School Timetabling Research Articles

GOAL solver: a hybrid local search based solver for high school timetabling

This work presents a local search approach to the High School Timetabling Problem. The addressed timetabling model is the one stated in the Third International Timetabling Competition (ITC 2011), which considered many instances from educational institutions around the world and attracted seventeen competitors. Our team, named GOAL (Group of Optimization and Algorithms), developed a solver built upon the Kingston High School Timetabling Engine. Several neighborhood structures were developed and used in a hybrid metaheuristic based on Simulated Annealing and Iterated Local Search. The developed algorithm was the winner of the competition and produced the best known solutions for almost all instances.

A review of hyper-heuristics for educational timetabling

Educational timetabling problems, namely, university examination timetabling, university course timetabling and school timetabling, are combinatorial optimization problems requiring the allocation of resources so as to satisfy a specified set of constraints. Hyper-heuristics have been successfully applied to a variety of combinatorial optimization problems. This is a rapidly growing field which aims at providing generalized solutions to combinatorial optimization problems by exploring a heuristic space instead of a solution space. From the research conducted thus far it is evident that hyper-heuristics are effective at solving educational timetabling problems and have the potential of advancing this field by providing a generalized solution to educational timetabling as a whole. Given this, the paper provides an overview and critical analysis of hyper-heuristics for educational timetabling and proposes future research directions, focusing on using hyper-heuristics to provide a generalized solution to educational timetabling.

A fix-and-optimize heuristic for the high school timetabling problem

The high school timetabling is a classical combinatorial optimization problem that takes a large number of variables and constraints into account. Due to its combinatorial nature, solving medium and large instances to optimality is a challenging task. When resources are tight, it is often difficult to find even a feasible solution. Among the different requirements that are considered in Brazilian schools, two compactness requirements must be met on a teacher׳s schedule: the minimization of working days and the avoidance of idle timeslots. In this paper, we present a mixed integer linear programming model and a fix-and-optimize heuristic combined with a variable neighborhood descent method. Our method uses three different types of decompositions - class, teacher and day – in order to solve the high school timetabling problem. The method is able to find new best known solutions for seven instances, including three optimal ones. A comparison with results reported in the literature shows that the proposed fix-and-optimize heuristic outperforms state-of-the-art techniques for the resolution of the problem at hand.

Feasibility of school-based computer-assisted robotic gaming technology for upper limb rehabilitation of children with cerebral palsy

Introduction: We investigated the feasibility of using computer-assisted arm rehabilitation (CAAR) computer games in schools. Outcomes were children's preference for single player or dual player mode, and changes in arm activity and kinematics. Method: Nine boys and two girls with cerebral palsy (6–12 years, mean 9 years) played assistive technology computer games in single-user mode or with school friends in an AB–BA design. Preference was determined by recording the time spent playing each mode and by qualitative feedback. We used the ABILHAND-kids and Canadian Occupational Performance Measure to evaluate activity limitation, and a portable laptop-based device to capture arm kinematics. Results: No difference was recorded between single-user and dual-user modes (median daily use 9.27 versus 11.2 min, p = 0.214). Children reported dual-user mode was preferable. There were no changes in activity limitation (ABILHAND-kids, p = 0.424; COPM, p = 0.484) but we found significant improvements in hand speed (p = 0.028), smoothness (p = 0.005) and accuracy (p = 0.007). Conclusion: School timetables prohibit extensive use of rehabilitation technology but there is potential for its short-term use to supplement a rehabilitation program. The restricted access to the rehabilitation games was sufficient to improve arm kinematics but not arm activity.Implications for RehabilitationSchool premises and teaching staff present no obstacles to the installation of rehabilitation gaming technology.Twelve minutes per day is the average amount of time that the school time table permits children to use rehabilitation gaming equipment (without disruption to academic attendance).The use of rehabilitation gaming technology for an average of 12 minutes daily does not appear to benefit children's functional performance, but there are improvements in the kinematics of children's upper limb.

