An XML format for benchmarks in High School Timetabling

The High School Timetabling Problem is amongst the most widely used timetabling problems. This problem has varying structures in different high schools even within the same country or educational system. Due to lack of standard benchmarks and data formats this problem has been studied less than other timetabling problems in the literature. In this paper we describe the High School Timetabling Problem in several countries in order to find a common set of constraints and objectives. Our main goal is to provide exchangeable benchmarks for this problem. To achieve this we propose a standard data format suitable for different countries and educational systems, defined by an XML schema. The schema and datasets are available online

Cyclic transfers in school timetabling

In this paper we propose a neighbourhood structure based on sequential/cyclic moves and a cyclic transfer algorithm for the high school timetabling problem. This method enables execution of complex moves for improving an existing solution, while dealing with the challenge of exploring the neighbourhood efficiently. An improvement graph is used in which certain negative cycles correspond to the neighbours; these cycles are explored using a recursive method. We address the problem of applying large neighbourhood structure methods on problems where the cost function is not exactly the sum of independent cost functions, as it is in the set partitioning problem. For computational experiments we use four real world data sets for high school timetabling in the Netherlands and England.We present results of the cyclic transfer algorithm with different settings on these data sets. The costs decrease by 8–28% if we use the cyclic transfers for local optimization compared to our initial solutions. The quality of the best initial solutions are comparable to the solutions found in practice by timetablers

Cyclic transfers in school timetabling

In this paper we propose a neighbourhood structure based\ud on sequential/cyclic moves and a Cyclic Transfer algorithm for the high school timetabling problem. This method enables execution of complex moves for improving an existing solution, while dealing with the challenge of exploring the neighbourhood efficiently. An improvement graph is used in which certain negative cycles correspond to the neighbours; these cycles are explored using a recursive method. We address the problem of applying large neighbourhood structure methods on problems where the cost function is not exactly the sum of independent cost functions, as it is in the set partitioning problem. For computational experiments we use four real world datasets for high school timetabling in the Netherlands and England. We present results of the cyclic transfer algorithm with different settings on these datasets. The costs decrease by 8% to 28% if we use the cyclic transfers for local optimization compared to our initial solutions. The quality of the best initial solutions are comparable to the solutions found in practice by timetablers

A time-predefined approach to course timetabling

A common weakness of local search metaheuristics, such as Simulated Annealing, in solving combinatorial optimization problems, is the necessity of setting a certain number of parameters. This tends to generate a significant increase in the total amount of time required to solve the problem and often requires a high level of experience from the user. This paper is motivated by the goal of overcoming this drawback by employing "parameter-free" techniques in the context of automatically solving course timetabling problems. We employ local search techniques with "straightforward" parameters, i.e. ones that an inexperienced user can easily understand. In particular, we present an extended variant of the "Great Deluge" algorithm, which requires only two parameters (which can be interpreted as search time and an estimation of the required level of solution quality). These parameters affect the performance of the algorithm so that a longer search provides a better result - as long as we can intelligently stop the approach from converging too early. Hence, a user can choose a balance between processing time and the quality of the solution. The proposed method has been tested on a range of university course timetabling problems and the results were evaluated within an International Timetabling Competition. The effectiveness of the proposed technique has been confirmed by a high level of quality of results. These results represented the third overall average rating among 21 participants and the best solutions on 8 of the 23 test problems.

Solving Challenging Real-World Scheduling Problems

This work contains a series of studies on the optimization of three real-world scheduling problems, school timetabling, sports scheduling and staff scheduling. These challenging problems are solved to customer satisfaction using the proposed PEAST algorithm. The customer satisfaction refers to the fact that implementations of the algorithm are in industry use. The PEAST algorithm is a product of long-term research and development. The first version of it was introduced in 1998. This thesis is a result of a five-year development of the algorithm. One of the most valuable characteristics of the algorithm has proven to be the ability to solve a wide range of scheduling problems. It is likely that it can be tuned to tackle also a range of other combinatorial problems. The algorithm uses features from numerous different metaheuristics which is the main reason for its success. In addition, the implementation of the algorithm is fast enough for real-world use.Siirretty Doriast

School timetabling problem

Orientador: Antonio Carlos MorettiDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaMestradoMatematica AplicadaMestre em Matemática Aplicad

