Matrix-Based Ant Colony System for Traveling Salesman Problem

Ant colony system algorithm (ACS), as an important evolutionary computation (EC) algorithm, has demonstrated significant advantages in solving complex optimization problems. However, traditional EC algorithms and traditional ACS algorithm often face the challenge of slow computational speed when dealing with large-scale problems. In recent years, matrix-based EC approaches have been proposed to accelerate the computational speed, which has obtained promising results in dealing with large-scale problems. However, most existing matrix-based EC algorithms are designed for continuous optimization problems, while the matrix-based approach integrated with ACS has not attracted enough attention, which will be efficient for solving large-scale discrete optimization problems. Therefore, in this paper, we propose a matrix-based ACS (MACS) algorithm and apply it to solve the traveling salesman problem (TSP). MACS is an innovative improvement over the traditional ACS algorithm, utilizing matrix operations to parallelly let ants select city and update pheromone. Experimental results show that the MACS algorithm has significantly better efficiency in accelerating computational speed while maintaining the remarkable problem-solving ability in solving large-scale TSP.