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2003 | Buch

Constraints of Availability in Timetabling and Scheduling Kapitel lesen Erstes Kapitel lesen

Practice and Theory of Automated Timetabling IV

4th International Conference, PATAT 2002, Gent, Belgium, August 21-23, 2002. Selected Revised Papers

herausgegeben von: Edmund Burke, Patrick De Causmaecker

Verlag: Springer Berlin Heidelberg

Buchreihe : Lecture Notes in Computer Science

Enthalten in: Professional Book Archive

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Thisvolumecontainsaselectionofpapersfromthe4thInternationalConference on the Practice and Theory of Automated Timetabling (PATAT 2002) held in Gent, August 21–23, 2002. Since the ?rst conference in Edinburgh in 1995, the range of timetabling applications at the conferences has become broader and more diverse. In the s- ected papers volume from the 1995 conference, there were just two contributions (out of 22) which did not speci?cally address school and university timetabling. In the selected papers volume from the 1997 conference in Toronto, the number of papers which tackled non-educational problems increased. Two of the papers addressed more than one timetabling application. In both of these papers, educational applications were considered in addition to other applications. A further three papers were concerned with non-educational applications. The conference steering and programme committees have worked hard to attract a wide range of timetabling applications. In the conference held in Konstanz in 2000, the diversi?cation of timetabling problems increased signi?cantly. Of the 21 selected papers in the postconference volume, just 13 were speci?cally concerned with educational timetabling. In the previous volumes, the papers had been sectioned according to solution technique. In the Konstanz volume the papers were classi?ed according to application domains. One section of the volume was entitled “Employee Timetabling,” while sports timetabling, air?eet scheduling, and general software architectures for timetabling were also represented. In the present volume, more than one-third of the 21 papers discuss problems in application areas other than academic and educational ones. Sports timetabling and hospital timetabling are particularly well represented.

Inhaltsverzeichnis

Frontmatter

General Issues

Frontmatter
Constraints of Availability in Timetabling and Scheduling
Abstract
The basic class–teacher timetabling problem is examined with the additional constraints due to the (un-)availability of source teachers and/or classes at some periods. We mention a generalization of this problem which occurs in image reconstruction problems in tomography. Complexity issues are discussed for both types of problems and some solvable cases are presented which can be derived from the image reconstruction formulation. Reductions to canonical forms are also described. Some other types of unavailability constraints (for classrooms or for lectures) are also reviewed.
Dominique de Werra
A Standard Framework for Timetabling Problems
Abstract
When timetabling experts are faced with a new timetabling problem, they usually develop a very specialised and optimised solution for this new underlying problem.
One disadvantage of this strategy is that even slight changes of the problem description often cause a complete redesign of data structures and algorithms. Furthermore, other timetabling problems cannot be fit to the data structures provided.
To avoid this, we have developed a standardised framework which can describe arbitrary timetabling problems such as university timetabling, examination timetabling, school timetabling, sports timetabling or employee timetabling. Thus, a general timetabling language has been developed which enables the definition of resources, events and constraints.
Furthermore, we provide a way to apply standard problem solving methods such as branch-and-bound or genetic algorithms to timetabling problems defined by means of the general timetabling language. These algorithms can be improved by problem-specific user-defined hybrid operators.
In this paper we present a generalised view on timetabling problems from which we derive our timetabling framework. The framework implementation and its application possibilities are shown with some concrete examples. The paper concludes with some preliminary results and an outlook.
Matthias Gröbner, Peter Wilke, Stefan Büttcher
Solving Dynamic Resource Constraint Project Scheduling Problems Using New Constraint Programming Tools
Abstract
Timetabling problems have been much studied over the last decade. Due to the complexity and the variety of such problems, most work concerns static problems in which activities to schedule and resources are known in advance, and constraints are fixed. However, every timetabling problem is subject to unexpected events (for example, for university timetabling problems, a missing teacher, or a slide projector breakdown). In such a situation, one has to quickly build a new solution which takes these events into account and which is preferably not too different from the current one. We introduce in this paper constraint-programming-based tools for solving dynamic timetabling problems modelled as Resource-Constrained Project Scheduling Problems. This approach uses explanation-based constraint programming and operational research techniques.
Abdallah Elkhyari, Christelle Guéret, Narendra Jussien

