Fuzzy methodologies for automated University timetabling solution construction and evaluation

This thesis presents an investigation into the use of fuzzy methodologies for University timetabling problems. The first area of investigation is the use of fuzzy techniques to combine multiple heuristic orderings within the construction of timetables. Different combinations of multiple heuristic ordering were examined, considering five graph-based heuristic orderings - Largest Degree, Saturation Degree, Largest Enrolment, Largest Coloured Degree and Weighted Largest Degree. The initial development utilised only two heuristic orderings simultaneously and subsequent development went on to incorporate three heuristic orderings simultaneously. A central hypothesis of this thesis is that this approach provides a more realistic scheme for measuring the difficulty of assigning events to time slots than the use of a single heuristic alone. Experimental results demonstrated that the fuzzy multiple heuristic orderings (with parameter tuning) outperformed all of the single heuristic orderings and non-fuzzy linear weighting factors. Comprehensive analysis has provided some key insights regarding the implementation of multiple heuristic orderings. Producing examination timetables automatically has been the subject of much research. It is generally the case that a number of alternative solutions that satisfy all the hard criteria are possible. Indeed, there are usually a very large number of such feasible solutions. Some method is required to permit the overall quality of different solutions to be quantified, in order to allow them to be compared, so that the best may be selected. In response to that demand, the second area of investigation of this thesis is concerned with a new evaluation function for examination timetabling problems. A novel approach, in which fuzzy methods are used to evaluate the end solution quality, separate from the objective functions used in solution generation, represents a significant addition to the literature. The proposed fuzzy evaluation function provides a mechanism to allow an overall decision in evaluating the quality of a timetable solution to be made based on common sense rules that encapsulate the notion that the timetable solution quality increases as both the average penalty and the highest penalty decrease. New algorithms to calculate what is loosely termed the lower limits and upper limits of the proximity cost function for any problem instance are also presented. These limits may be used to provide a good indication of how good any timetable solution is. Furthermore, there may be an association between the proposed lower limit and the formal lower bound. This is the first time that lower limits (other than zero) have been established for proximity cost evaluation of timetable solutions

Hybrid genetic algorithm for university examination timetabling problem

This paper considers a Hybrid Genetic Algorithm (HGA) for University Examination Timetabling Problem (UETP). UETP is defined as the assignment of a given number of exams and their candidates to a number of available timeslots while satisfying a given set of constraints. Solutions for uncapacitated UETP are presented where five domain-specific knowledge in the form of low-level heuristics are used to guide the construction of the timetable in the initial population. The main components of the genetic operators in a GA will be tested and the best combination of the genetic operators will be adopted to construct a Pure Genetic Algorithm (PGA). The PGA will then hybridised with three new local optimisation techniques, which will make up the HGA; to improve the solutions found. These new local optimisation techniques will arrange the timeslots and exams using new explicit equations, if and only if, the modification will reduce the penalty cost function. The performance of the proposed HGA is compared with other metaheuristics from literature using the Carter’s benchmark dataset which comprises of real-world timetabling problem from various universities. The computational results show that the proposed HGA outperformed some of the metaheuristic approaches and is comparable to most of the well-known metaheuristic approaches

Solving Examination Timetabling Problem using Partial Exam Assignment with Great Deluge Algorithm

Constructing a quality solution for the examination timetable problem is a difficult task. This paper presents a partial exam assignment approach with great deluge algorithm as the improvement mechanism in order to generate good quality timetable. In this approach, exams are ordered based on graph heuristics and only selected exams (partial exams) are scheduled first and then improved using great deluge algorithm. The entire process continues until all of the exams have been scheduled. We implement the proposed technique on the Toronto benchmark datasets. Experimental results indicate that in all problem instances, this proposed method outperforms traditional great deluge algorithm and when comparing with the state-of-the-art approaches, our approach produces competitive solution for all instances, with some cases outperform other reported result

