Hybrid Graph Heuristics within a Hyper-heuristic Approach to Exam Timetabling Problems

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.

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.

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.

Real-time alert correlation with type graphs

The premise of automated alert correlation is to accept that false alerts from a low level intrusion detection system are inevitable and use attack models to explain the output in an understandable way. Several algorithms exist for this purpose which use attack graphs to model the ways in which attacks can be combined. These algorithms can be classified in to two broad categories namely scenario-graph approaches, which create an attack model starting from a vulnerability assessment and type-graph approaches which rely on an abstract model of the relations between attack types. Some research in to improving the efficiency of type-graph correlation has been carried out but this research has ignored the hypothesizing of missing alerts. Our work is to present a novel type-graph algorithm which unifies correlation and hypothesizing in to a single operation. Our experimental results indicate that the approach is extremely efficient in the face of intensive alerts and produces compact output graphs comparable to other techniques.

Navigating a corpus of journal papers using Handles

For some years now the Internet and World Wide Web communities have envisaged moving to a next generation of Web technologies by promoting a globally unique, and persistent, identifier for identifying and locating many forms of published objects . These identifiers are called Universal Resource Names (URNs) and they hold out the prospect of being able to refer to an object by what it is (signified by its URN), rather than by where it is (the current URL technology). One early implementation of URN ideas is the Unicode-based Handle technology, developed at CNRI in Reston Virginia. The Digital Object Identifier (DOI) is a specific URN naming convention proposed just over 5 years ago and is now administered by the International DOI organisation, founded by a consortium of publishers and based in Washington DC. The DOI is being promoted for managing electronic content and for intellectual rights management of it, either using the published work itself, or, increasingly via metadata descriptors for the work in question. This paper describes the use of the CNRI handle parser to navigate a corpus of papers for the Electronic Publishing journal. These papers are in PDF format and based on our server in Nottingham. For each paper in the corpus a metadata descriptor is prepared for every citation appearing in the References section. The important factor is that the underlying handle is resolved locally in the first instance. In some cases (e.g. cross-citations within the corpus itself and links to known resources elsewhere) the handle can be handed over to CNRI for further resolution. This work shows the encouraging prospect of being able to use persistent URNs not only for intellectual property negotiations but also for search and discovery. In the test domain of this experiment every single resource, referred to within a given paper, can be resolved, at least to the level of metadata about the referred object. If the Web were to become more fully URN aware then a vast directed graph of linked resources could be accessed, via persistent names. Moreover, if these names delivered embedded metadata when resolved, the way would be open for a new generation of vastly more accurate and intelligent Web search engines.

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.

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.

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.

Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the hydrodynamic stability problem associated with the incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the eigenvalue problem in channel and pipe geometries. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to eigenvalue/stability problems. The underlying analysis consists of constructing both a dual eigenvalue problem and a dual problem for the original base solution. In this way, errors stemming from both the numerical approximation of the original nonlinear flow problem, as well as the underlying linear eigenvalue problem are correctly controlled. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented.

Threshold behaviour and final outcome of an epidemic on a random network with household structure

This paper considers a stochastic SIR (susceptible-infective-removed) epidemic model in which individuals may make infectious contacts in two ways, both within 'households' (which for ease of exposition are assumed to have equal size) and along the edges of a random graph describing additional social contacts. Heuristically-motivated branching process approximations are described, which lead to a threshold parameter for the model and methods for calculating the probability of a major outbreak, given few initial infectives, and the expected proportion of the population who are ultimately infected by such a major outbreak. These approximate results are shown to be exact as the number of households tends to infinity by proving associated limit theorems. Moreover, simulation studies indicate that these asymptotic results provide good approximations for modestly-sized finite populations. The extension to unequal sized households is discussed briefly.