A stochastic local search algorithm with adaptive acceptance for high-school timetabling

Automating high school timetabling is a challenging task. This problem is a well known hard computational problem which has been of interest to practitioners as well as researchers. High schools need to timetable their regular activities once per year, or even more frequently. The exact solvers might fail to find a solution for a given instance of the problem. A selection hyper-heuristic can be defined as an easy-to-implement, easy-to-maintain and effective ‘heuristic to choose heuristics’ to solve such computationally hard problems. This paper describes the approach of the team hyper-heuristic search strategies and timetabling (HySST) to high school timetabling which competed in all three rounds of the third international timetabling competition. HySST generated the best new solutions for three given instances in Round 1 and gained the second place in Rounds 2 and 3. It achieved this by using a fairly standard stochastic search method but significantly enhanced by a selection hyper-heuristic with an adaptive acceptance mechanism.

Phronesis and moral education: Treading beyond the truisms

Whereas most latter-day Aristotelian approaches to moral education highlight the early habituation phase of moral development, they rarely have much to say, beyond truisms from the Nicomachean ethics, about the ultimate Aristotelian goal of cultivating fully fledged phronesis. The aim of this article is to repair the dearth of attention given to phronesis in moral education circles and to bring considerations from other, but related, discourses (such as general Aristotelian scholarship and wisdom studies in psychology) to bear on it. I pay special attention to the so-called skill analogy, which considers virtue acquisition on par with the acquisition of ordinary practical skills, but argue that current articulations of it fail to account fully for the integrative, as distinct from the constitutive, function of phronesis. I argue that the skill analogy needs to be extended to account for the fact that in order to develop fully, phronesis requires direct teaching about the nature of the well-rounded life, providing the learner with an indirect blueprint for eudaimonia. Such a blueprint cannot eschew consequentialist considerations, and to be taught well within current school systems, it needs a discrete place in the school timetable.

Active Leisure

The philosophy of education of the first Jesuits—as delineated in the Ratio studiorum (1599) and embodied in the colleges’ practices—has become one of the preferred topics among historians of sixteenth-century education and philosophy. This paper seeks to present a heretofore rather neglected aspect of Jesuit education theory: the treatment of the body in the network of colleges during the first fifty years of the Society of Jesus. Among the key features of this treatment one finds leisure and rest, which Jesuits conceived as a means of measuring and punctuating the school timetable. While most medieval colleges did not usually leave much free time to their students, the Jesuits viewed leisure and rest as crucial for fostering spiritual and intellectual activities. Leisure and rest, however, ought not be understood as a cessation of action. This paper shows that the educational practices addressed to the body in the Jesuit colleges (such as the alternation of exercise and rest, the alternation of waking and sleep, the relationship between hygiene and the care of the body, and physical education) were deeply rooted in the Ignatian culture of the Spiritual Exercises. This experience stands out as one of most ingenious attempts to transform religious mystical practices from the medieval tradition in a manner that would make them resonate with the early modern way of life.

A Constraint‐Based Dental School Timetabling System

We describe a constraint‐based timetabling system that was developed for the dental school based at Cork University Hospital in Ireland. This system has been deployed since 2010. Dental school timetabling differs from other university course scheduling in that certain clinic sessions can be used by multiple courses at the same time, provided a limit on room capacity is satisfied. Starting from a constraint‐programming solution using a web interface, we have moved to a mixed integer programming‐based solver to deal with multiple objective functions, along with a dedicated Java application, which provides a rich user interface. Solutions for the years 2010, 2011, and 2012 have been used in the dental school, replacing a manual timetabling process, which could no longer cope with increasing student numbers and resulting resource bottlenecks. The use of the automated system allowed the dental school to increase the number of students enrolled to the maximum possible given the available resources. It also provides the school with a valuable “what‐if” analysis tool.

Variable Neighborhood Search based algorithms for high school timetabling

This work presents the application of Variable Neighborhood Search (VNS) based algorithms to the High School Timetabling Problem. The addressed model of the problem was proposed by the Third International Timetabling Competition (ITC 2011), which released many instances from educational institutions around the world and attracted 17 competitors. Some of the VNS algorithm variants were able to outperform the winner of Third ITC solver, which proposed a Simulated Annealing – Iterated local Search approach. This result coupled with another reports in the literature points that VNS based algorithms are a practical solution method for providing high quality solutions for some hard timetabling problems. Moreover they are easy to implement with few parameters to adjust.

Delivering Civic Education in Hong Kong: Why is it Not an Independent Subject?

