Singular Value Decomposition of the Pheromone Matrix for Enhancing Ant Colony Optimization

초록

How to obtain a pheromone matrix of high quality is significant and challenging in the optimization performance of ant colony optimization algorithms. Therefore, this paper proposes an enhanced ACO variant that leverages Singular Value Decomposition to achieve dimensionality reduction of the pheromone matrix, termed PSVD-ACO, with two novel designs. First, the Pheromone Matrix Singular Value Decomposition method is proposed to enable an approximate representation of the pheromone matrix, resulting in a smoothed pheromone distribution. The pheromone smoothing process significantly enhances PSVD-ACO's ability to escape local optima and strengthens its path exploration capability. Second, a threshold-based decay strategy is applied to the pheromones to reduce the selection probability of low-quality paths, accelerating the algorithm's convergence speed. Integrated with the Singular Value Decomposition of the pheromone matrix and the threshold-based decay strategy, PSVD-ACO achieves high-quality solutions within a limited number of iterations, effectively addressing large-scale Traveling Salesman Problems. Experimental validation across $11$ diverse TSP instances confirms that PSVD-ACO outperforms other methods in handling large-scale TSP challenges.

키워드