OPTIMIZATION APPROACHES AND MATHEMATICAL MODELING IN THE TRAVELING SALESMAN PROBLEM IN TOURISM COMPANIES

Аннотация

The Traveling Salesman Problem (TSP) is one of the most well-known and studied problems in mathematical optimization and computer science. The objective of the problem is to find the shortest possible route that allows a traveling salesman to visit a set of specified cities, visiting each city only once, and ultimately returning to the starting point. TSP is famous for its fully combinatorial nature and high complexity. It is classified as an NP-complete problem, meaning that finding an exact solution becomes increasingly difficult as the number of cities grows. Various algorithms have been developed to find solutions using computers, including network search algorithms, genetic algorithms, and simulated annealing methods. The Traveling Salesman Problem is applied in many practical fields, such as logistics, transportation, robotics, and various resource management systems. It is also of great theoretical importance as a toolused foroptimization andimproving efficiency. Keywords:Traveling Salesman Problem (TSP), optimization, combinatorics, NP-complete problem, shortest path, algorithms, logistics, transportation, robotics, resource management, simulatedannealing, genetic algorithms,network search algorithms, solutionfinding.