## 1 Introduction
The authors showed that using BFS and DFS algorithms generated routes for vessels faster than using genetic algorithms, although the routes were less accurate. A-star (A*), D-star (D*) and Dijkstra's algorithms are used to determine passage routes using graph search algorithms. A challenge with these methods is how to determine the transition weights between individual nodes. In the classical approach to the problem, the weight can be taken as the distance between points. In this case, the resulting route is optimized on the basis of distance. Such criteria have been used, for example, by the authors of publications [12; 13; 14; 15]. An alternative approach to determining the transition weights between individual points in the graph was presented by the authors of publications [16; 17], who used data collected from the Automatic Identification System (AIS) to develop a graph. In the first publication, the transition weights were inversely proportional to the number of ships passing between the vertices. In the second, the authors used Delaunay triangulation analysis to calculate transition weights. Publication [18] explored the potential use of graph search algorithms in conjunction with neural networks to predict fuel consumption and develop a route that minimizes energy consumption. In addition to solutions that focus on finding the shortest or least congested routes, the literature also includes studies that consider hydrometeorological conditions such as wave height, wind speed and ocean currents. Examples of such publications are [19; 20; 21; 22], where the authors used the A* algorithm and weather maps to determine a safe passage route for the ship. The final type of algorithm that is most commonly used to determine ship passage routes are swarm algorithms. Swarm algorithms are a category of optimization techniques inspired by the social behavior of animals such as insects, birds or fish. In nature, animals often interact in groups, forming swarms, flocks and schools, and their coordinated actions can lead to the solution of complex problems. Swarm algorithms include the following:  
* Ant colony algorithms: These are inspired by how ants find the shortest path to a food source. In ant colony algorithms, agents (virtual ants) explore the solution space and leave pheromone trails that guide other ants to optimal solutions. * Particle swarm algorithms: These are based on the behavior of schools of fish or flocks of birds. In particle swarm algorithms, particles (points in the solution space) move through the search space, guided by their own experience and information from other particles, to find an optimal solution. * Bee-inspired algorithms: These algorithms mimic the behavior of bees foraging for food, where bees identify the best food sources and recruit other bees to exploit those sources. * Firefly algorithms: The main principle of operation is the attraction of fireflies based on their brightness, which represents the quality of a given solution to the problem. The brighter the firefly (the better the solution), the greater the attraction it exerts on other fireflies. The brightness of a firefly depends on the objective function and decreases with distance: fireflies closer together are more attracted than those further apart. Fireflies with lower brightness move towards brighter ones, meaning that the algorithm iteratively improves its solution. In the literature dedicated to swarm algorithms, it is evident that all the aforementioned types find applications in determining ship passage routes. An example publication where the authors demonstrated how ant-inspired algorithms can be used to improve the efficiency of maritime navigation is [23]. The authors integrated the Electronic Chart Display and Information System (ECDIS) with a Geographic Information System (GIS) platform to model the maritime space. The algorithm simulates the behavior of ants searching for the optimal path to a food source, where the ants (ships) explore the search space to find the safest route.