Online teaching has become increasingly popular in recent years, particularly after Covid-19, in response to educational difficulties such as teacher shortages and remote learning. This paper proposes Adjusted Non-dominated Sorting Genetic Algorithm III (aNSGA-III) to overcome the poor convergence of Non-dominated Sorting Genetic Algorithm III (NSGA-III) in optimizing teaching timetables based on practical constraints such as class demand and teacher availability for an EdTech company in Vietnam (VET). By improving on mutation parameters, termination conditions, and the application of parallel processing has increased the algorithm's efficiency and accuracy. Furthermore, our empirical experiments demonstrate significant practical and academic contributions by cutting scheduling time up to 40% and operational costs in half. The findings highlight the potential of the automated management information system in order to enhance the efficiency and quality of timetable management in the EdTech sector.