This paper establishes a multi-objective optimization model for the process of yoga course ideology and politics in colleges and universities through the group paper technology, and adopts an improved genetic algorithm to solve the model. Integrating the online and offline hybrid teaching mode, the paper’s group paper technology is placed in the online assessment to realize the all-round reform of yoga course Civics teaching. The research results show that the improved genetic algorithm (IGA) in this paper has a higher grouping efficiency and quality compared with the traditional genetic algorithm (GA), and saves about 52.7% in the grouping time. At the same time, using the social network analysis method to analyze the online-offline hybrid teaching mode of this paper, we are able to derive the student objects that need to be focused on based on the results of the analysis of the centrality of the point degree and the centrality of the middle of the point degree. The experimental class adopting the teaching mode of this paper has an excellent class performance rate of 100% under the test of group paper technology, which fully demonstrates that the teaching reform method proposed in this paper for the ideology of yoga course in colleges and universities has significant practical application effects.