Abstract
In this paper, we investigate adaptive linear combinations of graph coloring heuristics with a heuristic modifier to address the examination timetabling problem. We invoke a normalisation strategy for each parameter in order to generalise the specific problem data. Two graph coloring heuristics were used in this study (largest degree and saturation degree). A score for the difficulty of assigning each examination was obtained from an adaptive linear combination of these two heuristics and examinations in the list were ordered based on this value. The examinations with the score value representing the higher difficulty were chosen for scheduling based on two strategies. We tested for single and multiple heuristics with and without a heuristic modifier with different combinations of weight values for each parameter on the Toronto and ITC2007 benchmark data sets. We observed that the combination of multiple heuristics with a heuristic modifier offers an effective way to obtain good solution quality. Experimental results demonstrate that our approach delivers promising results. We conclude that this adaptive linear combination of heuristics is a highly effective method and simple to implement.
Highlights
The examination timetabling problem has been much studied and a wide variety of approaches have been taken across a variety of associated problem descriptions
An adaptive linear combination of heuristics with a heuristic modifier under the framework of adaptive strategies has been proposed for solving examination timetabling problems
A difficulty_score is used to determine the ordering of the examinations and the most difficult examination with the highest difficulty_score is scheduled first based on two strategies. This approach is tested with single and multiple heuristics with and without a heuristic modifier on the Toronto benchmark datsets while the ITC2007 benchmark datasets are tested with only multiple heuristics with heuristic modifier
Summary
The examination timetabling problem has been much studied and a wide variety of approaches have been taken across a variety of associated problem descriptions. In our previous study (Abdul Rahman, Bargiela, Burke, McCollum, & Özcan, 2009), we introduced several strategies to choose examinations and time-slots using ordering heuristics within the framework of squeaky wheel optimisation. This work is an extension of the adaptive heuristic orderings technique proposed by Burke and Newall (2004) where the approach promotes early scheduling of difficult examinations based on a heuristic modifier. Another study, Qu, Burke, and McCollum (2009) implemented an adaptive approach to examination timetabling by hybridising the low level graph heuristics based on a learning mechanism and modifying the solutions by high-level heuristic indirectly. Based on the ‘difficulty factor’, Johnson (1990) used graph colouring heuristics, i.e. the combination of largest enrolment and largest degree as an ordering strategy for assigning examinations to time slots.
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