Similarity Measures for Exam Timetabling Problems

A large number of heuristic algorithms have been developed over the years which have been aimed at solving examination timetabling problems. However, many of these algorithms have been developed specifically to solve one particular problem instance or a small subset of instances related to a given real-life problem. Our aim is to develop a more general system which, when given any exam timetabling problem, will produce results which are comparative to those of a specially designed heuristic for that problem. We are investigating a Case based reasoning (CBR) technique to select from a set of algorithms which have been applied successfully to similar problem instances in the past. The assumption in CBR is that similar problems have similar solutions. For our system, the assumption is that an algorithm used to find a good solution to one problem will also produce a good result for a similar problem. The key to the success of the system will be our definition of similarity between two exam timetabling problems. The study will be carried out by running a series of tests using a simple Simulated Annealing Algorithm on a range of problems with differing levels of similarity and examining the data sets in detail. In this paper an initial investigation of the key factors which will be involved in this measure is presented with a discussion of how the definition of good impacts on this.

Knowledge discovery in hyper-heuristic using case-based reasoning on course timetabling

This paper presents a new hyper-heuristic method using Case-Based Reasoning (CBR) for solving course timetabling problems. The term Hyper-heuristics has recently been employed to refer to 'heuristics that choose heuristics' rather than heuristics that operate directly on given problems. One of the overriding motivations of hyper-heuristic methods is the attempt to develop techniques that can operate with greater generality than is currently possible. The basic idea behind this is that we maintain a case base of information about the most successful heuristics for a range of previous timetabling problems to predict the best heuristic for the new problem in hand using the previous knowledge. Knowledge discovery techniques are used to carry out the training on the CBR system to improve the system performance on the prediction. Initial results presented in this paper are good and we conclude by discussing the con-siderable promise for future work in this area.

Case-based reasoning in course timetabling: an attribute graph approach

An earlier Case-based Reasoning (CBR) approach developed by the authors for educational course timetabling problems employed structured cases to represent the complex relationships between courses. Previous solved cases represented by attribute graphs were organized hierarchically into a decision tree. The retrieval searches for graph isomorphism among these attribute graphs. In this paper, the approach is further developed to solve a wider range of problems. We also attempt to retrieve those graphs that have common similar structures but also have some differences. Costs that are assigned to these differences have an input upon the similarity measure. A large number of experiments are performed consisting of different randomly produced timetabling problems and the results presented here strongly indicate that a CBR approach could provide a significant step forward in the development of automated system to solve difficult timetabling problems. They show that using relatively little effort, we can retrieve these structurally similar cases to provide high quality timetables for new timetabling problems.

Analysing Similarity in Exam Timetabling

In this paper we carry out an investigation of some of the major features of exam timetabling problems with a view to developing a similarity measure. This similarity measure will be used within a case-based reasoning (CBR) system to match a new problem with one from a case-based of previously solved problems. The case base will also store the heuristic for meta-heuristic techniques applied most successfully to each problem stored. The technique(s) stored with the matched case will be retrieved and applied to the new case. The CBR assumption in our system is that similar problems can be solved equally well by the same technique.

Similarity Measures for Exam Timetabling Problems

A large number of heuristic algorithms have been developed over the years which have been aimed at solving examination timetabling problems. However, many of these algorithms have been developed specifically to solve one particular problem instance or a small subset of instances related to a given real-life problem. Our aim is to develop a more general system which, when given any exam timetabling problem, will produce results which are comparative to those of a specially designed heuristic for that problem. We are investigating a Case based reasoning (CBR) technique to select from a set of algorithms which have been applied successfully to similar problem instances in the past. The assumption in CBR is that similar problems have similar solutions. For our system, the assumption is that an algorithm used to find a good solution to one problem will also produce a good result for a similar problem. The key to the success of the system will be our definition of similarity between two exam timetabling problems. The study will be carried out by running a series of tests using a simple Simulated Annealing Algorithm on a range of problems with differing levels of similarity and examining the data sets in detail. In this paper an initial investigation of the key factors which will be involved in this measure is presented with a discussion of how the definition of good impacts on this.

