Structured cases in case-based reasoning: re-using and adapting cases for time-tabling problems

In this paper, we present a case-based reasoning (CBR) approach solving educational time-tabling problems. Following the basic idea behind CBR, the solutions of previously solved problems are employed to aid finding the solutions for new problems. A list of feature-value pairs is insufficient to represent all the necessary information. We show that attribute graphs can represent more information and thus can help to retrieve re-usable cases that have similar structures to the new problems. The case base is organised as a decision tree to store the attribute graphs of solved problems hierarchically. An example is given to illustrate the retrieval, re-use and adaptation of structured cases. The results from our experiments show the effectiveness of the retrieval and adaptation in the proposed method.

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.

Case-Based Reasoning as a Heuristic Selector in a Hyper-Heuristic for Course Timetabling Problems

This paper studies Knowledge Discovery (KD) using Tabu Search and Hill Climbing within Case-Based Reasoning (CBR) as a hyper-heuristic method for course timetabling problems. The aim of the hyper-heuristic is to choose the best heuristic(s) for given timetabling problems according to the knowledge stored in the case base. KD in CBR is a 2-stage iterative process on both case representation and the case base. Experimental results are analysed and related research issues for future work are discussed.

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.

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.

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.

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 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.

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.

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.