The ant colony algorithm faces dimensional catastrophe problems when solving the large-scale traveling salesman problem, which leads to unsatisfactory solution quality and convergence speed. To solve this problem, an adaptive ant colony optimization for large-scale traveling salesman problem (AACO-LST) is proposed. First, AACO-LST improves the state transfer rule to make it adaptively adjust with the population evolution, thus accelerating its convergence speed; then, the 2-opt operator is used to locally optimize the part of better ant paths to further optimize the solution quality of the proposed algorithm. Finally, the constructed adaptive pheromone update rules can significantly improve the search efficiency and prevent the algorithm from falling into local optimal solutions or premature stagnation. The simulation based on 45 traveling salesman problem instances shows that AACO-LST improves the solution quality by 79% compared to the ant colony system (ACS), and in comparison with other algorithms, the PE of AACO-LST is not more than 1% and the Err is not more than 2%, which indicates that AACO-LST can find high-quality solutions with high stability. Finally, the convergence speed of the proposed algorithm was tested. The data shows that the average convergence speed of AACO-LST is more than twice that of the comparison algorithm. The relevant code can be found on our project homepage.

Utilizing big data and artificial intelligence technologies, we developed the Collaborative Structure Search Framework (CSSF) algorithm to analyze students’ learning paths from real-world data to determine the optimal sequence of learning knowledge components. This study enhances sustainability and balance in education by identifying students’ learning paths. This allows teachers and intelligent systems to understand students’ strengths and weaknesses, thereby providing personalized teaching plans and improving educational outcomes. Identifying causal relationships within knowledge structures helps teachers pinpoint and address learning issues, forming the basis for adaptive learning systems. Using real educational datasets, the research introduces a multi-sub-population collaborative search mechanism to enhance search efficiency by maintaining individual-level superiority, population-level diversity, and solution-set simplicity across sub-populations. A bidirectional feedback mechanism is implemented to discern high-quality and low-quality edges within the knowledge graph. Oversampling high-quality edges and undersampling low-quality edges address optimization challenges in Learning Path Recognition (LPR) due to edge sparsity. The proposed Collaborative Structural Search Framework (CSSF) effectively uncovers relationships within knowledge structures. Experimental validations on real-world datasets show CSSF’s effectiveness, with a 14.41% improvement in F1-score over benchmark algorithms on a dataset of 116 knowledge structures. The algorithm helps teachers identify the root causes of students’ errors, enabling more effective educational strategies, thus enhancing educational quality and learning outcomes. Intelligent education systems can better adapt to individual student needs, providing personalized learning resources, facilitating a positive learning cycle, and promoting sustainable education development.