A Hybrid Approach to Optimization in Answer Set Programming

Peer reviewe

Evaluation of ILP-based approaches for partitioning into colorful components

The NP-hard Colorful Components problem is a graph partitioning problem on vertex-colored graphs. We identify a new application of Colorful Components in the correction of Wikipedia interlanguage links, and describe and compare three exact and two heuristic approaches. In particular, we devise two ILP formulations, one based on Hitting Set and one based on Clique Partition. Furthermore, we use the recently proposed implicit hitting set framework [Karp, JCSS 2011; Chandrasekaran et al., SODA 2011] to solve Colorful Components. Finally, we study a move-based and a merge-based heuristic for Colorful Components. We can optimally solve Colorful Components for Wikipedia link correction data; while the Clique Partition-based ILP outperforms the other two exact approaches, the implicit hitting set is a simple and competitive alternative. The merge-based heuristic is very accurate and outperforms the move-based one. The above results for Wikipedia data are confirmed by experiments with synthetic instances

Reduced Cost Fixing in MaxSAT

Peer reviewe

Set-theoretic duality: A fundamental feature of combinatorial optimisation

The duality between conflicts and diagnoses in the field of diagnosis, or between plans and landmarks in the field of planning, or between unsatisfiable cores and minimal co-satisfiable sets in SAT or CSP solving, has been known for many years. Recent wo

The Seesaw Algorithm: Function Optimization Using Implicit Hitting Sets

The paper introduces the Seesaw algorithm, which explores the Pareto frontier of two given functions. The algorithm is complete and generalizes the well-known implicit hitting set paradigm. The first given function determines a cost of a hitting set and is optimized by an exact solver. The second, called the oracle function, is treated as a black-box. This approach is particularly useful in the optimization of functions that are impossible to encode into an exact solver. We show the effectiveness of the algorithm in the context of static solver portfolio selection. The existing implicit hitting set paradigm is applied to cost function and an oracle predicate. Hence, the Seesaw algorithm generalizes this by enabling the oracle to be a function. The paper identifies two independent preconditions that guarantee the correctness of the algorithm. This opens a number of avenues for future research into the possible instantiations of the algorithm, depending on the cost and oracle functions used

A Core-Guided Approach to Learning Optimal Causal Graphs

Peer reviewe

Implicit Hitting Set Algorithms for Constraint Optimization

Computationally hard optimization problems are commonplace not only in theory but also in practice in many real-world domains. Even determining whether a solution exists can be NP-complete or harder. Good, ideally globally optimal, solutions to instances of such problems can save money, time, or other resources. We focus on a particular generic framework for solving constraint optimization problems, the so-called implicit hitting set (IHS) approach. The approach is based on a theory of duality between solutions and sets of mutually conflicting constraints underlying a problem. Recent years have seen a number of new instantiations of the IHS approach for various problems and constraint languages. As the main contributions, we present novel instantiations of this generic algorithmic approach to four different NP-hard problem domains: maximum satisfiability (MaxSAT), learning optimal causal graphs, propositional abduction, and answer set programming (ASP). For MaxSAT, we build on an existing IHS algorithm with a fresh implementation and new methods for integrating preprocessing. We study a specific application of this IHS approach to MaxSAT for learning optimal causal graphs. In particular we develop a number of domain-specific search techniques to specialize the IHS algorithm for the problem. Furthermore, we consider two optimization settings where the corresponding decision problem is beyond NP, in these cases Σᴾ₂-hard. In the first, we compute optimal explanations for propositional abduction problems. In the second, we solve optimization problems expressed as answer set programs with disjunctive rules. For each problem domain, we empirically evaluate the resulting algorithm and contribute an open-source implementation. These implementations improve or complement the state of the art in their respective domains.Käytännön sovellutuksista kumpuavat optimointiongelmat ovat usein laskennallisesti haastavia. Deklaratiiviset menetelmät tarjoavat keskeisen tavan lähestyä erinäisiä laskennallisesti haastavia optimointiongelmia. Deklaratiivisissa lähestymistavoissa ratkaistavana oleva ongelma mallinnetaan yleisesti matemaattisina rajoitteina siten, että alkuperäisen ongelman instanssien rajoitekuvauksen rajoitteet voidaan toteuttaa jos ja vain jos ongelmainstanssille on olemassa ratkaisu. Ratkaisujen löytäminen rajoitekuvaukselle edellyttää yleisten algoritmisten ratkaisumenetelmien kehittämistä rajoitekuvauskielille. Tässä väitöskirjassa kehitetään uudentyyppisiä käytännöllisiä eksakteja deklaratiivisia ratkaisumenetelmiä jotka pohjautuvat ns. implicit hitting set (IHS) -optimointialgoritmiparadigmaan. Erityisesti työssä kehitetään ja toteutetaan IHS-pohjaisia menetelmiä neljälle laskennallisesti haastavalle, tekoälytutkimuksen näkökulmasta motivoidulle NP-kovalle optimointiongelmalle: lauselogiikan optimointilaajennukselle (MaxSAT), keskeiselle epämonotonisen päättelyn lähestymistavalle (answer set optimization, ASP), lauseloogiselle abduktiolle, sekä optimaalisten kausaaliverkkojen löytämisongelmalle. Työssä kehitetään sekä yleisiä että ongelmakohtaisia hakutekniikoita IHS-kontekstissa, kehitetään avoimen lähdekoodin implementaatioita, ja osoitetaan empiriisten evaluaatioiden kautta näiden olevan käytännössä varteenotettavia vaihtoehtoja kunkin ongelman tehokkaaseen ratkaisemiseen