## 1 Introduction
The best collision avoidance strategy was learned from experience using a deep neural network, and a collision avoidance training method that combines ship maneuvering performance, crew maneuvering characteristics, and consideration of the rules was proposed. Simulation results showed that the algorithm performs better in terms of safety and efficiency than traditional collision avoidance methods. [PERSON] et al. [19], [PERSON] et al. [20], and [PERSON] et al. [21] have introduced PSO to solve the issue and achieved excellent effects. [PERSON] et al. [22] proposed a ship collision avoidance method based on an improved cultural particle swarm optimization (CPSO). The CPSO was used to derive the optimal steering angle for ship collision avoidance under the constraints of the rules, and the resulting decision method was finally integrated into electronic nautical charts for validation. The results showed that the method can safely and effectively achieve ship collision avoidance. Compared with other heuristic methods, PSO applied to this issue has the advantages of computational simplicity and fast convergence, which can be used to find the optimal solution for the high-latitude optimization issue in a short period of time [23]. In addition to the above heuristics, many other intelligent evolutionary algorithms have been used in this issue, such as Beetle Antennae Search (BAS) [24], the Danger-Immune Algorithm (DIA) [25], and the Cat-Swarm Biological Algorithm (CSO) [26]. This work compares the above heuristic algorithms when applied to the vessel collision avoidance issue, and analyses these methods item by item, focusing on five aspects: (1) the number of target vessels; (2) the collision avoidance operation of the vessel; (3) the application waters (4) whether the motion or maneuvering characteristics of the vessel are taken into account, classified in terms of high, medium and low; (5) whether the methods comply with the requirements set out in the Convention on the International Regulations for Preventing Collisions at Sea (COLREGS).The comparison results are shown in Table 1.  
Within the comparative analysis of the aforementioned literature, three primary issues are identified. Firstly, a significant limitation is found in the fact that some studies are geared towards single-vessel collision avoidance, primarily conducting simulation tests for encounter, crossover, and chase-over situations. However, there is still room for improvement in terms of the applicability of multi-vessel collision avoidance. The second predicament pertains to the collision avoidance measures employed in the majority of studies, which primarily focus on steering collision avoidance practices applicable to open-water scenarios. However, the efficacy of these measures in the context of narrow waterways has not been adequately addressed. Lastly, a fundamental concern relates to the alignment with the COLREGS, as well as the consideration of the target vessel's size, type, and maneuvering characteristics. It is important to ascertain the extent to which these factors are taken into account when formulating collision avoidance strategies. Based on the above issues, an adaptive particle swarm optimization based on a curve increment strategy (CIPSO) for the vessel speed-varying collision avoidance decision method is proposed in this work. Super-large vessels adopt speed-varying collision avoidance measures to ensure navigation safety in the face of multiple vessels encountered during navigation within the port. The method also considers the impact of super-large vessels, deceleration strokes and stroke time on collision avoidance. A vessel collision risk model based on a fuzzy comprehensive evaluation strategy is introduced in this work, wherein COLREGS, navigation safety, and economy are considered to establish a vessel speed-varying energy-loss model. Finally, the CIPSO algorithm is used to find the optimal decision value in the feasible solution domain.