# Navigation of Autonomous Tug via Evolutionary Algorithms with Radar Plot Fitness Evaluation
## 1 Introduction  
In recent years, we have witnessed the dynamic development of autonomous marine vehicles. Progress in the field of robotics and artificial intelligence has enabled the construction of vessels capable of independently performing complex tasks without human intervention. One of the key aspects of autonomous navigation is planning the optimal route of a ship's passage. Port tugs are specialized vessels whose task it is to assist larger ships during maneuvers within the port. Their work is local and takes place in a relatively small area, which translates into specific requirements for planning the passage route. Sea ports are characterized by high traffic density [1, 2], as many vessels of different sizes and purposes operate in a limited space, creating a high risk of collision. Tugs must navigate efficiently between them, while at the same time performing precise maneuvers near the assisted ships. Additionally, the port infrastructure includes numerous narrow channels, quays and breakwaters, which significantly restrict freedom of movement. Planning the tug's route must take into account these obstacles and ensure safe passage through the port. Recently, more and more port operators have decided to introduce electric or hybrid tugs into service [3]. These vessels are characterized by significantly lower pollutant emissions and allow for reducing the negative impact on the environment. However, this is associated with certain limitations. Electric tugs have a relatively small capacity of energy storage tanks compared to their counterparts with combustion engines. This translates into a limited range and operating time on a single battery charge. Therefore, route planning for an electric tug must be particularly careful and take into account the efficient use of available energy. Suboptimal maneuvers, rapid acceleration or long periods of work under high load can quickly drain the batteries and immobilize the vessel or prevent it from completing the task. The route planning algorithm should minimize energy consumption while ensuring the implementation of the tug's work schedule. This is a difficult optimization task that requires advanced computational methods. It should be emphasized that route planning for a full-size autonomous ship is a task requiring special responsibility [4]. It must take into account a number of factors such as energy consumption, travel time, weather conditions, and above all the safety of the vessel and its crew (if present) and the marine environment. Modern computational methods can find solutions to this problem, which are beneficial in many respects. These include graph-based methods, methods with a potential field or vector field, methods using evolutionary algorithms, methods with an artificial neural network, modifications of classic graph algorithms, or hybrid methods. Graph-based methods consist in representing the environment in the form of a graph, where the vertices correspond to the possible positions of the vessel, and the edges represent permissible transitions between them. Particularly popular are visibility graphs, which take into account mutual visibility between waypoints, and Voronoi diagrams [5], which divide space into regions based on the distance to obstacles, as well as sampling algorithms using Rapidly exploring Random Tree (RRT) search [6; 7; 8; 9]. Methods using Artificial Potential Fields (APF) and vector fields treat the environment as a force field, where obstacles generate repulsive forces and the destination generates an attractive force. The route is determined by finding a path with the lowest potential energy or following the resultant vector of forces [10; 11; 12; 13; 14; 15]. Methods based on evolutionary algorithms use mechanisms inspired by biological evolution, such as selection, crossover and mutation, to iteratively improve the population of potential solutions.