Operational Research in Education

Operational Research (OR) techniques have been applied, from the early stages of the discipline, to a wide variety of issues in education. At the government level, these include questions of what resources should be allocated to education as a whole and how these should be divided amongst the individual sectors of education and the institutions within the sectors. Another pertinent issue concerns the efficient operation of institutions, how to measure it, and whether resource allocation can be used to incentivise efficiency savings. Local governments, as well as being concerned with issues of resource allocation, may also need to make decisions regarding, for example, the creation and location of new institutions or closure of existing ones, as well as the day-to-day logistics of getting pupils to schools. Issues of concern for managers within schools and colleges include allocating the budgets, scheduling lessons and the assignment of students to courses. This survey provides an overview of the diverse problems faced by government, managers and consumers of education, and the OR techniques which have typically been applied in an effort to improve operations and provide solutions

Fairness in examination timetabling: student preferences and extended formulations

Variations of the examination timetabling problem have been investigated by the research community for more than two decades. The common characteristic between all problems is the fact that the definitions and data sets used all originate from actual educational institutions, particularly universities, including specific examination criteria and the students involved. Although much has been achieved and published on the state-of-the-art problem modelling and optimisation, a lack of attention has been focussed on the students involved in the process. This work presents and utilises the results of an extensive survey seeking student preferences with regard to their individual examination timetables, with the aim of producing solutions which satisfy these preferences while still also satisfying all existing benchmark considerations. The study reveals one of the main concerns relates to fairness within the students cohort; i.e. a student considers fairness with respect to the examination timetables of their immediate peers, as highly important. Considerations such as providing an equitable distribution of preparation time between all student cohort examinations, not just a majority, are used to form a measure of fairness. In order to satisfy this requirement, we propose an extension to the state-of-the-art examination timetabling problem models widely used in the scientific literature. Fairness is introduced as a new objective in addition to the standard objectives, creating a multi-objective problem. Several real-world examination data models are extended and the benchmarks for each are used in experimentation to determine the effectiveness of a multi-stage multi-objective approach based on weighted Tchebyceff scalarisation in improving fairness along with the other objectives. The results show that the proposed model and methods allow for the production of high quality timetable solutions while also providing a trade-off between the standard soft constraints and a desired fairness for each student

An iterated multi-stage selection hyper-heuristic

There is a growing interest towards the design of reusable general purpose search methods that are applicable to different problems instead of tailored solutions to a single particular problem. Hyper-heuristics have emerged as such high level methods that explore the space formed by a set of heuristics (move operators) or heuristic components for solving computationally hard problems. A selection hyper-heuristic mixes and controls a predefined set of low level heuristics with the goal of improving an initially generated solution by choosing and applying an appropriate heuristic to a solution in hand and deciding whether to accept or reject the new solution at each step under an iterative framework. Designing an adaptive control mechanism for the heuristic selection and combining it with a suitable acceptance method is a major challenge, because both components can influence the overall performance of a selection hyper-heuristic. In this study, we describe a novel iterated multi-stage hyper-heuristic approach which cycles through two interacting hyper-heuristics and operates based on the principle that not all low level heuristics for a problem domain would be useful at any point of the search process. The empirical results on a hyper-heuristic benchmark indicate the success of the proposed selection hyper-heuristic across six problem domains beating the state-of-the-art approach

Hybridizations within a graph based hyper-heuristic framework for university timetabling problems

A significant body of recent literature has explored various research directions in hyper-heuristics (which can be thought as heuristics to choose heuristics). In this paper, we extend our previous work to construct a unified graph-based hyper-heuristic (GHH) framework, under which a number of local search-based algorithms (as the high level heuristics) are studied to search upon sequences of low-level graph colouring heuristics. To gain an in-depth understanding on this new framework, we address some fundamental issues concerning neighbourhood structures and characteristics of the two search spaces (namely, the search spaces of the heuristics and the actual solutions). Furthermore, we investigate efficient hybridizations in GHH with local search methods and address issues concerning the exploration of the high-level search and the exploitation ability of the local search. These, to our knowledge, represent entirely novel directions in hyper-heuristics. The efficient hybrid GHH obtained competitive results compared with the best published results for both benchmark course and exam timetabling problems, demonstrating its efficiency and generality across different problem domains. Possible extensions upon this simple, yet general, GHH framework are also discussed