基于最大最小公平课程的排课问题的分解
A Decomposition of the Max-min Fair Curriculum-based Course Timetabling Problem
摘要：
我们提出了一个分解的最大-最小公平的基于排序的课程编排（MMF-CB-CTT）问题。分解模型的房间分配子问题作为一个广义字典瓶颈优化问题（LBOP）。我们表明，广义LBOP可以有效地解决，如果相应的总和优化问题可以有效地解决。因此，MMF-CB-CTT问题的房间分配子问题可以有效地解决。我们使用这个洞察力，以改善以前提出的启发式算法的MMF-CB-CTT问题。我们的实验结果表明，使用新的分解提高了算法的性能在大多数的21个ITC 2007测试实例的最佳解决方案的质量方面发现。此外，我们引入了一个最大-最小公平优化问题的解决方案的质量的措施。这一措施有助于克服一些限制所施加的定性性质的最大-最小公平性和艾滋病的统计评估性能的随机算法这样的问题。我们使用这个措施表明，使用新的分解算法优于原来的平均解决方案的质量在大多数情况下。
英文摘要：
We propose a decomposition of the max-min fair curriculum-based course timetabling (MMF-CB-CTT) problem. The decomposition models the room assignment subproblem as a generalized lexicographic bottleneck optimization problem (LBOP). We show that the generalized LBOP can be solved efficiently if the corresponding sum optimization problem can be solved efficiently. As a consequence, the room assignment subproblem of the MMF-CB-CTT problem can be solved efficiently. We use this insight to improve a previously proposed heuristic algorithm for the MMF-CB-CTT problem. Our experimental results indicate that using the new decomposition improves the performance of the algorithm on most of the 21 ITC2007 test instances with respect to the quality of the best solution found. Furthermore, we introduce a measure of the quality of a solution to a max-min fair optimization problem. This measure helps to overcome some limitations imposed by the qualitative nature of max-min fairness and aids the statistical evaluation of the performance of randomized algorithms for such problems. We use this measure to show that using the new decomposition the algorithm outperforms the original one on most instances with respect to the average solution quality.
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