ONE OF THE METHODS FOR IMPLEMENTING THE ANT ALGORITHM USING THE TRAVELING SALESMAN PROBLEM AS AN EXAMPLE

In today’s world, optimization problems play a crucial role in logistics, energy systems, industry, finance, healthcare, machine learning, and more. An optimization problem is a mathematical task aimed at finding the best possible solution from a set of feasible options, based on a defined criterion such as minimizing cost or time, or maximizing profit. There are exact methods, such as brute-force search and dynamic programming, which guarantee an optimal solution. However, they become computationally infeasible as the problem size grows. Heuristic and metaheuristic methods – including greedy algorithms, genetic algorithms, and ant colony optimization (ACO) – provide approximate but practically effective solutions for large-scale problems. One classical example of a combinatorial optimization problem is the Traveling Salesman Problem, where the goal is to find the shortest possible route that visits each city exactly once. The ant colony algorithm is one of the most efficient approaches for solving TSP and similar pathfinding problems on graphs. Inspired by the foraging behavior of real ants, the algorithm simulates how ants lay down pheromones along their paths and choose their ro