Effective computational models for timetabling problem

Timetabling is a table of information showing when certain events are scheduled to take place. Timetabling is in fact very essential in making sure that all events occur in the time and place required. It is critical in areas such as: education, production and manufacturing, sport competitions, transport and logistics. The difficulty in timetabling is satisfying all the restrictions and requirements. The restrictions relate to resources such as time and location as well as conflicts. The requirements relate to the preferences of customers and service providers. The problem is further complicated by the desire to optimize an objective function that usually relates to the cost or effectiveness of the schedule. The task of how to construct a high quality timetable which satisfies all requirements is definitely not an easy one. A further difficulty is the dynamic aspect of timetabling and the need to accommodate changes after the schedule has been announced. Our focus in this study is on university timetabling problems.Mathematically, the problem is to optimize an objective function that reflects the value of the schedule subject to a set of constraints that relate to various operational requirements and a range of resource constraints (lecturers, rooms, etc). The usual objective is to maximize the total preferences or to minimize the number of students affected by clashes. The problem can be conveniently expressed as an Integer Programming (IP) problem. The computational difficulty is due to the integer restrictions on the variables. Various computational models including both heuristics and exact methods have been proposed.The timetabling problem in universities courses has existed for a long time, but due to the complexity and its variation, many researchers are still trying to decipher the solution for this problem. Numerous methods have been developed over the years and most of them have been successful. However, according to McCollum (2006) based on the international review of Operational Research in the UK (Commissioned by the Engineering and Physical Sciences Research Council), a gap still exists between the theory and practice of timetabling. Additionally, Burke and Petrovic (2002) also mentioned that many methods that have succeeded in solving this problem are applicable to specific institutions where they are designed. Nevertheless, Benli and Botsali (2004) explained that there is no generalized model for this problem because of the variation present in each university. Moreover, the limited availability of facilities and growth of flexibility of the student’s choices of courses makes the problem even tighter.This thesis in whole outlines studies which gain a step in a pathway to develop a more general IP model for university course timetabling problem. We incorporate all important features of this problem which includes the hard constraints and the desirable soft constraints. AIMMS 3.11 mathematical software is employed as a tool to solve the models with CPLEX 12.1 as the solver.In the first study (Chapter 3), we aim to develop models for timetabling problems which are flexible in terms of the ability to be applied in various institutions. To achieve this, we gather the information obtained on features that are used in other studies, which is covered in the literature review (Chapter 2) of this thesis. From the information on the gathered features, we observed that some features are compulsory, being that they are always used in models to solve timetabling problems. These features therefore form a basic model of university course timetabling problem in this study. We then develop an extended model by incorporating additional features found from the literature. The extended model also contains a few more additional features which we generate that are significant to be included in a model for solving this problem.Different combinations of the features which form the extended model are extracted to produce a range of models. These models are useful to be used by any institutions which require some relevant features to solve their timetabling problem. These models are tested with a small randomly generated test problem. In the following chapter (Chapter 4), we apply the developed model into 3 case studies obtained from the literature. The objective of this is to test the efficiency of the developed models for application to larger problems. Appropriate variation models are used to solve each of the case studies. This application testing is further extended by including a number of additional features. This is to illustrate that the developed model is able to be applied in institutions even ivwhen changes of requirements occur. Results from these tests demonstrate successful outcomes from application of our developed models to the chosen case studies.In Chapter 5, we tested the application of the developed models application in a case study using a pre-assignment approach as a simplification in solving timetabling problem. In this approach, the core units are determined and prioritized to be assigned into prime time slots at the very beginning of the scheduling process. It then follows with the assignment of the remainder units subject to the university requirements. One case study which is applied in Chapter 4 is used for the purpose of testing the pre-assignment approach. From this testing, we show that the pre-assignment is a useful simplification tool in solving timetabling problem of the chosen case study using the developed model, especially in reducing the computational time. We believe that this approach can be applied in other case studies using the developed model.As an overview of the thesis, we believe that the developed models will be applicable to other problems apart from the ones tested

The Solution of Real Instances of the Timetabling Problem

This paper describes a computer program for high school timetabling which has completely solved an instance taken without simplification from a large and tightly constrained high school. A timetable specification language allows the program to handle the many idiosyncratic constraints of such instances in a uniform way. New algorithms are introduced which attack the problem more intelligently than traditional search methods. 10 August, The Solution of Real Instances of the Timetabling Problem Tim B. Cooper and Jeffrey H. Kingston Basser Department of Computer Science The University of Sydney 2006 Australia 1. Introduction The basic timetabling problem is to assign times, teachers, students, and rooms to a collection of classes and other meetings in such a way that none of the participants is required to attend two meetings simultaneously. Real instances can be very large, with hundreds of participants and hundreds of meetings squeezed into a week of about forty meeting times; and ..