness. The vessel was navigating normally in a port area with good visibility, and the ship pilots had excellent seamanship. At the same time, three vessels (numbered TG1-TG3) were encountered and were not in mutual view. The information regarding the encounter situation of each target vessel, obtained through radar plotting and AIS, is presented in Table 2. Here, a positive value of \(d_{CPA}\) indicates that TG passed through the bow of OS, while a negative value indicates passing through the stern of OS. In Table 2, it can be seen that if all four vessels comply with COLREGS, the safe encounter distance (\(d_{1}\)) is calculated to be 1.0463 n miles and the distance between the vessel and TG1, TG2, and TG3 is less than \(d_{1}\); then, OS needs to give way to all TGs. Priority should be given to avoiding the TG1 with the shortest \(t_{CPA}\), and the OS should adopt a reverse-deceleration collision avoidance method. Figure 6: Comparison of the change in the CRI of TG relative to OS in two collision avoidance operations. Figure 7: Comparison of \(d_{CPA}\) and \(t_{CPA}\) value changes between TG and OS in two collision avoidance operations. (**a**) The change of \(d_{CPA}\) value; (**b**) The change of \(t_{CPA}\) value. Model parameter settings: By analyzing the navigational environment and human factors of the case, the values of \(K_{1}\), \(K_{2}\) and \(K_{3}\) are taken as 1, 2 and 1, respectively. Following several iterations of the optimization algorithm, the final test resulted in an optimal weight assignment of \(\alpha\) = 0.8, \(\beta\) = 0.2. To verify the superiority of the proposed CIPSO algorithm, three classical intelligent algorithms were selected for comparison experiments: Simulated Annealing Algorithm (SA), GA, and PSO. The population size in all algorithms was set to 100 and the maximum number of iterations was set to 300. Parameter settings in SA were as follows: the initial temperature was set to 100\({}^{\circ}\), and the temperature decay coefficient was set to 0.95 [40]. Parameter settings in GA were as follows: the crossover probability was 0.8, and the variance probability was 0.05 [41]. Parameter settings in CIPSO were as follows: the update speed limit range of particles was [\(-\)1.5, 1.5], \(w_{max}\) was set to 1.2, and the individual position (vessel speed) constraint was set to [\(v_{se}\), \(v_{0}\)/2], that is, [2, 6.5]. The particle inertia weight \(w\) of the PSO algorithm was set to 0.9, the acceleration factors \(c_{1}\) and \(c_{2}\) were set to 2 [42], and other parameter settings were the same as CIPSO. Result analysis: Figure 8 shows the iteration process and convergence results of each algorithm. It is observed that the CIPSO algorithm converges faster and stabilizes around the 23 rd generation, and the standard PSO algorithm only stabilizes around the 41 st generation. However, the GA algorithm and SA algorithm only stabilized in the 35 th and 59 th generations, respectively, and did not find the optimal solution within the set number of iterations, so the accuracy of these algorithms remains to be discussed. The CIPSO algorithm takes 5-10 s to execute, which can ensure the real-time collision avoidance decision. This indicates that the curve incremental strategy adopted in this work can effectively adjust the behavior of the particles, enabling the algorithm to better balance the relationship between global and local searches, thus improving the search efficiency and convergence accuracy of the algorithm.