  Ant Colony Optimization (ACO) is renowned for its effectiveness in solving
Traveling Salesman Problems, yet it faces computational challenges in CPU-based
environments, particularly with large-scale instances. In response, we
introduce a Tensorized Ant Colony Optimization (TensorACO) to utilize the
advancements of GPU acceleration. As the core, TensorACO fully transforms ant
system and ant path into tensor forms, a process we refer to as tensorization.
For the tensorization of ant system, we propose a preprocessing method to
reduce the computational overhead by calculating the probability transition
matrix. In the tensorization of ant path, we propose an index mapping method to
accelerate the update of pheromone matrix by replacing the mechanism of
sequential path update with parallel matrix operations. Additionally, we
introduce an Adaptive Independent Roulette (AdaIR) method to overcome the
challenges of parallelizing ACO's selection mechanism on GPUs. Comprehensive
experiments demonstrate the superior performance of TensorACO achieving up to
1921$\times$ speedup over standard ACO. Moreover, the AdaIR method further
improves TensorACO's convergence speed by 80% and solution quality by 2%.
Source codes are available at https://github.com/EMI-Group/tensoraco.
