AAAI Publications, Sixteenth International Conference on Principles of Knowledge Representation and Reasoning

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A Hybrid Approach to Optimization in Answer Set Programming
Paul Saikko, Carmine Dodaro, Mario Alviano, Matti Järvisalo

Last modified: 2018-09-24


Answer set programming (ASP) is today a successful approach to knowledge representation and reasoning in various real-world problem domains. ASP offers an expressive rule-based constraint modelling language, supporting concise declarative modelling of both decision and optimization problems within the first or the second level of the polynomial hierarchy. In this paper, we propose a new approach to solving optimization problems via ASP, i.e., to the problem of finding optimal solutions (in terms of optimal answer sets or stable models) under a given weight function over soft atoms (weak constraints). Our approach constitutes the first adaptation of the so-called implicit hitting set approach in the context of ASP. In particular, in contrast to the earlier proposed family of core-guided algorithms for optimization in answer set programming, we present a hybrid approach which makes use of interactions between an ASP decision solver (as an unsatisfiable core extractor) and an integer programming solver (as a minimum-cost hitting set algorithm). We explain how various concepts and features specific to ASP and IP can be harnessed within the approach, including several ways for obtaining better upper and lower bounds during search, with the aim of speeding up the computation of an optimal answer set. By a careful integration of the interactions between state-of-the-art ASP and IP solvers, we show that already our first implementation provides a complementary approach when empirically compared to the currently available solvers supporting optimization in answer set programming.


knowledge representation and reasoning; answer set programming; optimization; integer programming; algorithms; solvers

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