论课程编排的公平性
Fairness in Academic Course Timetabling
摘要：
我们认为，在大学的设置公平的课程时间表的问题。我们的动机是提高有关个人（学生，教师等）的整体满意度。给他们一个公平的时间表。其中心思想是，课程时间表中不可取的安排，即，违反软约束的，应当以公平的方式在个人之间分配。我们提出了两个配方的公平课程编排问题，分别基于最大最小公平性和Jain的公平性指标。此外，我们提出了一种基于模拟退火的优化算法来解决最大-最小公平课程编排问题，并进行了实验评估。新的贡献涉及测量两个时间表之间的能量差，即，就最大-最小公平性而言，一个时间表与另一个时间表相比差多少。我们介绍了三种不同的能量差的措施，并评估其对整体算法性能的影响。第二个建议的问题制定集中在公平性和软约束违反总量之间的权衡。我们的实验评估表明，已知的最好的解决方案，以ITC 2007年基于教程的课程编排实例是相当公平的Jain的公平性指数。然而，实验也表明，公平性可以进一步提高只有一个相当小的增加，在软约束违反的总量。
英文摘要：
We consider the problem of creating fair course timetables in the setting of a university. Our motivation is to improve the overall satisfaction of individuals concerned (students, teachers, etc.) by providing a fair timetable to them. The central idea is that undesirable arrangements in the course timetable, i.e., violations of soft constraints, should be distributed in a fair way among the individuals. We propose two formulations for the fair course timetabling problem that are based on max-min fairness and Jain's fairness index, respectively. Furthermore, we present and experimentally evaluate an optimization algorithm based on simulated annealing for solving max-min fair course timetabling problems. The new contribution is concerned with measuring the energy difference between two timetables, i.e., how much worse a timetable is compared to another timetable with respect to max-min fairness. We introduce three different energy difference measures and evaluate their impact on the overall algorithm performance. The second proposed problem formulation focuses on the tradeoff between fairness and the total amount of soft constraint violations. Our experimental evaluation shows that the known best solutions to the ITC2007 curriculum-based course timetabling instances are quite fair with respect to Jain's fairness index. However, the experiments also show that the fairness can be improved further for only a rather small increase in the total amount of soft constraint violations.
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