A mixed-integer programming approach to a class timetabling problem: A case study with gender policies and traffic considerations

Al-Yakoob, Salem M.; Sherali, Hanif D.

doi:10.1016/j.ejor.2006.04.035

Cited by 35 publications

(19 citation statements)

References 18 publications

(24 reference statements)

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“…For instance, Daskalaki et al (2004Daskalaki et al ( , 2005 solved instances of up to 211 events using ILOG CPLEX, without introducing any user cuts. Al-Yakoob and Sherali (2007) and Schimmelpfeng and Helber (2007) modelled more complex problems, although they have not introduced any constraints penalising interaction between events in timetables (other than straightforward conflicts), which would have made the problem considerably more difficult. In some of the most rigorous recent Table 2 Linear programming relaxations of a compact formulation of the Udine Course Timetabling problem, referred to as Monolithic by , and of the subset of the proposed formulation with mildly exponential number of constraints we use at the root node, with all implied bounds added statically: dimensions of matrices after all automatic reductions inbuilt in CPLEX 10 and root relaxation time using default settings of CPLEX 10 (Dual Simplex) and manually tuned CPLEX 10 Barrier LP solver (2005) present a branch-and-cut solver for the Benevento Course Timetabling Problem, which forbids some interactions of events in timetables other than conflicts using hard constraints.…”

Section: Problem Descriptionmentioning

confidence: 99%

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

et al. 2011

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A branch-and-cut procedure for the Udine Course Timetabling problem is described. Simple compact integer linear programming formulations of the problem employ only binary variables. In contrast, we give a formulation with fewer variables by using a mix of binary and general integer variables. This formulation has an exponential number of constraints, which are added only upon violation. The number of constraints is exponential. However, this is only with respect to the upper bound on the general integer variables, which is the number of periods per day in the Udine Course Timetabling problem.A number of further classes of cuts are also introduced, arising from: enumeration of event/free-period patterns; bounds on the numbers of days of instruction; the desire to exploit integrality of the objective function value; the graph colouring component; and also from various implied bounds. An implementation of the corresponding branch-and-cut procedure is evaluated on the instances from Track 3 of the International Timetabling Competition 2007.

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Section: Problem Descriptionmentioning

confidence: 99%

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

et al. 2011

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“…To the best of our knowledge, the studies in [29], [30], [34], [35], [36], and [37] are the only ones that, to a limited extent, incorporate student flows. AlYakoob and Sherali [29] present a Mixed Integer Programming (MIP) model for class timetabling problems and consider a related congestion topic. The authors address the problem of parking and traffic congestions for students and faculty members when lectures are inadequately spread over all the available timeslots.…”

Section: Student Flowsmentioning

confidence: 99%

Developing compact course timetables with optimized student flows

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et al. 2016

European Journal of Operational Research

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In university buildings with many rooms spread over different floors, large student flows between two consecutive lectures might cause congestion problems. These congestions result in long queues at elevators or at stairwells, which might lead to delays in lecture starts. The course timetable clearly has an important impact on these congestions. This paper presents a two-stage integer programming approach for building a university course timetable that aims at minimizing the resulting student flows. The first stage minimizes the violation of the teacher and educational preferences by assigning lectures to timeslots and rooms. The second stage reassigns classrooms to lectures of the timetable of the first stage and minimizes the student flow. The conceptual model is applied to the dataset of the Faculty of Economics and Business of the KU Leuven Campus Brussels and is tested and validated with 21 adapted instances from the literature. In contrast to a monolithic model, the two-stage model consistently succeeds in finding good quality feasible solutions. Moreover, the generated timetables entail significantly reduced student flows compared to the flows of the manually developed course timetable.

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“…Examples of these algorithms include graph colouring heuristics [2], Tabu Search [7], simulated annealing [8], evolutionary algorithms [10], case-based reasoning [11], two-stage heuristic algorithms [12], tabu search [13], ant colony [14] and so on. Interested readers are referred to [6] for a comprehensive survey of the automated approaches for university timetabling presented in recent years. This paper proposes three different metaheuristics, artificial immune, genetic and simulated annealing algorithms.…”

Section: Solution Algorithmsmentioning

confidence: 99%

“…UCS problems are usually different from one university to another [2,6]. It is very likely that each university has its own unique set of requirements to utilize its resources effectively, fulfil the requirements of its business, give a high level of satisfaction to its students and so forth.…”

Section: Introductionmentioning

confidence: 99%

Algorithms for university course scheduling problems

2017

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Orginal scientific paper This paper deals with the problem of course scheduling where we have a set of courses, lecturers and classrooms. Courses are assigned and scheduled in such a way that the total preference is maximized. We develop the mathematical model of the problem in form of a linear integer program. The small sized problem can be solved to optimality using commercial software. We then develop three different metaheuristics based on artificial immune, genetic and simulated annealing algorithms. These three solution methods are equipped with novel procedures such as move and crossing operators. The parameters of the proposed metaheuristics are first tuned, and then they are evaluated with optimal solutions found by the model. They are, furthermore, evaluated by comparing their performance. The experiments demonstrate that the artificial immune algorithm performs better than the other algorithms. Keywords: artificial immune algorithm; genetic algorithm; mathematical model; simulated annealing; university course scheduling Algoritmi za probleme planiranja fakultetskih predavanjaIzvorni znanstveni članak Rad se bavi problemom planiranja predavanja gdje postoji niz kolegija, predavača i učionica. Kolegiji se dodjeljuju i planiraju tako da se maksimalno zadovolje preferencije. Razvijamo matematički model problema u obliku linearnog programa cijelih brojeva. Manji se problem može optimalno riješiti primjenom komercijalnog softvera. Zatim razvijamo tri različite metaheuristike na temelju umjetnih imunih, genetičkih i algoritama simuliranog kaljenje. Te tri metode rješenja opremljene su novim postupcima kao što su operatori kretanja i križanja. Parametri predložene metaheuristike najprije se usklađuju, a zatim procjenjuju optimalnim rješenjima koje je model pronašao. Nadalje se procjenjuju usporedbom njihovih performansi. Eksperimenti pokazuju da je umjetni imuni algoritam uspješniji od drugih algoritama.

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A mixed-integer programming approach to a class timetabling problem: A case study with gender policies and traffic considerations

Cited by 35 publications

References 18 publications

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

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

Developing compact course timetables with optimized student flows

Algorithms for university course scheduling problems

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