Sports Timetabling

Frontmatter
Integer and Constraint Programming Approaches for Round-Robin Tournament Scheduling
Abstract
Real sports scheduling problems are difficult to solve due to the variety of different constraints that might be imposed. Over the last decade, through the work of a number of researchers, it has become easier to solve round-robin tournament problems. These tournaments can then become building blocks for more complicated schedules. For example, we have worked extensively with Major League Baseball on creating “what-if” schedules for various league formats. Success in providing those schedules has depended on breaking the schedule into easily solvable pieces. Integer programming and constraint programming methods each have their places in this approach, depending on the constraints and objective function.
Michael A. Trick
Characterizing Feasible Pattern Sets with a Minimum Number of Breaks
Abstract
In sports timetabling, creating an appropriate timetable for a round-robin tournament with home–away assignment is a significant problem. To solve this problem, we need to construct home–away assignment that can be completed into a timetable; such assignment is called a feasible pattern set. Although finding feasible pattern sets is at the heart of many timetabling algorithms, good characterization of feasible pattern sets is not known yet. In this paper, we consider the feasibility of pattern sets, and propose a new necessary condition for feasible pattern sets. In the case of a pattern set with a minimum number of breaks, we prove a theorem leading a polynomial-time algorithm to check whether a given pattern set satisfies the necessary condition. Computational experiment shows that, when the number of teams is less than or equal to 26, the proposed condition characterizes feasible pattern sets with a minimum number of breaks.
Ryuhei Miyashiro, Hideya Iwasaki, Tomomi Matsui
Solving the Travelling Tournament Problem: A Combined Integer Programming and Constraint Programming Approach
Abstract
The Travelling Tournament Problem is a sports timetabling problem requiring production of a minimum distance double round-robin tournament for a group of n teams. Even small instances of this problem seem to be very difficult to solve. In this paper, we present the first provably optimal solution for an instance of eight teams. The solution methodology is a parallel implementation of a branch-and-price algorithm that uses integer programming to solve the master problem and constraint programming to solve the pricing problem. Additionally, constraint programming is used as a primal heuristic.
Kelly Easton, George Nemhauser, Michael Trick

Employee Timetabling

Frontmatter
Personnel Scheduling in Laboratories
Abstract
We describe an assignment problem particular to the personnel scheduling of organisations such as laboratories. Here we have to assign tasks to employees. We focus on the situation where this assignment problem reduces to constructing maximal matchings in a set of interrelated bipartite graphs. We describe in detail how the continuity of tasks over the week is achieved to suit the wishes of the planner. Finally, we discuss the implementation of the algorithm in the package IPS. Its main characteristic is the introduction of profiles, which easily allows the user to steer the algorithm.
Philip Franses, Gerhard Post
Scheduling Doctors for Clinical Training Unit Rounds Using Tabu Optimization
Abstract
Hospitals must be staffed 24 hours a day, seven days a week by teams of doctors having certain combinations of skills. The construction of schedules for these doctors and the medical students who work with them is known to be a difficult NP-complete problem known as personnel scheduling, employee timetabling, labour scheduling or rostering. We have constructed a program that uses a constraint logic formalism to enforce certain scheduling rules followed by a tabu search heuristic optimizing algorithm to produce a call schedule that is used at the Ottawa Hospital. This call schedule can be later changed by the chief resident to accommodate last-minute personnel changes by means of a spreadsheet-based program.
Christine A. White, George M. White
Relaxation of Coverage Constraints in Hospital Personnel Rostering
Abstract
Hospital personnel scheduling deals with a large number of constraints of a different nature, some of which need to be satisfied at all costs. It is, for example, unacceptable not to fully support patient care needs and therefore a sufficient number of skilled personnel has to be scheduled at any time. In addition to personnel coverage constraints, nurse rostering problems deal with time-related constraints arranging work load, free time, and personal requests for the staff.
Real-world nurse rostering problems are usually over-constrained but schedulers in hospitals manage to produce solutions anyway. In practice, coverage constraints, which are generally defined as hard constraints, are often relaxed by the head nurse or personnel manager.
The work presented in this paper builds upon a previously developed nurse rostering system that is used in several Belgian hospitals. In order to deal with widely varying problems and objectives, all the data in the model are modifiable by the users.
We introduce a set of specific algorithms for handling and even relaxing coverage constraints, some of which were not supposed to be violated in the original model. The motivation is that such practices are common in real scheduling environments. Relaxations enable the generation of better-quality schedules without enlarging the search space or the computation time.
Patrick De Causmaecker, Greet Vanden Berghe
Storing and Adapting Repair Experiences in Employee Rostering
Abstract
The production of effective workforce rosters is a common management problem. Rostering problems are highly constrained and require extensive experience to solve manually. The decisions made by expert rosterers are often subjective and are difficult to represent systematically. This paper presents a formal description of a new technique for capturing rostering experience using case-based reasoning methodology. Examples of previously encountered constraint violations and their corresponding repairs are used to solve new rostering problems. We apply the technique to real-world data from a UK hospital.
Sanja Petrovic, Gareth Beddoe, Greet Vanden Berghe
Scheduling Agents – Distributed Timetabling Problems
Abstract
Many real-world Timetabling Problems are composed of organizational parts that need to timetable their staff in an independent way, while adhering to some global constraints. Later, the departmental timetables are combined to yield a coherent, consistent solution. This last phase involves negotiations with the various agents and requests for changes in their own solutions.
Most of the real-world distributed timetabling problems that fall into this class have global constraints that involve many of the agents in the system. Models that use networks of binary constraints are inadequate. As a result, this paper proposes a new model that contains only one additional agent: the Central Agent that coordinates the search process of all Scheduling Agents (SAs). Preliminary experiments show that a sophisticated heuristic is needed for the CA to effectively interact with its scheduling agents in order to find an optimal solution. The approach and the results reported in this paper are an initial attempt to investigate possible solution methods for networks of SAs.
Amnon Meisels, Eliezer Kaplansky

