5,162 research outputs found
Decomposition, Reformulation, and Diving in University Course Timetabling
In many real-life optimisation problems, there are multiple interacting
components in a solution. For example, different components might specify
assignments to different kinds of resource. Often, each component is associated
with different sets of soft constraints, and so with different measures of soft
constraint violation. The goal is then to minimise a linear combination of such
measures. This paper studies an approach to such problems, which can be thought
of as multiphase exploitation of multiple objective-/value-restricted
submodels. In this approach, only one computationally difficult component of a
problem and the associated subset of objectives is considered at first. This
produces partial solutions, which define interesting neighbourhoods in the
search space of the complete problem. Often, it is possible to pick the initial
component so that variable aggregation can be performed at the first stage, and
the neighbourhoods to be explored next are guaranteed to contain feasible
solutions. Using integer programming, it is then easy to implement heuristics
producing solutions with bounds on their quality.
Our study is performed on a university course timetabling problem used in the
2007 International Timetabling Competition, also known as the Udine Course
Timetabling Problem. In the proposed heuristic, an objective-restricted
neighbourhood generator produces assignments of periods to events, with
decreasing numbers of violations of two period-related soft constraints. Those
are relaxed into assignments of events to days, which define neighbourhoods
that are easier to search with respect to all four soft constraints. Integer
programming formulations for all subproblems are given and evaluated using ILOG
CPLEX 11. The wider applicability of this approach is analysed and discussed.Comment: 45 pages, 7 figures. Improved typesetting of figures and table
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
Feature-based tuning of simulated annealing applied to the curriculum-based course timetabling problem
We consider the university course timetabling problem, which is one of the
most studied problems in educational timetabling. In particular, we focus our
attention on the formulation known as the curriculum-based course timetabling
problem, which has been tackled by many researchers and for which there are
many available benchmarks.
The contribution of this paper is twofold. First, we propose an effective and
robust single-stage simulated annealing method for solving the problem.
Secondly, we design and apply an extensive and statistically-principled
methodology for the parameter tuning procedure. The outcome of this analysis is
a methodology for modeling the relationship between search method parameters
and instance features that allows us to set the parameters for unseen instances
on the basis of a simple inspection of the instance itself. Using this
methodology, our algorithm, despite its apparent simplicity, has been able to
achieve high quality results on a set of popular benchmarks.
A final contribution of the paper is a novel set of real-world instances,
which could be used as a benchmark for future comparison
Operational Research in Education
Operational Research (OR) techniques have been applied, from the early stages of the discipline, to a wide variety of issues in education. At the government level, these include questions of what resources should be allocated to education as a whole and how these should be divided amongst the individual sectors of education and the institutions within the sectors. Another pertinent issue concerns the efficient operation of institutions, how to measure it, and whether resource allocation can be used to incentivise efficiency savings. Local governments, as well as being concerned with issues of resource allocation, may also need to make decisions regarding, for example, the creation and location of new institutions or closure of existing ones, as well as the day-to-day logistics of getting pupils to schools. Issues of concern for managers within schools and colleges include allocating the budgets, scheduling lessons and the assignment of students to courses. This survey provides an overview of the diverse problems faced by government, managers and consumers of education, and the OR techniques which have typically been applied in an effort to improve operations and provide solutions
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 8â28% 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
Railway timetabling from an operations research
In this paper we describe Operations Research (OR) models andtechniques that can be used for determining (cyclic) railwaytimetables. We discuss the two aspects of railway timetabling: ()the determination of arrival and departure times of the trains atthe stations and other relevant locations such as junctions andbridges, and () the assignment of each train to an appropriateplatform and corresponding inbound and outbound routes in everystation. Moreover, we discuss robustness aspects of bothsubproblems.
Aspects of computerised timetabling
This research considers the problem of constructing high school timetables using a
computer. In the majority of high schools, termly or yearly timetables are still
being produced manually. Constructing a timetable is a hard and time consuming
task which is carried out repeatedly thus a computer program for assisting with this
problem would be of great value. This study is in three parts. First. an overall
analysis of the problem is undertaken to provide background knowledge and to
identify basic principles in the construction of a school timetable. The
characteristics of timetabling problems are identified and the necessary data for the
construction of a timetable is identified. The first part ends with the production of
a heuristic model for generating an initial solution that satisfies all the hard
constraints embodied in the curriculum requirements.
The second stage of the research is devoted to designing a heuristic model for
solving a timetable problem with hard and medium constraints. These include
constraints like the various numbers of common periods, double periods and
reducing the repeated allocation of a subject within any day. The approaches taken
are based on two recently developed techniques, namely tabu search and simulated
annealing. Both of these are used and comparisons of their efficiency are
provided. The comparison is based on the percentage fulfilment of the hard and
medium requirements.
The third part is devoted to one of the most difficult areas in timetable
construction, that is the softer requirements which are specific to particular schools
and whose satisfaction is not seen as essential. This section describes the
development of an expert system based on heuristic production rules to satisfy a
range of soft requirements. The soft requirements are studied and recorded as
rules and a heuristic solution is produced for each of the general requirements.
Different levels of rule are developed, from which the best possible solution to a
particular timetable problem is expertly produced.
Finally, possible extensions of the proposed method and its application to other
types of the timetabling problem are discussed
A New Initialisation Method for Examination Timetabling Heuristics
This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.Timetabling problems are widespread, but are particularly prevalent in the educational domain. When sufficiently large, these are often only effectively tackled by timetabling meta-heuristics. The effectiveness of these in turn are often largely dependant on their initialisation protocols. There are a number of different initialisation approaches used in the literature for starting examination timetabling heuristics. We present a new iterative initialisation algorithm here --- which attempts to generate high-quality and legal solutions, to feed into a heuristic optimiser. The proposed approach is empirically verified on the ITC 2007 and Yeditepe benchmark sets. It is compared to popular initialisation approaches commonly employed in exam timetabling heuristics: the largest degree, largest weighted degree, largest enrollment, and saturation degree graph-colouring approaches, and random schedule allocation. The effectiveness of these approaches are also compared via incorporation in an exemplar evolutionary algorithm. The results show that the proposed method is capable of producing feasible solutions for all instances, with better quality and diversity compared to the alternative methods. It also leads to improved optimiser performance.Saudi Arabia Cultural Burea
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