Relation-algebraic specification and solution of special university timetabling problems

AbstractIn this paper, we are concerned with a special timetabling problem. It was posed to us by the administration of our university and stems from the adoption of the British-American system of university education in Germany. This change led to the concrete task of constructing a timetable that enables the undergraduate education of secondary school teachers within three years in the “normal case” and within four years in the case of exceptional combinations of subjects. We develop two relation-algebraic models of the timetabling problem and in each case algorithms for computing solutions. The latter easily can be implemented in the Kiel RelView tool showing that RelView can be used for timetabling

Vectors and vector predicates and their use in the development of relational algorithms

In dieser Arbeit wird der Frage nachgegangen, inwieweit sich randomisierte Suchverfahren wie Evolutionäre Algorithmen mittels relationaler Methoden entwickeln und durch relationale Programme implementieren lassen. Einen besonderen Schwerpunkt bildet dabei die Auswertung von Suchpunkten, der im Selektionsprozess Evolutionärer Algorithmen eine zentrale Bedeutung zukommt. Zur Bewertung der Suchpunkte wird das Konzept der Vektorabbildungen und Vektorprädikate entwickelt, welches nicht nur bei der relationalen Modellierung Evolutionärer Algorithmen eine wichtige Rolle spielt, sondern auch in anderen Bereichen einsetzbar ist. Wir geben eine Reihe von Beispielen an, bei denen der Einsatz von Vektorabbildungen und Vektorprädikaten zu einer schnellen und unkomplizierten Entwicklung von relationalen Algorithmen beiträgt.In this work, we try to combine randomized search heuristics like Evolutionary Algorithms with relational methods. For the evaluation of searchpoints in the selection step of an Evolutionary Algorithm, we introduce the concept of vector predicates and testmappings. We present different examples to show how vector predicates can be used to develop relational Algorithms

Multi-objective Problems in Terms of Relational Algebra

Abstract. Relational algebra has been shown to be a powerful tool for solving a wide range of combinatorial optimization problems with small computational and programming effort. The problems considered in recent years are single- objective ones where one single objective function has to be optimized. With this paper we start considerations on the use of relational algebra for multi-objective problems. In contrast to singleobjective optimization multiple objective functions have to be optimized at the same time usually resulting in a set of different trade-offs with respect to the different functions. On the one hand, we examine how to solve the mentioned problem exactly by using relational algebraic programs. On the other hand, we address the problem of objective reduction that has recently been shown to be NP-hard. We propose an exact algorithm for this problem based on relational algebra. Our experimental results show that this algorithm drastically outperforms the currently best one.