Internationally there have been serious efforts to identify effective modes of delivering civic education for preparing youth for the future challenges of citizenship. This article addresses the research question, ‘why is an independent subject not preferred in civic education by Hong Kong civic education teachers?’. It starts with a brief review of international debates and of the development of civic education policy in Hong Kong. Then it moves on to discuss why teachers tend to reject civic education as an independent subject based on the findings from an interview informed research study. The findings reveal that teachers' misunderstandings of the nature of civic education are the major reasons. Treating civic education as comprising educational activities involving the nurturing of attitudes, values and skills of students with little content knowledge, the teachers consider that civic education is best accomplished through, for example, extra-curricular activities and not as a subject that demands time slots in the school timetable. It is argued that these misunderstandings will have negative impacts on the effectiveness of civic education, which is unfavourable to the nurturing of democratic cultures necessary for the development of the democratic system in Hong Kong and has to be rectified. Lastly, some recommendations for rectification that relate to civil society are discussed. Hopefully, this article can shed light on the understanding of the preferences towards the modes of implementation of front line practitioners in schools internationally, since this phenomenon is common in some other nations.

A graph edge colouring approach for school timetabling problems

School timetabling problems require weekly scheduling of lectures for subjects between teachers and classes in fixed time periods such that a set of constraints are satisfied. In this paper, a school timetabling problem is solved using a graph edge coloring algorithm in two phases. A bipartite multigraph is used in the first phase to get daily requirement matrices for each day of the week from weekly requirement matrix obtained by solving a system of linear equations for the variables taking integer values. Next, bipartite graphs are used in the second phase to assign lectures over unconstrained time slots for each day. The algorithm is tested on a number of randomly generated data sets and a timetable for a simple data set is given. The performance of the algorithm measured in terms of the number of iterations required and amount of CPU time in seconds is summarised in a table.

The PEAST algorithm - the key to optimising workforce management and professional sports league schedules

This paper summarises our work with real-world workforce scheduling and professional sports league scheduling. Furthermore, the paper presents a computational intelligence method called the PEAST algorithm. The algorithm has been used to solve school timetabling problems, many different workforce management problems and several sports scheduling problems. The algorithm has been integrated into market-leading workforce management software in Finland and it is used to generate the schedule for the Finnish Major Ice Hockey League.

Repairing high school timetables with polymorphic ejection chains

This paper introduces polymorphic ejection chains, and applies them to the problem of repairing time assignments in high school timetables while preserving regularity. An ejection chain is a sequence of repairs, each of which removes a defect introduced by the previous repair. Just as the elements of a polymorphic list may have different types, so in a polymorphic ejection chain the individual repairs may have different types. Methods for the efficient realization of these ideas, implemented in the author’s KHE framework, are given, and some initial experiments are presented.

A Two-Stage Decomposition of High School Timetabling applied to cases in Denmark

Integer Programming (IP) has been used to model educational timetabling problems since the very early days of Operations Research. It is well recognized that these IP models in general are hard to solve, and this area of research is dominated by heuristic solution approaches. In this paper a Two-Stage Decomposition of an IP model for a practical case of high school timetabling is shown. This particular timetabling problem consists of assigning lectures to both a timeslot and a classroom, which is modeled using a very large amount of binary variables. The decomposition splits this model into two separate problems (Stage I and Stage II) with far less variables. These two separate problems are solved in sequence, such that the solution for the Stage I model is given as input to the Stage II model, implying that irreversible decisions are made in Stage I. However, the objective of the Stage II model is partly incorporated in the Stage I model by exploiting that Stage II can be seen as a minimum weight maximum matching problem in a bipartite graph. This theoretically strengthens the decomposition in terms of global optimality. The approach relies on Hall's theorem for the existence of matchings in bipartite graphs, which in its basic form yields an exponential amount of constraints in the Stage I model. However, it is shown that only a small subset of these constraints is needed, making the decomposition tractable in practice for IP solvers. To evaluate the decomposition, 100 real-life problem instances from the database of the high school ERP system Lectio are used. Computational results show that the decomposition performs significantly better than solving the original IP, in terms of both found solutions and bounds.

Do we really know the composition of our foods?