A graph-based hyper heuristic for timetabling problems

This paper presents an investigation of a simple generic hyper-heuristic approach upon a set of widely used constructive heuristics (graph coloring heuristics) in timetabling. Within the hyperheuristic framework, a Tabu Search approach is employed to search for permutations of graph heuristics which are used for constructing timetables in exam and course timetabling problems. This underpins a multi-stage hyper-heuristic where the Tabu Search employs permutations upon a different number of graph heuristics in two stages. We study this graph-based hyper-heuristic approach within the context of exploring fundamental issues concerning the search space of the hyper-heuristic (the heuristic space) and the solution space. Such issues have not been addressed in other hyper-heuristic research. These approaches are tested on both exam and course benchmark timetabling problems and are compared with the fine-tuned bespoke state-of-the-art approaches. The results are within the range of the best results reported in the literature. The approach described here represents a significantly more generally applicable approach than the current state of the art in the literature. Future work will extend this hyper-heuristic framework by employing methodologies which are applicable on a wider range of timetabling and scheduling problems.

Multiple-retrieval case-based reasoning for course timetabling problems

The structured representation of cases by attribute graphs in a Case-Based Reasoning (CBR) system for course timetabling has been the subject of previous research by the authors. In that system, the case base is organised as a decision tree and the retrieval process chooses those cases which are sub attribute graph isomorphic to the new case. The drawback of that approach is that it is not suitable for solving large problems. This paper presents a multiple-retrieval approach that partitions a large problem into small solvable sub-problems by recursively inputting the unsolved part of the graph into the decision tree for retrieval. The adaptation combines the retrieved partial solutions of all the partitioned sub-problems and employs a graph heuristic method to construct the whole solution for the new case. We present a methodology which is not dependant upon problem specific information and which, as such, represents an approach which underpins the goal of building more general timetabling systems. We also explore the question of whether this multiple-retrieval CBR could be an effective initialisation method for local search methods such as Hill Climbing, Tabu Search and Simulated Annealing. Significant results are obtained from a wide range of experiments. An evaluation of the CBR system is presented and the impact of the approach on timetabling research is discussed. We see that the approach does indeed represent an effective initialisation method for these approaches.

Case Based Heuristic Selection for Timetabling Problems

This paper presents a case-based heuristic selection approach for automated university course and exam timetabling. The method described in this paper is motivated by the goal of developing timetabling systems that are fundamentally more general than the current state of the art. Heuristics that worked well in previous similar situations are memorized in a case base and are retrieved for solving the problem in hand. Knowledge discovery techniques are employed in two distinct scenarios. Firstly, we model the problem and the problem solving situations along with specific heuristics for those problems. Secondly, we refine the case base and discard cases which prove to be non-useful in solving new problems. Experimental results are presented and analyzed. It is shown that case based reasoning can act effectively as an intelligent approach to learn which heuristics work well for particular timetabling situations. We conclude by outlining and discussing potential research issues in this critical area of knowledge discovery for different difficult timetabling problems.

Hybrid Variable Neighborhood HyperHeuristics for Exam Timetabling Problems

This paper presents our work on analysing the high level search within a graph based hyperheuristic. The graph based hyperheuristic solves the problem at a higher level by searching through permutations of graph heuristics rather than the actual solutions. The heuristic permutations are then used to construct the solutions. Variable Neighborhood Search, Steepest Descent, Iterated Local Search and Tabu Search are compared. An analysis of their performance within the high level search space of heuristics is also carried out. Experimental results on benchmark exam timetabling problems demonstrate the simplicity and efficiency of this hyperheuristic approach. They also indicate that the choice of the high level search methodology is not crucial and the high level search should explore the heuristic search space as widely as possible within a limited searching time. This simple and general graph based hyperheuristic may be applied to a range of timetabling and optimisation problems.

