University timetabling is one of the classic schedule optimization problems that has attracted the attention of researchers for many years. Case studies in each school have unique characteristics, so this is a challenging task without a general solution. Through a long period of in-depth research, it can be divided into parts, and teaching assignment is one of them. Assigning tasks to lecturers needs to consider many complex constraints to ensure that classes are taught by people with good expertise as well as satisfy the lecturers’ wishes. In this study, we build a model from hard constraints that cannot be violated to ensure compliance with institutional regulations, quality standards and especially soft constraints that can be violated, and even add fuzzy elements that represent lecturers’ expectations. Then, the genetic algorithm will be used to optimize the model on the actual data set at FPT University and achieve reasonable and logical results. Moreover, the experiment was also tried on data sets with changes in the number of lecturers and their positions.