Comparative analysis of the effectiveness of using metaheuristic modeling methods to solve the traveling salesman problem

<p><strong>Context and relevance.</strong>The traveling salesman problem (TSP) is one of the key NP-hard combinatorial optimization problems with wide applications in logistics, transportation planning, and other fields. Exact methods for solving TSP become inefficient as the problem dimension increases, making the use of metaheuristic methods such as simulated annealing (SA), ant colony optimization (ACO), and particle swarm optimization (PSO) relevant. <strong>Objective. </strong>To conduct a comparative analysis of the effectiveness of SA, ACO and PSO for solving the traveling salesman problem with 100 points, to evaluate their convergence and to identify the optimal parameters. <strong>Hypothesis. </strong>The ant algorithm, due to the pheromone trail mechanism, will provide higher accuracy of solutions compared to SA and PSO, but will require more computational resources. <strong>Methods and materials. </strong>The study conducted computational experiments with varying parameters of each algorithm. For SA, the initial temperature and cooling coefficient were analyzed, for ACO, the influence of pheromones and distances, for PSO, the cognitive and social coefficients. <strong>Results. </strong>ACO showed the best results, finding a route with a length of 9.23, demonstrating high efficiency for medium-sized problems. PSO took an intermediate position with a route length of 32.64, making it suitable for moderately complex problems. SA was the least effective, with a route length of 45.2, which limits its use for complex routing networks. <strong>Conclusions. </strong>The ant algorithm demonstrated the greatest efficiency due to the balance between exploring the solution space and exploiting the found routes, which is especially important for maritime Arctic logistics, where sustainable route optimization is required under high uncertainty. PSO showed good convergence, but it is inferior to ACO in terms of accuracy. SA, despite its simplicity, is less effective for high-dimensional problems. The obtained results are of particular practical value for route optimization in the Arctic region, where traditional methods often prove to be ineffective.</p>