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Shift Design with Answer Set Programming

Abseher M., Musliu N., Woltran S., Gebser M., Schaub T.

Fundamenta Informaticae

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2016

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Vol. 147, nr 1

1--25

EN

Answer Set Programming (ASP) is a powerful declarative programming paradigm that has been successfully applied to many different domains. Recently, ASP has also proved successful for hard optimization problems like course timetabling and travel allotment. In this paper, we approach another important task, namely, the shift design problem, aiming at an alignment of a minimum number of shifts in order to meet required numbers of employees (which typically vary for different time periods) in such a way that over- and understaffing is minimized. We provide an ASP encoding of the shift design problem, which, to the best of our knowledge, has not been addressed by ASP yet. Our experimental results demonstrate that ASP is capable of improving the best known solutions to some benchmark problems. Other instances remain challenging and make the shift design problem an interesting benchmark for ASP-based optimization methods.

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Answer Set Programming Modulo Acyclicity

Bomanson J., Janhunen T., Schaub T., Gebser M., Kaufmann B.

Fundamenta Informaticae

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2016

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Vol. 147, nr 1

63--91

EN

Acyclicity constraints are prevalent in knowledge representation and applications where acyclic data structures such as DAGs and trees play a role. Recently, such constraints have been considered in the satisfiability modulo theories (SMT) framework, and in this paper we carry out an analogous extension to the answer set programming (ASP) paradigm. The resulting formalism, ASP modulo acyclicity, offers a rich set of primitives to express constraints related to recursive structures. In the technical results of the paper, we relate the new generalization with standard ASP by showing (i) how acyclicity extensions translate into normal rules, (ii) how weight constraint programs can be instrumented by acyclicity extensions to capture stability in analogy to unfounded set checking, and (iii) how the gap between supported and stable models is effectively closed in the presence of such an extension. Moreover, we present an efficient implementation of acyclicity constraints by incorporating a respective propagator into the stateof- the-art ASP solver CLASP. The implementation provides a unique combination of traditional unfounded set checking with acyclicity propagation. In the experimental part, we evaluate the interplay of these orthogonal checks by equipping logic programs with supplementary acyclicity constraints. The performance results show that native support for acyclicity constraints is a worthwhile addition, furnishing a complementary modeling construct in ASP itself as well as effective means for translation-based ASP solving.

3

Graphs and Colorings for Answer Set Programming with Preferences

Konczak K., Schaub T., Linke T.

Fundamenta Informaticae

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2003

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Vol. 57, nr 2-4

393--421

EN

The integration of preferences into answer set programming constitutes an important practical device for distinguishing certain preferred answer sets from non-preferred ones. To this end, we elaborate upon rule dependency graphs and their colorings for characterizing different preference handling strategies found in the literature. We start from a characterization of (three types of) preferred answer sets in terms of totally colored dependency graphs. In particular, we demonstrate that this approach allows us to capture all three approaches to preferences in a uniform setting by means of the concept of a height function. In turn, we exemplarily develop an operational characterization of preferred answer sets in terms of operators on partial colorings for one particular strategy. In analogy to the notion of a derivation in proof theory, our operational characterization is expressed as a (non-deterministically formed) sequence of colorings, gradually turning an uncolored graph into a totally colored one.