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.

To solve the problems of slow convergence and low accuracy when the traditional ant colony optimization (ACO) algorithm is applied to online learning path recommendation problems, this study proposes an online personalized learning path recommendation model (OPLPRM) based on the saltatory evolution ant colony optimization (SEACO) algorithm to achieve fast, accurate, real-time interactive and high-quality learning path recommendations. Consequently, an online personalized learning path optimization model with a time window was constructed first. This model not only considers the learning order of the recommended learning resources, but also further takes the review behavior pattern of learners into consideration, which improves the quality of the learning path recommendation. Then, this study constructed a SEACO algorithm suitable for online personalized learning path recommendation, from the perspective of optimal learning path prediction, which predicts path pheromone evolution by mining historical data, injecting the domain knowledge of learning path prediction that can achieve best learning effects extracted from domain experts and reducing invalid search, thus improving the speed and accuracy of learning path optimization. A simulation experiment was carried out on the proposed online personalized learning path recommendation model by using the real leaner learning behavior data set from the British “Open University” platform. The results illustrate that the performance of the proposed online personalized learning path recommendation model, based on the SEACO algorithm for improving the optimization speed and accuracy of the learning path, is better than traditional ACO algorithm, and it can quickly and accurately recommend the most suitable learning path according to the changing needs of learners in a limited time.