A Decomposition of the Max-min Fair Curriculum-based Course Timetabling Problem

TL;DR

This paper introduces a novel decomposition approach for the max-min fair curriculum-based course timetabling problem, improving heuristic algorithms' efficiency and solution quality through a generalized lexicographic bottleneck optimization model.

Contribution

It models the room assignment as a generalized LBOP, enabling more efficient solutions and enhancing existing heuristics for the MMF-CB-CTT problem.

Findings

Improved heuristic performance on 21 ITC2007 instances.

New solution quality measure for max-min fair optimization.

Algorithm outperforms original on most instances.

Abstract

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.