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A Survey of Automated Timetabling
 ARTIFICIAL INTELLIGENCE REVIEW
, 1999
"... The timetabling problem consists in fixing a sequence of meetings between teachers and students in a prefixed period of time (typically a week), satisfying a set of constraints of various types. A large number of variants of the timetabling problem have been proposed in the literature, which diff ..."
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Cited by 154 (14 self)
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The timetabling problem consists in fixing a sequence of meetings between teachers and students in a prefixed period of time (typically a week), satisfying a set of constraints of various types. A large number of variants of the timetabling problem have been proposed in the literature, which differ from each other based on the type of institution involved (university or high school) and the type of constraints. This problem, that has been traditionally considered in the operational research field, has recently been tackled with techniques belonging also to artificial intelligence (e.g. genetic algorithms, tabu search, simulated annealing, and constraint satisfaction). In this paper, we survey the various formulations of the problem, and the techniques and algorithms used for its solution.
A Column Generation Approach For Graph Coloring
 INFORMS Journal on Computing
, 1995
"... We present a method for solving the independent set formulation of the graph coloring problem (where there is one variable for each independent set in the graph). We use a column generation method for implicit optimization of the linear program at each node of the branchandbound tree. This approac ..."
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Cited by 80 (2 self)
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We present a method for solving the independent set formulation of the graph coloring problem (where there is one variable for each independent set in the graph). We use a column generation method for implicit optimization of the linear program at each node of the branchandbound tree. This approach, while requiring the solution of a difficult subproblem as well as needing sophisticated branching rules, solves small to moderate size problems quickly. We have also implemented an exact graph coloring algorithm based on DSATUR for comparison. Implementation details and computational experience are presented. 1 INTRODUCTION The graph coloring problem is one of the most useful models in graph theory. This problem has been used to solve problems in school timetabling [10], computer register allocation [7, 8], electronic bandwidth allocation [11], and many other areas. These applications suggest that effective algorithms for solving the graph coloring problem would be of great importance. D...
Tabu Search Techniques for Large HighSchool Timetabling Problems
 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS
, 1996
"... The highschool timetabling problem regards the weekly scheduling for all the lectures of a high school. The problem consists in assigning lectures to periods in such a way that no teacher (or class) is involved in more than one lecture at a time, and other side constraints are satisfied. The pro ..."
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Cited by 56 (8 self)
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The highschool timetabling problem regards the weekly scheduling for all the lectures of a high school. The problem consists in assigning lectures to periods in such a way that no teacher (or class) is involved in more than one lecture at a time, and other side constraints are satisfied. The problem is NPcomplete and is usually tackled using heuristic methods. This paper describes a solution algorithm (and its implementation) based on tabu search. The algorithm interleaves different types of moves and makes use of an adaptive relaxation of the hard constraints. The implementation of the algorithm has been successfully experimented in some large high schools with various kinds of side constraints.
Solving Examination Timetabling Problems through Adaption of Heuristic Orderings
, 2003
"... Heuristic ordering based methods, very similar to those used for graph colouring problems, have long been applied successfully to the examination timetabling problem. Despite the success of these methods on real life problems, even with limited computing resources, the approach has the fundamenta ..."
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Cited by 56 (26 self)
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Heuristic ordering based methods, very similar to those used for graph colouring problems, have long been applied successfully to the examination timetabling problem. Despite the success of these methods on real life problems, even with limited computing resources, the approach has the fundamental flaw that it is only as effective as the heuristic that is used. One of the motivations of this paper is to attempt to develop approaches that can operate at a higher level of generality and that can adapt heuristics to suit the particular problem instance in hand.
A comparison of annealing techniques for academic course scheduling
 Lecture Notes in Computer Science
, 1998
"... Abstract. In this study we have tackled the NPhard problem of academic class scheduling (or timetabling) at the university level. We have investigated a variety of approaches based on simulated annealing, including meanfield annealing, simulated annealing with three different cooling schedules, an ..."
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Cited by 43 (0 self)
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Abstract. In this study we have tackled the NPhard problem of academic class scheduling (or timetabling) at the university level. We have investigated a variety of approaches based on simulated annealing, including meanfield annealing, simulated annealing with three different cooling schedules, and the use of a rulebased preprocessor to provide a good initial solution for annealing. The best results were obtained using simulated annealing with adaptive cooling and reheating as a function of cost, and a rulebased preprocessor. This approach enabled us to obtain valid schedules for the timetabling problem for a large university, using a complex cost function that includes student preferences. None of the other methods were able to provide a complete valid schedule. 1
NPSPEC: An Executable Specification Language for Solving All Problems in NP
 in NP. Computer Languages
, 2001
"... In this paper a logicbased specification language, called NPSPEC, is presented. The language is obtained by extending DATALOG through allowing a limited use of some secondorder predicates of predefined form. NPSPEC programs specify solutions to problems in a very abstract and concise way, and ar ..."
