Andrea Schaerf

A Survey of Automated Timetabling

The timetabling problem consists in scheduling a sequence of lectures between teachers and students in a prefixed period of time (typically a week), satisfying a set of constraints of various types. A large number of variants of the timetabling problem have been proposed in the literature, which differ from each other based on the type of institution involved (university or school) and the type of constraints. This problem, that has been traditionally considered in the operational research field, has recently been tackled with techniques belonging also to Artificial Intelligence (e.g., genetic algorithms, tabu search, and constraint satisfaction). In this paper, we survey the various formulations of the problem, and the techniques and algorithms used for its solution.

{\cal A}{\cal L} -log: Integrating Datalog and Description Logics

We present an integrated system for knowledge representation, calledAL -log, based on description logics and the deductive database language Datalog. AL-log embodies two subsystems, called structural and relational. The former allows for the definition of structural knowledge about classes of interest (concepts) and membership relation between objects and classes. The latter allows for the definition of relational knowledge about objects described in the structural component. The interaction between the two components is obtained by allowing constraints within Datalog clauses, thus requiring the variables in the clauses to range over the set of instances of a specified concept. We propose a method for query answering in AL-log based on constrained resolution, where the usual deduction procedure defined for Datalog is integrated with a method for reasoning on the structural knowledge.

Decidable reasoning in terminological knowledge representation systems

Terminological Knowledge Representation Systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). The TKRS we consider in this paper is of practical interest since it goes beyond the capabilities of presently available TKRSs. First, our TKRS is equipped with a highly expressive concept, language, called ALCNR, including general complements of concepts, number restrictions and role conjunction. Second, it allows one to express inclusion statements between general concepts, in particular to express terminological cycles. We provide a sound, complete and terminating calculus for reasoning in ALCNR-knowledge bases based on the general technique of constraint systems.

Tabu Search Techniques for Examination Timetabling

The EXAMINATION TIMETABLING problem regards the scheduling for the exams of a set of university courses, avoiding the overlapping of exams having students in common, fairly spreading the exams for the students, and satisfying room capacity constraints. We present a family of solution algorithms for a set of variants of the EXAMINATION TIMETABLING problem. The algorithms are based on tabu search, and they import several features from the research on the GRAPH COLOURING problem. Our algorithms are tested on both public benchmarks and random instances, and they are compared with previous results in the literature. The comparison shows that the presented algorithms performs as well as constructive methods and memetic algorithms, and only a decomposition based approach outperforms them in most cases.

Adaptive load balancing: a study in multi-agent learning

We study the process of multi-agent reinforcement learning in the context of load balancing in a distributed system, without use of either central coordination or explicit communication. We first define a precise framework in which to study adaptive load balancing, important features of which are its stochastic nature and the purely local information available to individual agents. Given this framework, we show illuminating results on the interplay between basic adaptive behavior parameters and their effect on system efficiency. We then investigate the properties of adaptive load balancing in heterogeneous populations, and address the issue of exploration vs. exploitation in that context. Finally, we show that naive use of communication may not improve, and might even harm system efficiency.

Setting the Research Agenda in Automated Timetabling: The Second International Timetabling Competition

The Second International Timetabling Competition (TTC2007) opened in August 2007. Building on the success of the first competition in 2002, this sequel aimed to further develop research activity in the area of educational timetabling. The broad aim of the competition was to create better understanding between researchers and practitioners by allowing emerging techniques to be developed and tested on real-world models of timetabling problems. To support this, a primary goal was to provide researchers with models of problems faced by practitioners through incorporating a significant number of real-world constraints. Another objective of the competition was to stimulate debate within the widening timetabling research community. The competition was divided into three tracks to reflect the important variations that exist in educational timetabling within higher education. Because these formulations incorporate an increased number of “real-world” issues, it is anticipated that the competition will now set the research agenda within the field. After finishing in January 2008, final results were made available in May 2008. Along with background to the competition, the competition tracks are described here along with a brief overview of the techniques used by the competition winners.

Local search techniques for large high school timetabling problems

The high school timetabling problem regards the weekly scheduling for all the lectures of a high school. The problem consists in assigning lectures to periods in such a way that no teacher (or class) is involved in more than one lecture at a time, and other constraints are satisfied. The problem is NP-complete and is usually tackled using heuristic methods, This paper describes a solution algorithm (and its implementation) based on local search techniques. The algorithm alternates different techniques and different types of moves and makes use of an adaptive relaxation of the hard constraints. The implementation of the algorithm has been successfully experimented with in some large high schools with various kinds of side constraints.

An epistemic operator for description logics

Abstract Description logics (also called terminological logics, or concept languages) are fragments of first-order logic that provide a formal account of the basic features of frame-based systems. However, there are aspects of frame-based systems—such as nonmonotonic reasoning and procedural rules—that cannot be characterized in a standard first-order framework. Such features are needed for real applications, and a clear understanding of the logic underlying them is necessary for principled implementations. We show how description logics enriched with an epistemic operator can formalize such aspects. The logic obtained is a fragment of a first-order nonmonotonic modal logic. We show that the epistemic operator formalizes procedural rules, as provided in many knowledge representation systems, and enables sophisticated query formulation, including various forms of closed-world reasoning. We provide an effective procedure for answering epistemic queries posed to a knowledge base expressed in a description logic and extend this procedure in order to deal with rules. We also address the computational complexity of reasoning with the epistemic operator, identifying cases in which an appropriate use of the epistemic operator can help in decreasing the complexity of reasoning.

Deduction in Concept Languages: from Subsumption to Instance Checking

It is a common opinion that subsumption is the central reasoning task in frame-based knowledge representation languages (or concept languages). Intuitively, a concept C subsumes another concept D if the set of objects represented by C is a superset of the one represented by D. When individual objects are taken into account, the basic deduc-tive task for retrieving information from a knowledge base is instance checking, that amounts to checking whether the knowledge base implies that an individual is an instance of a given concept. In this paper, we address the question of whether instance checking can be solved by means of subsumption algorithms. We do so by considering several languages where subsumption belongs to diierent complexity classes. For such languages we present methods for the instance checking problem, provide a complexity analysis of this problem, and compare it with the subsumption problem. The main result of the paper is that instance checking is not always easily reducible to subsumption. In particular, there are cases where it is strictly harder than subsumption. This impacts on the design of reasoning algorithms for knowledge representation systems based on concept languages.

Reasoning with individuals in concept languages

One of the main characteristics of knowledge representation systems based on the description of concepts is the clear distinction between terminological and assertional knowledge. Although this characteristic leads to several computational and representational advantages, it usually limits the expressive power of the system. For this reason, some attempts have been done, allowing for a limited form of amalgamation between the two components and a more complex interaction between them. In particular, one of these attempts is based on letting the individuals to be referenced in the concept expressions. This is generally performed by admitting a constructor for building a concept from a set of enumerated individuals. In this paper we investigate on the consequences of introducing this type of constructor in the concept description language and we provide some complexity results on it.