The aim of this paper is to give a brief introduction to some recent approaches to timetabling problems that have been developed or are under development in the Automated Scheduling, Optimisation and Planning Research Group (ASAP) at the University of Nottingham. We have concentrated upon university timetabling but we believe that some of the methodologies that are described can be used for different timetabling problems such as employee timetabling, timetabling of sports fixtures, etc. The paper suggests a number of approaches and comprises three parts. Firstly, recent heuristic and evolutionary timetabling algorithms are discussed. In particular, two evolutionary algorithm developments are described: a method for decomposing large real-world timetabling problems and a method for heuristic initialisation of the population. Secondly, an approach that considers timetabling problems as multicriteria decision problems is presented. Thirdly, we discuss a case-based reasoning approach that employs previous experience to solve new timetabling problems. Finally, we outline some new research ideas and directions in the field of timetabling. The overall aim of these research directions is to explore approaches that can operate at a higher level of generality than is currently possible. Keywords: Combinatorial optimisation; Timetabling/Scheduling; Meta-heuristic approaches; Multiple criteria analysis; Case-based reasoning, Hyper-heuristics.

Examination timetabling is a well-studied combinatorial optimization problem. We present a new hybrid algorithm for examination timetabling, consisting of three phases: a constraint programming phase to develop an initial solution, a simulated annealing phase to improve the quality of solution, and a hill climbing phase for further improvement.

Abstract. It is well known that domain-specific heuristics can produce good-quality solutions for timetabling problems in a short amount of time. However, they often lack the ability to do any thorough optimisation. In this paper we will study the effects of applying local search techniques to improve good-quality initial solutions generated using a heuristic construction method. While the same rules should apply to any heuristic construction, we use here an adaptive approach to timetabling problems. The focus of the experiments is how parameters to the local search methods affect quality when started on already good solutions. We present experimental results which show that this combined approach produces the best published results on several benchmark problems and we briefly discuss the implications for future work in the area.

Ordering exams by simultaneously considering two ordering criteria using a fuzzy expert system is presented in this paper. Combinations of two of the three ordering criteria largest degree, saturation degree and largest enrollment are considered. The fuzzy weight of an exam is used to represent how difficult it is to schedule. The decreasingly ordered exams are sequentially chosen to be assigned to the last slot with least penalty cost value while the feasibility of the timetable is maintained throughout the process. Unscheduling and rescheduling exams is performed until all exams are scheduled. The proposed algorithm has been tested on 12 benchmark examination timetabling datasets and the results show that this approach can produce good quality solutions. Moreover, there is significant potential to extend the approach by including a larger range of criteria.

Two ant algorithms solving a simplified version of a typical university course timetabling problem are presented -- Ant Colony System and MAX-MIN Ant System. The algorithms are tested over a set of instances from three classes of the problem. Results are compared with recent results obtained with several metaheuristics using the same local search routine (or neighborhood definition), and a reference random restart local search algorithm. Further, both ant algorithms are compared on an additional set of instances. Conclusions are drawn about the performance of ant algorithms on timetabling problems in comparison to other metaheuristics. Also the design, implementation, and parameters of ant algorithms solving the university course timetabling problem are discussed. It is shown that the particular implementation of an ant algorithm has significant influence on the observed algorithm performance.

A hybrid Multi-Objective Evolutionary Algorithm is used to tackle the uncapacitated exam proximity problem. In this hybridization, local search operators are used instead of the traditional genetic recombination operators. One of the search operators is designed to repair unfeasible timetables produced by the initialization procedure and the mutation operator. The other search operator implements a simplified Variable Neighborhood Descent meta-heuristic and its role is to improve the proximity cost. The resulting non dominated timetables are compared with thouse produced by other optimization methods using 15 public domain datasets. Without special fine-tuning, the hybrid algorithm was able to produce timetables ranking first and second in 9 of the 15 datasets.

Abstract: This paper is concerned with the hybridization of two graph coloring heuristics (Saturation Degree and Largest Degree), and their application within a hyperheuristic for exam timetabling problems. Hyper-heuristics can be seen as algorithms which intelligently select appropriate algorithms/heuristics for solving a problem. We developed a Tabu Search based hyper-heuristic to search for heuristic lists (of graph heuristics) for solving problems and investigated the heuristic lists found by employing knowledge discovery techniques. Two hybrid approaches (involving Saturation Degree and Largest Degree) including one which employs Case Based Reasoning are presented and discussed. Both the Tabu Search based hyper-heuristic and the hybrid approaches are tested on random and real-world exam timetabling problems. Experimental results are comparable with the best state-of-the-art approaches (as measured against established benchmark problems). The results also demonstrate an increased level of generality in our approach. Key words: case based reasoning, exam timetabling problems, graph heuristics, hyperheuristics, knowledge discovery, tabu search.

This paper investigates a tabu search based hyper-heuristic for solving examination timetabling problems. The hyper-heuristic framework uses a tabu list to monitor the performance of a collection of low-level heuristics and then make tabu heuristics that have been applied too many times, thus allowing other heuristics to be applied. Experiments carried out on examination timetabling datasets from the literature show that this approach is able to produce good quality solutions.

Abstract. Hyper-heuristics are proposed as a higher level of abstraction as compared to the metaheuristics. Hyper-heuristic methods deploy a set of simple heuristics and use only nonproblem-specific data, such as, fitness change or heuristic execution time. A typical iteration of a hyper-heuristic algorithm consists of two phases: heuristic selection method and move acceptance. In this paper, heuristic selection mechanisms and move acceptance criteria in hyperheuristics are analyzed in depth. Seven heuristic selection methods, and five acceptance criteria are implemented. The performance of each selection and acceptance mechanism pair is evaluated on fourteen well-known benchmark functions and twenty-one exam timetabling problem instances. 1

Scheduling exams at universities can be formulated as a combinatorial optimization problem. Given a planning horizon with a fixed number of periods the objective is to avoid situations, or at least to minimize them, when a student is enrolled in two exams that are scheduled for the same period. Ant colony approaches have been proven to be a powerful solution approach for various combinatorial optimization problems. In this paper a Max-Min and a ANTCOL approach will be presented. Its performance is compared with other approaches presented in the literature and with modified graph coloring algorithms.