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Cited by 42 (5 self)
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In this paper a logicbased specification language, called NPSPEC, is presented. The language is obtained by extending DATALOG through allowing a limited use of some secondorder predicates of predefined form. NPSPEC programs specify solutions to problems in a very abstract and concise way, and are executable. In the present prototype they are compiled to PROLOG code, which is run to construct outputs. Secondorder predicates of suitable form allow to limit the size of search spaces in order to obtain reasonably efficient construction of problem solutions. NPSPEC expressive power is precisely characterized as to express exactly the problems in the class NP. The specification of several combinatorial problems in NPSPEC is shown, and the efficiency of the generated programs is evaluated.
Fuzzy Multiple Ordering Criteria for Examination Timetabling
 Selected Papers from the 5 th International Conference on the Practice and Theory of Automated Timetabling, to appear in Lecture Notes in Computer Science
, 2004
"... Ordering exams by simultaneously considering two ordering criteria using a fuzzy expert system is presented in this paper. Combinations of two of the three ordering criteria largest degree, saturation degree and largest enrollment are considered. The fuzzy weight of an exam is used to represent ..."
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Cited by 40 (23 self)
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Ordering exams by simultaneously considering two ordering criteria using a fuzzy expert system is presented in this paper. Combinations of two of the three ordering criteria largest degree, saturation degree and largest enrollment are considered. The fuzzy weight of an exam is used to represent how difficult it is to schedule. The decreasingly ordered exams are sequentially chosen to be assigned to the last slot with least penalty cost value while the feasibility of the timetable is maintained throughout the process. Unscheduling and rescheduling exams is performed until all exams are scheduled. The proposed algorithm has been tested on 12 benchmark examination timetabling datasets and the results show that this approach can produce good quality solutions. Moreover, there is significant potential to extend the approach by including a larger range of criteria.
A MAXMIN Ant System for the University Course Timetabling Problem
 in Proceedings of the 3rd International Workshop on Ant Algorithm, ANTS 2002, Lecture Notes in Computer Science
, 2002
"... We consider a simplification of a typical university course timetabling problem involving three types of hard and three types of soft constraints. A MAXMIN Ant System, which makes use of a separate local search routine, is proposed for tackling this problem. We devise an appropriate construction gr ..."
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Cited by 35 (0 self)
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We consider a simplification of a typical university course timetabling problem involving three types of hard and three types of soft constraints. A MAXMIN Ant System, which makes use of a separate local search routine, is proposed for tackling this problem. We devise an appropriate construction graph and pheromone matrix representation after considering alternatives. The resulting algorithm is tested over a set of eleven instances from three classes of the problem. The results demonstrate that the ant system is able to construct significantly better timetables than an algorithm that iterates the local search procedure from random starting solutions.
Multilevel Refinement for Combinatorial Optimisation Problems
 SE10 9LS
, 2001
"... Abstract. We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found (some ..."
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Cited by 31 (5 self)
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Abstract. We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found (sometimes for the original problem, sometimes the coarsest) and then iteratively refined at each level. As a general solution strategy, the multilevel paradigm has been in use for many years and has been applied to many problem areas (most notably in the form of multigrid techniques). However, with the exception of the graph partitioning problem, multilevel techniques have not been widely applied to combinatorial optimisation problems. In this paper we address the issue of multilevel refinement for such problems and, with the aid of examples and results in graph partitioning, graph colouring and the travelling salesman problem, make a case for its use as a metaheuristic. The results provide compelling evidence that, although the multilevel framework cannot be considered as a panacea for combinatorial problems, it can provide an extremely useful addition to the combinatorial optimisation toolkit. We also give a possible explanation for the underlying process and extract some generic guidelines for its future use on other combinatorial problems.
A Deductive and ObjectOriented Approach to a Complex Scheduling Problem
 Proc. of DOOD'93
, 1993
"... . This paper presents the application of combined deductive and objectoriented technologies to a complex scheduling (timetable) problem. This approach emphasizes local propagation of constraints, which we perform with deductive rules, and combines it with global pruning heuristics, which we represe ..."
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Cited by 28 (6 self)
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. This paper presents the application of combined deductive and objectoriented technologies to a complex scheduling (timetable) problem. This approach emphasizes local propagation of constraints, which we perform with deductive rules, and combines it with global pruning heuristics, which we represent with methods (in a procedural manner) attached to objects. Because both components are essential to ensure success, we see this scheduling application as an interesting demonstration of the synergy between objectoriented and deductive technology. We provide a precise description of the problem, discuss what makes it difficult, and present detailed techniques that we used for its resolution. 1. Introduction Timetable scheduling problems (e.g., course scheduling for universities [Car86]) are common problems that are usually solved by adhoc algorithms packaged as dedicated software. Such problems are not only difficult from a theoretical perspective (most of them are NPhard problems) but...