Case Based Heuristic Selection for Timetabling Problems

This paper presents a case-based heuristic selection approach for automated university course and exam timetabling. The method described in this paper is motivated by the goal of developing timetabling systems that are fundamentally more general than the current state of the art. Heuristics that worked well in previous similar situations are memorized in a case base and are retrieved for solving the problem in hand. Knowledge discovery techniques are employed in two distinct scenarios. Firstly, we model the problem and the problem solving situations along with specific heuristics for those problems. Secondly, we refine the case base and discard cases which prove to be non-useful in solving new problems. Experimental results are presented and analyzed. It is shown that case based reasoning can act effectively as an intelligent approach to learn which heuristics work well for particular timetabling situations. We conclude by outlining and discussing potential research issues in this critical area of knowledge discovery for different difficult timetabling problems.

An Estimation of Distribution Algorithm with Intelligent Local Search for Rule-based Nurse Rostering

This paper proposes a new memetic evolutionary algorithm to achieve explicit learning in rule-based nurse rostering, which involves applying a set of heuristic rules for each nurse's assignment. The main framework of the algorithm is an estimation of distribution algorithm, in which an ant-miner methodology improves the individual solutions produced in each generation. Unlike our previous work (where learning is implicit), the learning in the memetic estimation of distribution algorithm is explicit, i.e. we are able to identify building blocks directly. The overall approach learns by building a probabilistic model, i.e. an estimation of the probability distribution of individual nurse-rule pairs that are used to construct schedules. The local search processor (i.e. the ant-miner) reinforces nurse-rule pairs that receive higher rewards. A challenging real world nurse rostering problem is used as the test problem. Computational results show that the proposed approach outperforms most existing approaches. It is suggested that the learning methodologies suggested in this paper may be applied to other scheduling problems where schedules are built systematically according to specific rules.

Investigating a Hybrid Metaheuristic For Job Shop Rescheduling

Previous research has shown that artificial immune systems can be used to produce robust schedules in a manufacturing environment. The main goal is to develop building blocks (antibodies) of partial schedules that can be used to construct backup solutions (antigens) when disturbances occur during production. The building blocks are created based upon underpinning ideas from artificial immune systems and evolved using a genetic algorithm (Phase I). Each partial schedule (antibody) is assigned a fitness value and the best partial schedules are selected to be converted into complete schedules (antigens). We further investigate whether simulated annealing and the great deluge algorithm can improve the results when hybridised with our artificial immune system (Phase II). We use ten fixed solutions as our target and measure how well we cover these specific scenarios.

Improved Squeaky Wheel Optimisation for Driver Scheduling

This paper presents a technique called Improved Squeaky Wheel Optimisation (ISWO) for driver scheduling problems. It improves the original Squeaky Wheel Optimisation’s (SWO) effectiveness and execution speed by incorporating two additional steps of Selection and Mutation which implement evolution within a single solution. In the ISWO, a cycle of Analysis-Selection-Mutation-Prioritization-Construction continues until stopping conditions are reached. The Analysis step first computes the fitness of a current solution to identify troublesome components. The Selection step then discards these troublesome components probabilistically by using the fitness measure, and the Mutation step follows to further discard a small number of components at random. After the above steps, an input solution becomes partial and thus the resulting partial solution needs to be repaired. The repair is carried out by using the Prioritization step to first produce priorities that determine an order by which the following Construction step then schedules the remaining components. Therefore, the optimisation in the ISWO is achieved by solution disruption, iterative improvement and an iterative constructive repair process performed. Encouraging experimental results are reported.

'Investigating Artificial Immune Systems For Job Shop Rescheduling In Changing Environments'

ABSTRACT Artificial immune system can be used to generate schedules in changing environments and it has been proven to be more robust than schedules developed using a genetic algorithm. Good schedules can be produced especially when the number of the antigens is increased. However, an increase in the range of the antigens had somehow affected the fitness of the immune system. In this research, we are trying to improve the result of the system by rescheduling the same problem using the same method while at the same time maintaining the robustness of the schedules.