Various studies have shown that the ant colony optimization (ACO) algorithm has a good performance in approximating complex combinatorial optimization problems such as traveling salesman problem (TSP) for real-world applications. However, disadvantages such as long running time and easy stagnation still restrict its further wide application in many fields. In this study, a saltatory evolution ant colony optimization (SEACO) algorithm is proposed to increase the optimization speed. Different from the past research, this study innovatively starts from the perspective of near-optimal path identification and refines the domain knowledge of near-optimal path identification by quantitative analysis model using the pheromone matrix evolution data of the traditional ACO algorithm. Based on the domain knowledge, a near-optimal path prediction model is built to predict the evolutionary trend of the path pheromone matrix so as to fundamentally save the running time. Extensive experiment results on a traveling salesman problem library (TSPLIB) database demonstrate that the solution quality of the SEACO algorithm is better than that of the ACO algorithm, and it is more suitable for large-scale data sets within the specified time window. This means it can provide a promising direction to deal with the problem about slow optimization speed and low accuracy of the ACO algorithm.