Solving Symmetric and Asymmetric Traveling Salesman Problems Using Ant Colony Optimization Algorithm

Application Background Ant Colony Optimization was initially developed for solving Traveling Salesman Problems and has demonstrated remarkable superiority due to its distributed characteristics, strong robustness, and easy integration with other algorithms. However, it also presents certain limitations such as slow convergence speed and susceptibility to local optimal solutions. The Traveling Salesperson Problem (TSP), sometimes referred to as the Chinese Postman Problem, is an NP-hard problem. Conventional algorithms find it extremely challenging to obtain optimal solutions for such problems, making heuristic algorithms like Genetic Algorithm (GA), Ant Colony Optimization (ACO), and Particle Swarm Optimization (PSO) essential tools for resolution. Key Technologies Ant Colony Optimization is a swarm intelligence algorithm where groups of simple or minimally intelligent agents demonstrate intelligent behavior through collaboration, offering new possibilities for solving complex problems. The algorithm was first proposed by Italian scholars Colorni A. and Dorigo M. in 1991. After more than two decades of development, ACO has achieved significant progress in both theoretical research and practical applications. As a bionic algorithm, ACO draws inspiration from ants' foraging behavior in nature. In natural environments, ants consistently discover optimal paths from their nests to food sources through pheromone trail deposition and following mechanisms. Code implementation typically involves constructing solution paths iteratively using probability-based selection rules that combine pheromone intensity and heuristic information, followed by pheromone update procedures that include evaporation and reinforcement phases.