A branch-and-cut procedure for the Udine Course Timetabling problem

Burke, Edmund K.; Mareček, Jakub; Parkes, Andrew J.; Rudová, Hana

doi:10.1007/s10479-010-0828-5

Cited by 49 publications

(41 citation statements)

References 48 publications

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“…see our preliminary work in [5]). Also, although we have used stochastic local search methods, for small problems it may be feasible to use exact integer programming methods, possibly in the form of non-linear extensions along the lines of branch-and-cut in [74]. Of course, many other meta-heuristics may by applicable.…”

Section: Resultsmentioning

confidence: 99%

Fairness in examination timetabling: Student preferences and extended formulations

Muklason

Parkes

zcan

et al. 2017

Applied Soft Computing

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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 * Corresponding author of high quality timetable solutions while also providing a trade-off between the standard soft constraints and a desired fairness for each student.

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Section: Resultsmentioning

confidence: 99%

Fairness in examination timetabling: Student preferences and extended formulations

Muklason

Parkes

zcan

et al. 2017

Applied Soft Computing

Self Cite

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“…The impact of these cuts has been explored for some hard timetabling problems [4,14]. Considering generic clique separation routines, the most common ones are the star clique and the row clique method [21,29,7].…”

Section: Dual Bound Improvement : Cutting Planesmentioning

confidence: 99%

“…Some previous results indicate that this is the best strategy. In [14], for example, although authors used a branch-and-bound code to search for the most violated clique, computational results motivated the inclusion of non-optimally violated cuts found during the search. This result is consistent with reports of application of other cuts applied to different models, such as Chvàtal-Gomory cuts [23].…”

Section: Dual Bound Improvement : Cutting Planesmentioning

confidence: 99%

Integer programming techniques for the nurse rostering problem

et al. 2014

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This work presents Integer Programming (IP) techniques to tackle the problem of the International Nurse Rostering Competition. Starting from a compact and monolithic formulation in which the current generation of solvers performs poorly, improved cut generation strategies and primal heuristics are proposed and evaluated. A large number of computational experiments with these techniques produced the following results: the optimality of the vast majority of instances was proved, the best known solutions were improved by up to 15% and strong dual bounds were obtained. In the spirit of reproducible science, all code was implemented using the Computational Infrastructure for Operations Research (COIN-OR).

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“…Additionally, the most straight-forward MIP model, which we will discuss below, is often alluded to but seldom constructed (Burke et al, 2012). It is referred to in nearly every MIP paper with varying degrees of depth and then the researchers proceed to make their changes to it without ever running it as a baseline (Rudová et al, 2011).…”

Section: Mixed Integer Programming Modelsmentioning

confidence: 99%

“…Schaerf (1999) pointed out that very few researchers make an optimal baseline model to compare to. If researchers do compare methods, it is typically with standardized data sets, often the University of Toronto benchmark data or the Udine Course Timetabling Problem, and researchers only run their model and compare the speed and accuracy to others who have used that dataset (Burke et al, 2012;Qu et al, 2009). This practice is especially questionable because the differences in the computers' memory and processor are likely to contribute significantly to the variability in run time.…”

Section: Mixed Integer Programming Modelsmentioning

confidence: 99%

A Set Union Based Formulation for Course Scheduling and Timetabling

Bukenberger¹

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The Course Timetabling Problem is a widely studied optimization problem where a number of sections are scheduled in concert with the assignment of students to sections in order to maximize the desirability of the resulting schedule for all stakeholders. This problem is commonly solved as a linear program with variables for each student or group of students with identical schedules. In this paper we explore an alternative formulation that aggregates binary student variables into integer variables denoting the number of students enrolled in a course. Our solution method assumes decomposition of the general schedule into time blocks, and applies a unique set theory based, integer linear programming formulation that seeks to maximize the total number of students enrolled in their desired sections across the time blocks. Once the problem has been solved, the simpler problem of disaggregating the solution is resolved. This approach can be used to find exact solutions, given sufficient computing power, or simplified to quickly find solutions within calculable bounds of optimality. Case studies with a local elementary school and a local high school show that the new formulation is significantly faster and can be made to be reasonably accurate.

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A branch-and-cut procedure for the Udine Course Timetabling problem

Cited by 49 publications

References 48 publications

Fairness in examination timetabling: Student preferences and extended formulations

Fairness in examination timetabling: Student preferences and extended formulations

Integer programming techniques for the nurse rostering problem

A Set Union Based Formulation for Course Scheduling and Timetabling

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