Mathematical model and simulated annealing algorithm for Chinese high school timetabling problems under the new curriculum innovation

作者:Xingxing Hao, Jing Liu, Yutong Zhang, Gustaph Sanga

摘要

As the first attempt, this paper proposes a model for the Chinese high school timetabling problems (CHSTPs) under the new curriculum innovation which was launched in 2014 by the Chinese government. According to the new curriculum innovation, students in high school can choose subjects that they are interested in instead of being forced to select one of the two study directions, namely, Science and Liberal Arts. Meanwhile, they also need to attend compulsory subjects as traditions. CHSTPs are student-oriented and involve more student constraints that make them more complex than the typical “Class-Teacher model”, in which the element “Teacher” is the primary constraint. In this paper, we first describe in detail the mathematical model of CHSTPs and then design a new two-part representation for the candidate solution. Based on the new representation, we adopt a two-phase simulated annealing (SA) algorithm to solve CHSTPs. A total number of 45 synthetic instances with different amounts of classes, teachers, and levels of student constraints are generated and used to illustrate the characteristics of the CHSTP model and the effectiveness of the designed representation and algorithm. Finally, we apply the proposed model, the designed two-part representation and the two-phase SA on10 real high schools.

论文关键词:timetabling, Chinese high school timetabling problem, simulated annealing, two-part representation

论文评审过程:

论文官网地址:https://doi.org/10.1007/s11704-020-9102-4

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