The Modified Genetic Algorithm for Solving the Traveling Salesman Problem

The Traveling Salesman Problem is one of the most relevant challenges today, as the need to solve it arises in various fields. However, there is no clear algorithm for its solution. It falls within the realm of NP-complete problems and is optimization-oriented. While it is assumed that the solution to these problems involves exhaustive search, in practice, various algorithms and approaches are often used to reduce the volume of analyzed solutions, aiming to find a way to solve the problem without exhaustive search. This includes methods like branch and bound to expedite the search or artificial intelligence approaches such as the ant colony algorithm and genetic algorithms to accelerate the process while achieving the closest possible solution. Genetic methods are one of the most powerful tools for solving such tasks. These algorithms model evolutionary processes, which, thanks to the basic principles of evolution, allow finding better solutions. This approach allows representing the task as a certain evolutionary process. It is based on the fact that from the very beginning, a certain set of solutions is chosen, and they start competing with each other. Each solution represents an individual, and a set of its solutions represents a "gene". Each of these genes during the algorithm's operation can evolve, adapt, or mutate according to the rules of the environment. In the end, only the strongest genes should remain, which will be the approximate optimal solution. A characteristic of these algorithms is that each implementation can be unique. An important task in building algorithms is precisely the optimization of their parameters, as well as choosing the right approach to some of its stages, where only the best of them will remain in the end. This methodology not only allows finding approximately optimal solutions but also provides flexibility and adaptability for various requirements and constraints.