In view of the problem that the traditional learning service recommendation does not fully consider the distinct differences between individuals, it is easy to lead to the contradiction between unchanging learning resources and learners’ personalized learning needs that are constantly improving, so an adaptive learning service recommendation improvement algorithm based on big data is proposed. Idea is based on adaptive learning platform and function modules. We consider the individual differences between students, to students as the center, collect students’ personalized learning demand data, and according to the data information to build student demand model. On the basis of using data mining methods for clustering recommendation service resources in learning, the adaptive recommend according to students’ individual need is proposed. The experimental results show that the adaptive learning service recommendation algorithm based on big data has high recommendation accuracy, coverage rate and recall rate, which is of great significance in the actual learning service recommendation.

In the competitive landscape of online learning, developing robust and effective learning resource recommendation systems is paramount, yet the field faces challenges due to high-dimensional, sparse matrices and intricate user–resource interactions. Our study focuses on geometric matrix completion (GMC) and introduces a novel approach, graph-based truncated norm regularization (GBTNR) for problem solving. GBTNR innovatively incorporates truncated Dirichlet norms for both user and item graphs, enhancing the model’s ability to handle complex data structures. This method synergistically combines the benefits of truncated norm regularization with the insightful analysis of user–user and resource–resource graph relationships, leading to a significant improvement in recommendation performance. Our model’s unique application of truncated Dirichlet norms distinctively positions it to address the inherent complexities in user and item data structures more effectively than existing methods. By bridging the gap between theoretical robustness and practical applicability, the GBTNR approach offers a substantial leap forward in the field of learning resource recommendations. This advancement is particularly critical in the realm of online education, where understanding and adapting to diverse and intricate user–resource interactions is key to developing truly personalized learning experiences. Moreover, our work includes a thorough theoretical analysis, complete with proofs, to establish the convergence property of the GMC-GBTNR model, thus reinforcing its reliability and effectiveness in practical applications. Empirical validation through extensive experiments on diverse real-world datasets affirms the model’s superior performance over existing methods, marking a groundbreaking advancement in personalized education and deepening our understanding of the dynamics in learner–resource interactions.

Complex multimodal optimization problems are widespread in machine learning, engineering design, and data science, where multiple local optima often trap conventional algorithms. Balancing global exploration and local exploitation remains a fundamental challenge for population-based optimization algorithms when solving such problems. This paper proposes a dynamic search framework optimization algorithm based on an energy level collaboration mechanism, termed DSF-ELC. The algorithm introduces two synergistic strategies. First, a population dynamic reorganization strategy adaptively adjusts particle migration between two fitness-stratified subpopulations based on real-time diversity measurements, effectively balancing exploration and exploitation. Second, a comprehensive learning strategy enables each dimension of inferior solutions to learn from the corresponding dimension of superior solutions in a randomized manner, thereby enhancing search capability on complex multimodal functions. The two strategies work synergistically to achieve an adaptive exploration-exploitation balance. Experimental validation on the CEC 2017 benchmark suite demonstrates that DSF-ELC achieves superior solution accuracy and stability compared to six representative algorithms on the vast majority of functions. Wilcoxon signed-rank tests, box plot visualization, and convergence curve analysis further validate the effectiveness of the proposed strategies. The results indicate that DSF-ELC has significant advantages and broad application prospects for complex multimodal optimization problems.