We are currently witnessing important changes in the feeding patterns of the world population, especially in developing countries. These changes are leading to higher incidence of overweight, obesity, and non-communicable chronic diseases. These changes are influenced by a series of factors regarding the food, the individual, and the environment, which determine the selection of foods to buy and consume. The knowledge of our foods, such as their composition and the technological and cooking processes, among others, is important given their impact on the nutritional status and health. One of the key steps in the decision of what foods we incorporate to our diet is the time spent for shopping. Therefore, it would be important to develop standardized and computerized systems for food classification that connected to databases of foods composition could bring real time information about nutrients and energy content, as well as other food components. The most developed system so far is Lan guaL ("Langua aLimentaria"). We should also be knowledgeable on how cooking modifies not only the orosensorial properties but also the nutritional and health aspects of foods. Nowadays it is almost essential to also be informed about the foods we consume out of our homes, such as in collective canteens or restaurants given the work and school timetables, as well as leisure time.

A Tabu Search Algorithm With Efficient Diversification Strategy for High School Timetabling Problem

The school timetabling problem can be described as scheduling a set of lessons (combination of classes, teachers, subjects and rooms) in a weekly timetable. This paper presents a novel way to generate timetables for high schools. The algorithm has three phases. Pre-scheduling, initial phase and optimization through tabu search. In the first phase, a graph based algorithm used to create groups of lessons to be scheduled simultaneously; then an initial solution is built by a sequential greedy heuristic. Finally, the solution is optimized using tabu search algorithm based on frequency based diversification. The algorithm has been tested on a set of real problems gathered from Iranian high schools. Experiments show that the proposed algorithm can effectively build acceptable timetables.

Change and Development: A Case Study of the Implementation of Mandarin Chinese into the UK School Timetable

Change and Development: A Case Study of the Implementation of Mandarin Chinese into the UK School Timetable

A greedy gradient-simulated annealing selection hyper-heuristic

Educational timetabling problem is a challenging real world problem which has been of interest to many researchers and practitioners. There are many variants of this problem which mainly require scheduling of events and resources under various constraints. In this study, a curriculum based course timetabling problem at Yeditepe University is described and an iterative selection hyper-heuristic is presented as a solution method. A selection hyper-heuristic as a high level methodology operates on the space formed by a fixed set of low level heuristics which operate directly on the space of solutions. The move acceptance and heuristic selection methods are the main components of a selection hyper-heuristic. The proposed hyper-heuristic in this study combines a simulated annealing move acceptance method with a learning heuristic selection method and manages a set of low level constraint oriented heuristics. A key goal in hyper-heuristic research is to build low cost methods which are general and can be reused on unseen problem instances as well as other problem domains desirably with no additional human expert intervention. Hence, the proposed method is additionally applied to a high school timetabling problem, as well as six other problem domains from a hyper-heuristic benchmark to test its level of generality. The empirical results show that our easy-to-implement hyper-heuristic is effective in solving the Yeditepe course timetabling problem. Moreover, being sufficiently general, it delivers a reasonable performance across different problem domains.

The Deployment of a Constraint-Based Dental School Timetabling System

We describe a constraint-based timetabling system that was developed for the dental school based at Cork University Hospital in Ireland. This system has been deployed since 2010. Dental school timetabling differs from other university course scheduling in that certain clinic sessions can be used by multiple courses at the same time, provided a limit on room capacity is satisfied. Starting from a constraint programming solution using a web interface, we have moved to a mixed integer programming-based solver to deal with multiple objective functions, along with a dedicated Java application, which provides a rich user interface. Solutions for the years 2010, 2011 and 2012 have been used in the dental school, replacing a manual timetabling process, which could no longer cope with increasing student numbers and resulting resource bottlenecks. The use of the automated system allowed the dental school to increase student numbers to the maximum possible given the available resources. It also provides the school with a valuable “what-if” analysis tool.

Tiempos escolares y conciliación: análisis de familias con hijos en Educación Secundaria Obligatoria (12-16 años)

The aim of this study was to explore the impact of a number of factors on parents´ work-life balance, such as the socio-demographic context, school timetables, and family co-responsibility in tasks pertaining to children’s schooling. A sample of 859 Galician families with children in secondary education (12-16 years old) completed a self-administered questionnaire on time management. The results showed that work-life balance may be influenced by family structure, parents´ employment status, and children’s age. The worst work-life balance was associated with low levels of satisfaction with school schedules and holiday distribution. Also, there was a low level of co-responsibility in tasks pertaining to children’s schooling, being mostly women the ones in charge of tasks. Co-responsibility was positively related to work-life balance when tasks demand day-to-day participation.