An integer programming approach to curriculum-based examination timetabling

Cataldo, Alejandro; Ferrer, Juan Carlos; Miranda, J. Jaime; Rey, P.; Sauré, Antoine

doi:10.1007/s10479-016-2321-2

Cited by 19 publications

(10 citation statements)

References 75 publications

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“…Often timetabling problems can be modeled as integer linear programs that involve very large number of binary decision variables and linear constraints [10], [11]. These problems are known to be NP-complete and are difficult to solve for optimality [12].…”

Section: Introductionmentioning

confidence: 99%

A Convex LASSO Framework for Linear Timetabling

Al-Matouq

2020

IEEE Access

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A new convex optimization framework for approximately solving timetabling problems that can be described as integer linear programs is proposed. The method is based on converting the timetabling problem into a cardinality constrained problem while viewing the operational constraints of the timetable as noisy measurements with an unknown average slack. The problem is then iteratively solved using weighted Lasso with weights that are updated using a simple linear program to satisfy the cardinality constraint while respecting the operational constraints in the least squares sense. Compared with previous convex relaxations for solving timetabling problems, our solution technique will converge to a binary solution without the need for subsequent randomized rounding. Moreover, the number of Lasso iterations required are in the order of the number of events to be scheduled and hence the method can handle very large timetabling problems using efficient Lasso solvers. We provide the assumptions required on the linear timetabling model and establish the associated error bound of the technique upon convergence assuming restricted strong convexity and uniqueness. We also study the effect of the Lasso regularization parameter and the effect of relaxing the objective on the extent of constraint satisfaction through several simulation experiments. Our experiment on one of the datasets of the international timetabling competition for university examination improved the best documented result given in the 2007 international timetabling competition by more than 30% with 99.9% of all constraints satisfied.

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Section: Introductionmentioning

confidence: 99%

A Convex LASSO Framework for Linear Timetabling

Al-Matouq

2020

IEEE Access

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“…Some viable approaches are operations research (OR) and artificial intelligence (AI) techniques that handle the problem often by mathematical programming as well as different heuristics, meta-heuristic, and hyper-heuristic algorithms [1]. Some of these procedures are constraint programming [2], integer programming [3], graph heuristics [4], great deluge algorithm [5], hill-climbing [6], tabu search [7], simulated annealing [8], genetic algorithm [9], particle swarm optimization [10], artificial bee colony algorithm [11] and memetic algorithm [12].…”

Section: Introductionmentioning

confidence: 99%

Development of an Interactive Tool based on Combining Graph Heuristic with Local Search for Examination Timetable Problem

Mandal¹

2020

IJACSA

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Every university faces a lot of challenges to solve the examination timetabling problem because the problem is NPhard and contains numerous institutional constraints. Although several attempts have been taken to address the issue, there are scarcities of interactive and automated tools in this domain that can schedule exams effectively by considering institutional resources, different constraints, and student enrolment in courses. This paper presents the development of a system as a graphical and interactive tool for examination timetabling problem. To develop the system, combining graph coloring heuristic and local search meta-heuristic algorithms are employed. The graph heuristic ordering is incorporated for constructing initial solution(s), whereas the local search meta-heuristic algorithms are used to produce quality exam timetables. Different constraints and objective functions from ITC2007 exam competition rules are adopted, as it is a complex real word exam timetabling problem. Finally, the system is tested on the ITC2007 exam benchmark dataset, and test results are presented. The main aspect of the system is to deliver an easy-to-handle tool that can generate quality timetables based on institutional demands and smoothly manage several key components. These components are collecting data associated with the enrolment of students in exams, defining hard and soft constraints, and allocating times and resources. Overall, this software can be used as a commercial scheduler in order to provide institutions with automated, accurate, and quick exam timetable.

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“…On the other hand, instructors of the courses as well as the students prefer having the examination timetable as soon as possible. For this reason, Cataldo et al (2017) proposed an IP to tackle the curriculum-based ETP where the examination timetable was produced without complete information on student enrollments. Sancar Edis and Edis (2019) also studied the curriculum-based ETP and in addition, they introduced a set of constraints to increase the satisfaction of the instructors and the students.…”

Section: Introductionmentioning

confidence: 99%

Conflict Management in University Examination Timetabling Problem: A case study of summer school mid-terms

Bayar¹,

Bayar

2020

CEREM

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Abstract: Aim: This study is on tackling Examination Timetabling Problem (ETP) of the Faculty of Economics And Administrative Sciences (FEAS) of the Ankara HBV University summer school, where the courses of fall and spring semesters are offered simultaneously and regulations on restricting enrollments in inter-department electives or in-department courses of distinct years are relaxed. Thus, the complexity of the nature of the ETP problem is exacerbated. The direct heuristics based on successive assignments that the university normally adopts was proven inadequate for assuming standard regulations hence, another approach we explain in this paper was needed. Design / Research methods: The ETP was formulated as a Linear Mixed-Integer Program (LMIP) and decomposed into three stages; timetabling exams, room assignment, student allocation. To manage the conflict between the stakeholders of the examination procedure, a lexicographic optimization process based on the priority of the parties was undertaken. Conclusions / findings: After a recursive timetabling process based on a trial-and-error method a clash-free timetable was generated and, a room assignment plan that minimizes the total number of proctoring duties, usage of higher floor rooms and total crowdedness of rooms respectively was put into action. Therefore no student group experienced any clashing exams, the faculty members saved time that can be spent on research instead, since the room usage was better planned the costs (elevator usage, lighting, air conditioning, the labor of the janitors) were assumed to be decreased. Originality / value of the article: Each examination period bares a different ETP due to its problem-specific nature (number of courses offered, structure of student enrollments, availability of rooms, etc.). Summer schools provide a more irregular structure that demands special attention, a trial-and-error reformulation of the ETP in our case. In addition, the traditional formulations of the ETP, to the extent we have been able to scan, do not include the minimization of the crowdedness of the rooms. Thus, in creating a more comfortable environment, easier to monitor exams and, ability in handling unexpected dysfunctionalities (broken classroom equipment, etc.) this study is novel. Limitations of the research: The algorithms to solve an ETP formulated as an LMIP are of high complexity therefore, we are not able to assert the optimality of our suggested solutions acquired within time limitations. Keywords: examination timetabling, group decision making, lexicographic optimization, linear mixed-integer programming JEL: C44, C61, M12

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An integer programming approach to curriculum-based examination timetabling

Cited by 19 publications

References 75 publications

A Convex LASSO Framework for Linear Timetabling

A Convex LASSO Framework for Linear Timetabling

Development of an Interactive Tool based on Combining Graph Heuristic with Local Search for Examination Timetable Problem

Conflict Management in University Examination Timetabling Problem: A case study of summer school mid-terms

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