## 1 Introduction  
The development of modern navigation, in particular the determination of optimal routes for ships, has long attracted the attention of researchers and practitioners in the field of maritime transport. Contemporary navigation faces challenges arising from the increasing number of ships on the seas and oceans, the growing demand for efficient maritime transport, and the increasingly complex aspects related to safety at sea and environmental protection. In response to these challenges, scientists and engineers have developed methods and algorithms to effectively determine ship passage routes, taking into account a range of factors such as weather conditions, the movement of other vessels, water depth and environmental constraints. The first attempts to use computers to determine shipping routes date back to the 1950s and 1960s, when [PERSON] wrote a paper on the subject [1]. The author proposed a special program to increase the safety of naval vessels by determining passage routes based on predictable hydrometeorological conditions. At the time when the first computers capable of performing analytical calculations appeared, weather charts, ocean current charts and wind charts were used to determine the passage routes of ships, as well as the methods introduced by the authors [2; 3] and maps showing the strength of sea waves in specific areas. In the years that followed, technological advances made it possible to use more sophisticated techniques and algorithms. There are three main types of algorithms, and their various variations, that can be found in the contemporary literature related to the determination of ship passage routes. These include genetic algorithms, graph search algorithms and swarm algorithms. Genetic algorithms are inspired by biological processes and include concepts such as natural selection, recombination and mutation. When analyzing the literature related to this type of algorithm, several primary applications can be distinguished:  
* Finding a safe route in areas with limited maneuverability: An example of using a genetic algorithm to determine a route between islands and reefs is presented in [4]. The authors of this publication found that traditional algorithms, such as ant colony algorithms, did not perform well in this context, so they proposed their own algorithm using environmental information. Another approach to determining a ship's route in restricted waters was presented by the authors of [5]. They focused on a parallel genetic algorithm, and additionally, considered criteria related to water depth and travel time. * Determining routes where the criteria include minimizing energy consumption, travel time, etc. : This type of approach was taken by the authors of publications [6; 7]. They presented an algorithm using elements of particle swarm optimization and genetic algorithms to determine the route. This approach successfully optimized fuel consumption. * Determination of collision avoidance routes: This category includes publications that do not directly address the determination of a route from a starting point to an end point, but instead present algorithms that adapt local segments of the route to the new conditions surrounding the ship, for example, to perform a collision avoidance maneuver. Examples of publications related to this type of algorithm are [8; 9; 10]. The authors presented different approaches to collision avoidance maneuvers, ranging from harbor operations to applications related to autonomous vehicles. Another type of algorithm used to determine ship passage routes are graph search algorithms. These algorithms are used to search, analyze and navigate through graphs, which are data structures containing nodes and edges between them. Basic graph-related techniques such as Breadth-First Search (BFS) and Depth-First Search (DFS) are used in cases where the time to generate a passage route is more critical than its optimization. An example of a publication where the authors use these methods to determine routes for small vessels is [11].