Linear Combinations of Heuristics for Examination Timetabling

Although they are simple techniques from the early days of timetabling research, graph colouring heuristics are still attracting significant research interest in the timetabling research community. These heuristics involve simple ordering strategies to first select and colour those vertices that are most likely to cause trouble if deferred until later. Most of this work used a single heuristic to measure the difficulty of a vertex. Relatively less attention has been paid to select an appropriate colour for the selected vertex. Some recent work has demonstrated the superiority of combining a number of different heuristics for vertex and colour selection. In this paper, we explore this direction and introduce a new strategy of using linear combinations of heuristics for weighted graphs which model the timetabling problems under consideration. The weights of the heuristic combinations define specific roles that each simple heuristic contributes to the process of ordering vertices. We include specific explanations for the design of our strategy and present the experimental results on a set of benchmark real world examination timetabling problem instances. New best results for several instances have been obtained using this method when compared with other constructive methods applied to this benchmark dataset

Domain transformation approach to deterministic optimization of examination timetables

In this paper we introduce a new optimization method for the examinations scheduling problem. Rather than attempting direct optimization of assignments of exams to specific time-slots, we perform permutations of slots and reassignments of exams upon the feasible (but not optimal) schedules obtained by the standard graph colouring method with Largest Degree ordering. The proposed optimization methods have been evaluated on the University of Toronto, University of Nottingham and International Timetabling Competition (ITC2007) datasets. It is shown that the proposed method delivers competitive results compared to other constructive methods in the timetabling literature on both the Nottingham and Toronto datasets, and it maintains the same optimization pattern of the solution improvement on the ITC2007 dataset. A deterministic pattern obtained for all benchmark datasets, makes the proposed method more understandable to the users

Hybridising heuristics within an estimation distribution algorithm for examination timetabling

This paper presents a hybrid hyper-heuristic approach based on estimation distribution algorithms. The main motivation is to raise the level of generality for search methodologies. The objective of the hyper-heuristic is to produce solutions of acceptable quality for a number of optimisation problems. In this work, we demonstrate the generality through experimental results for different variants of exam timetabling problems. The hyper-heuristic represents an automated constructive method that searches for heuristic choices from a given set of low-level heuristics based only on non-domain-specific knowledge. The high-level search methodology is based on a simple estimation distribution algorithm. It is capable of guiding the search to select appropriate heuristics in different problem solving situations. The probability distribution of low-level heuristics at different stages of solution construction can be used to measure their effectiveness and possibly help to facilitate more intelligent hyper-heuristic search methods

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

Disminución de la mortalidad académica en instituciones de educación básica y media mediante el empleo de técnicas inteligentes en la asignación de horarios

Esta investigación plantea la solución del problema de programación de horarios escolares bajo las características de la escuela pública colombiana incluyendo como factor primordial dentro del proceso de optimización, la ubicación horaria de las asignaturas en función de los ritmos cognitivos que presentan los estudiantes durante la jornada escolar. Para ello, se presenta el desarrollo de una aplicación en la cual se implementaron tres diferentes técnicas inteligentes a través de los cuales se busca la minimización de una función de evaluación que representa la calidad de la solución de acuerdo al enfoque establecido. Los resultados muestran una mayor eficiencia del algoritmo NSGA-II en comparación con los otros dos métodos aplicados al mismo problema y evaluados con la misma métrica. A nivel experimental, la metodología evidencia que los grupos programados mediante la orientación descrita presentan una reducción en los niveles de mortalidad académicaAbstract : This research raises the solution to school timetabling problem under the characteristics of Colombian public school including as a primary factor in the optimization process, the time location of the subjects according to cognitive rhythms presented by students during the school day. For this purpose, a development application is presented in which three different techniques were implemented through which the minimization for a Fitness function is looked for that represents the quality of the solution according to the established approach. The results show a higher efficiency of the NSGA-II algorithm compared to the other two methods applied to the same problem and evaluated with the same metric. At the experimental level, the methodology shows that the programmed groups through the guidance described show a reduction in the academic mortality levelsMaestrí

Transformation of the university examination timetabling problem space through data pre-processing

This research investigates Examination Timetabling or Scheduling, with the aim of producing good quality, feasible timetables that satisfy hard constraints and various soft constraints. A novel approach to scheduling, that of transformation of the problem space, has been developed and evaluated for its effectiveness. The examination scheduling problem involves many constraints due to many relationships between students and exams, making it complex and expensive in terms of time and resources. Despite the extensive research in this area, it has been observed that most of the published methods do not produce good quality timetables consistently due to the utilisation of random-search. In this research we have avoided random-search and instead have proposed a systematic, deterministic approach to solving the examination scheduling problem. We pre-process data and constraints to generate more meaningful aggregated data constructs with better expressive power that minimise the need for cross-referencing original student and exam data at a later stage. Using such aggregated data and custom-designed mechanisms, the timetable construction is done systematically, while assuring its feasibility. Later, the timetable is optimized to improve the quality, focusing on maximizing the gap between consecutive exams. Our solution is always reproducible and displays a deterministic optimization pattern on all benchmark datasets. Transformation of the problem space into new aggregated data constructs through pre-processing represents the key novel contribution of this research

Transformation of the university examination timetabling problem space through data pre-processing

This research investigates Examination Timetabling or Scheduling, with the aim of producing good quality, feasible timetables that satisfy hard constraints and various soft constraints. A novel approach to scheduling, that of transformation of the problem space, has been developed and evaluated for its effectiveness. The examination scheduling problem involves many constraints due to many relationships between students and exams, making it complex and expensive in terms of time and resources. Despite the extensive research in this area, it has been observed that most of the published methods do not produce good quality timetables consistently due to the utilisation of random-search. In this research we have avoided random-search and instead have proposed a systematic, deterministic approach to solving the examination scheduling problem. We pre-process data and constraints to generate more meaningful aggregated data constructs with better expressive power that minimise the need for cross-referencing original student and exam data at a later stage. Using such aggregated data and custom-designed mechanisms, the timetable construction is done systematically, while assuring its feasibility. Later, the timetable is optimized to improve the quality, focusing on maximizing the gap between consecutive exams. Our solution is always reproducible and displays a deterministic optimization pattern on all benchmark datasets. Transformation of the problem space into new aggregated data constructs through pre-processing represents the key novel contribution of this research

Linear combinations of heuristics for examination timetabling

Although they are simple techniques from the early days of timetabling research, graph colouring heuristics are still attracting significant research interest in the timetabling research community. These heuristics involve simple ordering strategies to first select and colour those vertices that are most likely to cause trouble if deferred until later. Most of this work used a single heuristic to measure the difficulty of a vertex. Relatively less attention has been paid to select an appropriate colour for the selected vertex. Some recent work has demonstrated the superiority of combining a number of different heuristics for vertex and colour selection. In this paper, we explore this direction and introduce a new strategy of using linear combinations of heuristics for weighted graphs which model the timetabling problems under consideration. The weights of the heuristic combinations define specific roles that each simple heuristic contributes to the process of ordering vertices. We include specific explanations for the design of our strategy and present the experimental results on a set of benchmark real world examination timetabling problem instances. New best results for several instances have been obtained using this method when compared with other constructive methods applied to this benchmark dataset