Abstract. In this work we present the Partner Units Problem as a novel challenge for optimization methods. It captures a certain type of configuration problem that frequently occurs in industry. Unfortunately, it can be shown that in the most general case an optimization version of the problem is intractable. We present and evaluate encodings of the problem in the frameworks of answer set programming, propositional satisfiability testing, constraint solving, and integer programming. We also show how to adapt these encodings to a class of problem instances that we have recently shown to be tractable.

General action languages, like e.g. the Situation Calculus, use full classical logic to represent knowledge of actions and their effects in dynamic domains. Description Logics, on the other hand, have been developed to represent static knowledge with the help of decidable subsets of first-order logic. In this paper, we show how to use Description Logic as the basis for a decidable yet still expressive action formalism. To this end, we use ABoxes as decidable state descriptions in the basic Fluent Calculus. As a second contribution, we thus obtain an independent semantics-based on a general action formalism-for a recent method for ABox-Update.

The Partner Units Problem is a challenging combinatorial search problem that originates in the domain of security and surveillance. Technically it consists of partitioning a bipartite graph under side conditions. In this work we describe how constraint programming technology can be leveraged to tackle the problem. We address problem modelling, symmetry breaking and problem-specific search strategies. We introduce the best search strategy known to date as well as a powerful new implied constraint for pruning the search space. Finally, we present implementations in ECL i PS e Prolog and the MINION constraint solver and compare these to a state-of-the-art dedicated algorithm.

In this paper we present the core of LoCo, a logic-based high-level representation language for expressing configuration problems. LoCo shall allow to model these problems in an intuitive and declarative way, the dynamic aspects of configuration notwithstanding. Our logic enforces that configurations contain only finitely many components and reasoning can be reduced to the task of model construction.

No abstract