Abstract <p>The article is devoted to the study and development of modifications of the ant colony optimization (ACO) method to improve the performance of solving complex parametric problems using parallel computing technology on graphics processing units (GPUs) with the CUDA architecture. An approach is proposed and studied with dividing the algorithm into three parts: matrix preparation, calculation of ant agent paths, and changing pheromone weights. Using CUDA allows accelerating the modification of the ACO matrix up to 43 times. The limitations of using constant and local memory are studied, and algorithms for automatic memory switching are proposed depending on the problem dimension, as well as on the number of ant agents.</p>