Examination Timetabling

Frontmatter
A Multiobjective Optimisation Technique for Exam Timetabling Based on Trajectories
Abstract
The most common approach to multiobjective examination timetabling is the weighted sum aggregation of all criteria into one cost function and application of some single-objective metaheuristic. However, the translation of user preferences into the weights of criteria is a sophisticated task, which requires experience on the part of the user, especially for problems with a high number of criteria. Moreover, the results produced by this technique are usually substantially scattered. Thus, the outcome of weighted sum algorithms is often far from user expectation.
In this paper we suggest a more transparent method, which enables easier expression of user preferences. This method requires the user to specify a reference solution, which can be either produced manually or chosen among the set of solutions, generated by any automated method. Our aim is to improve the values of the reference objectives, i.e. to produce a solution which dominates the reference one. In order to achieve this, a trajectory is drawn from the origin to the reference point and a Great Deluge local search is conducted through the specified trajectory. During the search the weights of the criteria are dynamically changed.
The proposed technique was experimentally tested on real-world exam timetabling problems on both bi-criteria and nine-criteria cases. All results obtained by the variable weights Great Deluge algorithm outperformed the ones published in the literature by all criteria.
Sanja Petrovic, Yuri Bykov
Enhancing Timetable Solutions with Local Search Methods
Abstract
It is well known that domain-specific heuristics can produce good-quality solutions for timetabling problems in a short amount of time. However, they often lack the ability to do any thorough optimisation. In this paper we will study the effects of applying local search techniques to improve good-quality initial solutions generated using a heuristic construction method. While the same rules should apply to any heuristic construction, we use here an adaptive approach to timetabling problems. The focus of the experiments is how parameters to the local search methods affect quality when started on already good solutions. We present experimental results which show that this combined approach produces the best published results on several benchmark problems and we briefly discuss the implications for future work in the area.
E. K. Burke, J. P. Newall
A Hybrid Algorithm for the Examination Timetabling Problem
Abstract
Examination timetabling is a well-studied combinatorial optimization problem. We present a new hybrid algorithm for examination timetabling, consisting of three phases: a constraint programming phase to develop an initial solution, a simulated annealing phase to improve the quality of solution, and a hill climbing phase for further improvement. The examination timetabling problem at the University of Melbourne is introduced, and the hybrid method is proved to be superior to the current method employed by the University. Finally, the hybrid method is compared to established methods on the publicly available data sets, and found to perform well in comparison.
Liam T. G. Merlot, Natashia Boland, Barry D. Hughes, Peter J. Stuckey
GRASPing the Examination Scheduling Problem
Abstract
This paper presents a Greedy Randomised Adaptive Search Procedure for solving the examination scheduling problem. GRASP is a two-phased multi-start or iterative method consisting of a construction phase and an improvement phase. Each iteration builds a feasible solution using a probabilistic selection procedure, and then optimises the solution using a local search technique.
Stephen Casey, Jonathan Thompson

