## 1 Introduction
Experimental results showed that routes determined using the ant algorithm were more efficient than those determined using the great circle method. However, the authors of publication [24] had a different perspective on ant algorithms. In their work, they argued that the classical ant algorithm has drawbacks, such as a tendency to get stuck in local minima and low convergence speed, which affect the quality and speed of route determination. In addition to determining passage routes for ships, ant algorithms can also be used for various applications, including route planning for mobile robots [25; 26], determining passage routes for units involved in maritime rescue missions [27; 28], and planning collision avoidance routes [29]. In contrast to ant algorithms, particle swarm algorithms are characterized by faster convergence and the ability to optimize multiple variables. This property has been demonstrated in [30]. The authors combined the particle swarm algorithm with [PERSON]'s algorithm to find the shortest route between start and end points, taking into account obstacles. The algorithm presented in this publication uses a cost function based on the total length of the route. Another example of a publication focusing on ship route planning and extending the particle swarm algorithm is [31]. In this paper, the authors introduced the concept of Chaos Multi-Population Particle Swarm Optimization (CMPSO), which is an improved particle swarm algorithm enhanced by chaos theory. Bee-inspired swarm algorithms also have applications in route optimization, particularly in the context of maritime navigation. They use mechanisms inspired by the way bees search for and share information about food sources. This gives these algorithms a high capacity to explore the solution space and effectively avoid local minima. The use of bee algorithms in route optimization for surface and underwater vessels allows dynamic adaptation to changing conditions, such as obstacles along the route or variations in the weather, making them valuable tools for managing the safety and efficiency of maritime navigation. This feature was exploited by the authors of [32], who presented an algorithm that determines an escape route for submarines to avoid detection by hostile vessels. This paper demonstrates the use of a modified version of [PERSON]'s algorithm and position-keeping Capability Plots (CP) to determine a passage route that minimizes the impact of environmental forces on the ship's hull, thereby reducing energy consumption. This method has been developed for autonomous vessels equipped with a positioning system based on a set of anchors. For such vessels, the challenge is to move from the starting point to the pre-planned anchorage area. As the thrusters are not involved in the positioning operation, their power is significantly lower than the thrusters used in Dynamic Positioning (DP) systems, resulting in reduced maneuverability. For this reason, the ship's passage route should be chosen in such a way as to minimize the influence of disturbance factors. The verification of the presented algorithm was carried out using a simulator developed in the Unity3D environment.