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

Search methodologies for examination timetabling

Working with examination timetabling is an extremely challenging task due to the difficulty of finding good quality solutions. Most of the studies in this area rely on improvement techniques to enhance the solution quality after generating an initial solution. Nevertheless, the initial solution generation itself can provide good solution quality even though the ordering strategies often using graph colouring heuristics, are typically quite simple. Indeed, there are examples where some of the produced solutions are better than the ones produced in the literature with an improvement phase. This research concentrates on constructive approaches which are based on squeaky wheel optimisation i.e. the focus is upon finding difficult examinations in their assignment and changing their position in a heuristic ordering. In the first phase, the work is focused on the squeaky wheel optimisation approach where the ordering is permutated in a block of examinations in order to find the best ordering. Heuristics are alternated during the search as each heuristic produces a different value of a heuristic modifier. This strategy could improve the solution quality when a stochastic process is incorporated. Motivated by this first phase, a squeaky wheel optimisation concept is then combined with graph colouring heuristics in a linear form with weights aggregation. The aim is to generalise the constructive approach using information from given heuristics for finding difficult examinations and it works well across tested problems. Each parameter is invoked with a normalisation strategy in order to generalise the specific problem data. In the next phase, the information obtained from the process of building an infeasible timetable is used. The examinations that caused infeasibility are given attention because, logically, they are hard to place in the timetable and so they are treated first. In the adaptive decomposition strategy, the aim is to automatically divide examinations into difficult and easy sets so as to give attention to difficult examinations. Within the easy set, a subset called the boundary set is used to accommodate shuffling strategies to change the given ordering of examinations. Consequently, the graph colouring heuristics are employed on those constructive approaches and it is shown that dynamic ordering is an effective way to permute the ordering. The next research chapter concentrates on the improvement approach where variable neighbourhood search with great deluge algorithm is investigated using various neighbourhood orderings and initialisation strategies. The approach incorporated with a repair mechanism in order to amend some of infeasible assignment and at the same time aiming to improve the solution quality

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

Search methodologies for examination timetabling

Working with examination timetabling is an extremely challenging task due to the difficulty of finding good quality solutions. Most of the studies in this area rely on improvement techniques to enhance the solution quality after generating an initial solution. Nevertheless, the initial solution generation itself can provide good solution quality even though the ordering strategies often using graph colouring heuristics, are typically quite simple. Indeed, there are examples where some of the produced solutions are better than the ones produced in the literature with an improvement phase. This research concentrates on constructive approaches which are based on squeaky wheel optimisation i.e. the focus is upon finding difficult examinations in their assignment and changing their position in a heuristic ordering. In the first phase, the work is focused on the squeaky wheel optimisation approach where the ordering is permutated in a block of examinations in order to find the best ordering. Heuristics are alternated during the search as each heuristic produces a different value of a heuristic modifier. This strategy could improve the solution quality when a stochastic process is incorporated. Motivated by this first phase, a squeaky wheel optimisation concept is then combined with graph colouring heuristics in a linear form with weights aggregation. The aim is to generalise the constructive approach using information from given heuristics for finding difficult examinations and it works well across tested problems. Each parameter is invoked with a normalisation strategy in order to generalise the specific problem data. In the next phase, the information obtained from the process of building an infeasible timetable is used. The examinations that caused infeasibility are given attention because, logically, they are hard to place in the timetable and so they are treated first. In the adaptive decomposition strategy, the aim is to automatically divide examinations into difficult and easy sets so as to give attention to difficult examinations. Within the easy set, a subset called the boundary set is used to accommodate shuffling strategies to change the given ordering of examinations. Consequently, the graph colouring heuristics are employed on those constructive approaches and it is shown that dynamic ordering is an effective way to permute the ordering. The next research chapter concentrates on the improvement approach where variable neighbourhood search with great deluge algorithm is investigated using various neighbourhood orderings and initialisation strategies. The approach incorporated with a repair mechanism in order to amend some of infeasible assignment and at the same time aiming to improve the solution quality

Hybridizations within a graph based hyper-heuristic framework for university timetabling problems

A significant body of recent literature has explored various research directions in hyper-heuristics (which can be thought as heuristics to choose heuristics). In this paper, we extend our previous work to construct a unified graph-based hyper-heuristic (GHH) framework, under which a number of local search-based algorithms (as the high level heuristics) are studied to search upon sequences of low-level graph colouring heuristics. To gain an in-depth understanding on this new framework, we address some fundamental issues concerning neighbourhood structures and characteristics of the two search spaces (namely, the search spaces of the heuristics and the actual solutions). Furthermore, we investigate efficient hybridizations in GHH with local search methods and address issues concerning the exploration of the high-level search and the exploitation ability of the local search. These, to our knowledge, represent entirely novel directions in hyper-heuristics. The efficient hybrid GHH obtained competitive results compared with the best published results for both benchmark course and exam timetabling problems, demonstrating its efficiency and generality across different problem domains. Possible extensions upon this simple, yet general, GHH framework are also discussed