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Hybridising heuristics within an estimation distribution algorithm for examination timetabling

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Abstract

This paper presents a hybrid hyper-heuristic approach based on estimation distribution algorithms. The main motivation is to raise the level of generality for search methodologies. The objective of the hyper-heuristic is to produce solutions of acceptable quality for a number of optimisation problems. In this work, we demonstrate the generality through experimental results for different variants of exam timetabling problems. The hyper-heuristic represents an automated constructive method that searches for heuristic choices from a given set of low-level heuristics based only on non-domain-specific knowledge. The high-level search methodology is based on a simple estimation distribution algorithm. It is capable of guiding the search to select appropriate heuristics in different problem solving situations. The probability distribution of low-level heuristics at different stages of solution construction can be used to measure their effectiveness and possibly help to facilitate more intelligent hyper-heuristic search methods.

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Authors and Affiliations

  1. Automated Scheduling, Optimisation and Planning, School of Computer Science University of Nottingham, Nottingham, NG8 1BB, UK

    Rong Qu, Nam Pham & Graham Kendall

  2. School of Computer Science, University of Nottingham Ningbo, China, Ningbo, 315100, China

    Ruibin Bai

  3. University of Nottingham Malaysia Campus, Nottingham, Malaysia

    Graham Kendall

Authors
  1. Rong Qu
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  2. Nam Pham
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  3. Ruibin Bai
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  4. Graham Kendall
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Correspondence to Rong Qu.

Appendix – The Carter Benchmark Dataset

Appendix – The Carter Benchmark Dataset

The Carter examination timetabling benchmark dataset [16] (details available at http://www.cs.nott.ac.uk/~rxq/data.htm) is one of the most widely tested sets in timetabling research community. Since its introduction in 1996, it has attracted much research effort from the community. During the years, researchers are reporting the best results obtained along with the development of advanced algorithms. This dataset still remains an interesting challenge as optimal solutions for all instances have not been found yet. Therefore, we evaluate our method on this dataset to compare results against many other existing methodologies. Table A-1 shows characteristics of the instances.

Table A-1 Details of the Carter benchmark dataset [16, 31]
Full size table

Two versions of the dataset have been circulated under the same name over the last ten years. We used the naming convention provided in [31]. An extensive survey is also provided in [31] on all search methodologies with associated best reported results for this dataset.

The hard constraint requires that any two exams having common students must be assigned to two different timeslots. The soft constraint concerns the spread of exams for students. If two exams are assigned into two timeslots t i and t j , then each student taking both of these exams will cause a penaltyof: 2 5−|i−j| if 0< |i – j | ≤5. The objective is to minimise the soft constraint penalty cost: total_penalty / number_of_students. This objective represents a preference to timetables where fewer students have to take exams too close to each other.

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Qu, R., Pham, N., Bai, R. et al. Hybridising heuristics within an estimation distribution algorithm for examination timetabling. Appl Intell 42, 679–693 (2015). https://doi.org/10.1007/s10489-014-0615-0

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