University Course and School Timetabling

Frontmatter
Search Strategy for Constraint-Based Class–Teacher Timetabling
Abstract
The paper deals with a scheduling problem: the computation of class–teacher timetables. Two cases are taken into consideration: high school problems and university department problems. The timetable was constructed using constraint programming techniques. The timetabling needs to take into account a variety of complex constraints and use special-purpose search strategies. The concurrent constraint language Mozart/Oz was used, which provides high-level abstraction, and allows the expression of complex constraints and the creation of a complicated, custom-tailored distribution strategy. This strategy, consisting of six stages, was crucial for finding a feasible solution. The space-based search allows the incorporation of local search into constraint programming; this is very useful for timetable optimization. Technical details and results of the implementation are presented.
Wojciech Legierski
Multi-neighbourhood Local Search with Application to Course Timetabling
Abstract
A recent trend in local search concerns the exploitation of several different neighbourhood functions so as to increase the ability of the algorithm to navigate the search space.
In this paper we investigate the use of local search techniques based on various combinations of neighbourhood functions, and we apply this to a timetabling problem. In particular, we propose a set of generic operators that automatically compose neighbourhood functions, giving rise to more complex ones. In the exploration of large neighbourhoods, we rely on constraint techniques to prune the list of candidates. In this way, we are able to select the most effective search technique through a systematic analysis of all possible combinations built upon a set of basic, human-defined, neighbourhood functions.
The proposed ideas are applied to a practical problem, namely the Course Timetabling problem. Our algorithms are systematically tested and compared on real-world instances. The experimental analysis shows that neighbourhood composition leads to much better results than traditional local search techniques.
Luca Di Gaspero, Andrea Schaerf
Knowledge Discovery in a Hyper-heuristic for Course Timetabling Using Case-Based Reasoning
Abstract
This paper presents a new hyper-heuristic method using Case-Based Reasoning (CBR) for solving course timetabling problems. The term hyper-heuristics has recently been employed to refer to “heuristics that choose heuristics” rather than heuristics that operate directly on given problems. One of the overriding motivations of hyper-heuristic methods is the attempt to develop techniques that can operate with greater generality than is currently possible. The basic idea behind this is that we maintain a case base of information about the most successful heuristics for a range of previous timetabling problems to predict the best heuristic for the new problem in hand using the previous knowledge. Knowledge discovery techniques are used to carry out the training on the CBR system to improve the system performance on the prediction. Initial results presented in this paper are good and we conclude by discussing the considerable promise for future work in this area.
E. K. Burke, B. L. MacCarthy, S. Petrovic, R. Qu
Generalizing Bipartite Edge Colouring to Solve Real Instances of the Timetabling Problem
Abstract
In this paper we introduce a new algorithm for secondary school timetabling, inspired by the classical bipartite graph edge colouring algorithm for basic class–teacher timetabling. We give practical methods for generating large sets of meetings that can be timetabled to run simultaneously, and for building actual timetables based on these sets. We report promising empirical results for one real-world instance of the problem.
David J. Abraham, Jeffrey H. Kingston
Flow Formulations for the Student Scheduling Problem
Abstract
We discuss the student scheduling problem as it generally applies to high schools in North America. We show that the problem is NP-hard. We discuss various multi-commodity flow formulations, with fractional capacities and integral gains, and we show how a number of practical objectives can be accommodated by the models.
Eddie Cheng, Serge Kruk, Marc Lipman
University Course Timetabling with Soft Constraints
Abstract
An extension of constraint logic programming that allows for weighted partial satisfaction of soft constraints is described and applied to the development of an automated timetabling system for Purdue University. The soft-constraint solver implemented in the proposed solution approach allows constraint propagation for hard constraints together with preference propagation for soft constraints. A new repair search algorithm is proposed to improve upon initially generated (partial) assignments of the problem variables. The model and search methods applied to the solution of the large lecture room component are presented and discussed along with the computational results.
Hana Rudová, Keith Murray
A Comparison of the Performance of Different Metaheuristics on the Timetabling Problem
Abstract
The main goal of this paper is to attempt an unbiased comparison of the performance of straightforward implementations of five different metaheuristics on a university course timetabling problem. In particular, the metaheuristics under consideration are Evolutionary Algorithms, Ant Colony Optimization, Iterated Local Search, Simulated Annealing, and Tabu Search. To attempt fairness, the implementations of all the algorithms use a common solution representation, and a common neighbourhood structure or local search. The results show that no metaheuristic is best on all the timetabling instances considered. Moreover, even when instances are very similar, from the point of view of the instance generator, it is not possible to predict the best metaheuristic, even if some trends appear when focusing on particular instance classes. These results underline the difficulty of finding the best metaheuristics even for very restricted classes of timetabling problem.
Olivia Rossi-Doria, Michael Sampels, Mauro Birattari, Marco Chiarandini, Marco Dorigo, Luca M. Gambardella, Joshua Knowles, Max Manfrin, Monaldo Mastrolilli, Ben Paechter, Luis Paquete, Thomas Stützle
Backmatter
Metadaten
Titel
Practice and Theory of Automated Timetabling IV
herausgegeben von
Edmund Burke
Patrick De Causmaecker
Copyright-Jahr
2003
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-540-45157-0
Print ISBN
978-3-540-40699-0
DOI
https://doi.org/10.1007/b11828