A novel greedy heuristic algorithm for university course timetabling problem

Although the university course timetabling problem (UCTP) is an old, classical problem in the field of optimization problems, there are still a few challenges for the practical-relevant problems considering customers´ requirements. In particular with respect to the UCTP of China, the timetable planning based on the uniform teaching resources of a university for all degree types of undergraduates and graduates, is still not considered and tackled in the previous researches. In this paper, a novel greedy heuristic approach for UCTP is presented with considering complex multi-constraint conditions on the basis of the uniform teaching resources of a university, which include students, teachers and classrooms with feasible timeslots, respectively. Firstly, the constraints are modelled and then the objective function is proposed based on the evenness for all the curriculums of a student and a teacher´s satisfaction for his/her lecturing time. Secondly, transform the constraints to relational calculus among of the variables expressed by relation algebra; thereby the heuristic rules are formed by the relational calculus. And the greedy strategies are applied to search the optimal solutions in the remaining parts of feasible solution space. A greedy heuristic algorithm is designed to implement the approach. Finally, a course timetabling instance from a graduate school is carried out and the result adopted in the graduate school show that the novel greedy heuristic algorithm is effective and the runtime is significantly shortened comparing with the earlier approaching used in the timetabling system.