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Incremental Cardinality Constraints for MaxSAT
"... Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a succession of SAT solver calls to reach an optimum solution making extensive use of cardinality constraints. Many of these algorithms are nonincremental i ..."
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Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a succession of SAT solver calls to reach an optimum solution making extensive use of cardinality constraints. Many of these algorithms are nonincremental in nature, i.e. at each iteration the formula is rebuilt and no knowledge is reused from one iteration to another. In this paper, we exploit the knowledge acquired across iterations using novel schemes to use cardinality constraints in an incremental fashion. We integrate these schemes with several MaxSAT algorithms. Our experimental results show a significant performance boost for these algorithms as compared to their nonincremental counterparts. These results suggest that incremental cardinality constraints could be beneficial for other constraint solving domains.
Relaxation Search: A Simple Way of Managing Optional Clauses
"... A number of problems involve managing a set of optional clauses. For example, the soft clauses in a MAXSAT formula are optional—they can be falsified for a cost. Similarly, when computing a Minimum Correction Set for an unsatisfiable formula, all clauses are optional—some can be falsified in order t ..."
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A number of problems involve managing a set of optional clauses. For example, the soft clauses in a MAXSAT formula are optional—they can be falsified for a cost. Similarly, when computing a Minimum Correction Set for an unsatisfiable formula, all clauses are optional—some can be falsified in order to satisfy the remaining. In both of these cases the task is to find a subset of the optional clauses that achieves some criteria, and whose removal leaves a satisfiable formula. Relaxation search is a simple method of using a standard SAT solver to solve this task. Relaxation search is easy to implement, sometimes requiring only a simple modification of the variable selection heuristic in the SAT solver; it offers considerable flexibility and control over the order in which subsets of optional clauses are examined; and it automatically exploits clause learning to exchange information between the two phases of finding a suitable subset of optional clauses and checking if their removal yields satisfiability. We demonstrate how relaxation search can be used to solve MAXSAT and to compute Minimum Correction Sets. In both cases relaxation search is able to achieve stateoftheart performance and solve some instances other solvers are not able to solve.
Exploiting Relevance to Improve Robustness and Flexibility in Plan Generation and Execution
, 2014
"... Automated plan generation and execution is an essential component of most autonomous agents. An agent’s model of the world is often incomplete or incorrect, and its environment is typically noisy. To account for potential discrepancies between the agent’s model of the world and the true state of th ..."
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Automated plan generation and execution is an essential component of most autonomous agents. An agent’s model of the world is often incomplete or incorrect, and its environment is typically noisy. To account for potential discrepancies between the agent’s model of the world and the true state of the world, the planning techniques and representations used should enable flexible and robust agent behaviour. The agent should react swiftly when unexpected changes occur to assess the impact of the discrepancy and to accommodate as necessary. In particular, the agent should avoid unnecessary replanning and recognize changes that are irrelevant for its plan to achieve the goal. In this dissertation we address various aspects of the planning process including (1) how to synthesize a plan, (2) what a plan should constitute and how we should represent one, and (3) how to effectively execute a plan. We enable robust and flexible agent behaviour by exploiting the notion of relevance in each of the key planning areas. Intuitively, relevance characterizes what is important to consider as a sufficient condition for some property to hold. We apply relevance to the key areas of automated planning to achieve the following contributions: (1) increased flexibility of partialorder plans, (2)
Solving QBF by Clause Selection∗ (preprint of an IJCAI ’15 paper)
"... Algorithms based on the enumeration of implicit hitting sets find a growing number of applications, which include maximum satisfiability and model based diagnosis, among others. This paper exploits enumeration of implicit hitting sets in the context of Quantified Boolean Formulas (QBF). The paper st ..."
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Algorithms based on the enumeration of implicit hitting sets find a growing number of applications, which include maximum satisfiability and model based diagnosis, among others. This paper exploits enumeration of implicit hitting sets in the context of Quantified Boolean Formulas (QBF). The paper starts by developing a simple algorithm for QBF with two levels of quantification, which is shown to relate with existing work on enumeration of implicit hitting sets, but also with recent work on QBF based on abstraction refinement. The paper then extends these ideas and develops a novel QBF algorithm, which generalizes the concept of enumeration of implicit hitting sets. Experimental results, obtained on representative problem instances, show that the novel algorithm is competitive with, and often outperforms, the state of the art in QBF solving. 1
1Maximal Falsifiability Definitions, Algorithms, and Applications
"... Similarly to Maximum Satisfiability (MaxSAT), Minimum Satisfiability (MinSAT) is an optimization extension of the Boolean Satisfiability (SAT) decision problem. In recent years, both problems have been studied in terms of exact and approximation algorithms. In addition, the MaxSAT problem has been ..."
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Similarly to Maximum Satisfiability (MaxSAT), Minimum Satisfiability (MinSAT) is an optimization extension of the Boolean Satisfiability (SAT) decision problem. In recent years, both problems have been studied in terms of exact and approximation algorithms. In addition, the MaxSAT problem has been characterized in terms of Maximal Satisfiable Subsets (MSSes) and Minimal Correction Subsets (MCSes), as well as Minimal Unsatisfiable Subsets (MUSes) and minimal hitting set dualization. However, and in contrast with MaxSAT, no such characterizations exist for MinSAT. This paper addresses this issue by casting the MinSAT problem in a more general framework. The paper studies Maximal Falsifiability, the problem of computing a subsetmaximal set of clauses that can be simultaneously falsified, and shows that MinSAT corresponds to the complement of a largest subsetmaximal set of simultaneously falsifiable clauses, i.e. the solution of the Maximum Falsifiability (MaxFalse) problem. Additional contributions of the paper include novel algorithms for Maximum and Maximal Falsifiability, as well as minimal hitting set dualization results for the MaxFalse problem. Moreover, the proposed algorithms are validated on practical instances.
Incremental Cardinality Constraints for MaxSAT‡
"... Abstract. Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a succession of SAT solver calls to reach an optimum solution making extensive use of cardinality constraints. Many of these algorithms are nonincr ..."
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Abstract. Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a succession of SAT solver calls to reach an optimum solution making extensive use of cardinality constraints. Many of these algorithms are nonincremental in nature, i.e. at each iteration the formula is rebuilt and no knowledge is reused from one iteration to another. In this paper, we exploit the knowledge acquired across iterations using novel schemes to use cardinality constraints in an incremental fashion. We integrate these schemes with several MaxSAT algorithms. Our experimental results show a significant performance boost for these algorithms as compared to their nonincremental counterparts. These results suggest that incremental cardinality constraints could be beneficial for other constraint solving domains. 1