Optimization design of online platform courses in university mathematics teaching reform based on genetic algorithm

This study proposes an optimization model that integrates adaptive genetic algorithm and probabilistic matrix decomposition.The category features are quantified by WOE coding, and the global search capability of the genetic algorithm is improved by combining adaptive cross-mutation strategy, simulated annealing algorithm and orthogonal table initialization to filter out a subset of highly discriminative features.Further, the student-course nearest neighbor similarity is embedded into the probability matrix decomposition model, and the feature distribution is constrained by the logistic Steele function to optimize the personalized recommendation accuracy.Experiments based on the real MOOC dataset of Academy Online show that the model in this paper achieves optimal performance when the crossover probability Pc is 0.9, with HR and NDCG of 60.58% and 32.99%, respectively.When the variation probability Pm is 0.001, HR is 59.67% and NDCG is 32.78%, which performs close to the optimal value.In the Top-K recommendation, the Precision@5 and mAP@15 increased to 60.44% and 96.32%, respectively, which was significantly better than the XGBoost of the traditional model (34.15% and 59.48%).The results show that the multi-strategy fusion of genetic algorithm and probabilistic matrix decomposition model can effectively solve the course recommendation problem in highly sparse scenarios.