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Intelligent Backtracking On Constraint Satisfaction Problems: Experimental And Theoretical Results
, 1995
"... The Constraint Satisfaction Problem is a type of combinatorial search problem of much interest in Artificial Intelligence and Operations Research. The simplest algorithm for solving such a problem is chronological backtracking, but this method suffers from a malady known as "thrashing," in which ess ..."
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Cited by 47 (0 self)
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The Constraint Satisfaction Problem is a type of combinatorial search problem of much interest in Artificial Intelligence and Operations Research. The simplest algorithm for solving such a problem is chronological backtracking, but this method suffers from a malady known as "thrashing," in which essentially the same subproblems end up being solved repeatedly. Intelligent backtracking algorithms, such as backjumping and dependencydirected backtracking, were designed to address this difficulty, but the exact utility and range of applicability of these techniques have not been fully explored. This dissertation describes an experimental and theoretical investigation into the power of these intelligent backtracking algorithms. We compare the empirical performance of several such algorithms on a range of problem distributions. We show that the more sophisticated algorithms are especially useful on those problems with a small number of constraints that happen to be difficult for chronologica...
A General Stochastic Approach to Solving Problems with Hard and Soft Constraints
 The Satisfiability Problem: Theory and Applications
, 1996
"... . Many AI problems can be conveniently encoded as discrete constraint satisfaction problems. It is often the case that not all solutions to a CSP are equally desirable  in general, one is interested in a set of "preferred" solutions (for example, solutions that minimize some cost function) . Pref ..."
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Cited by 46 (1 self)
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. Many AI problems can be conveniently encoded as discrete constraint satisfaction problems. It is often the case that not all solutions to a CSP are equally desirable  in general, one is interested in a set of "preferred" solutions (for example, solutions that minimize some cost function) . Preferences can be encoded by incorporating "soft" constraints in the problem instance. We show how both hard and soft constraints can be handled by encoding problems as instances of weighted MAXSAT (finding a model that maximizes the sum of the weights of the satisfied clauses that make up a problem instance). We generalize a localsearch algorithm for satisfiability to handle weighted MAXSAT. To demonstrate the effectiveness of our approach, we present experimental results on encodings of a set of wellstudied network Steinertree problems. This approach turns out to be competitive with some of the best current specialized algorithms developed in operations research. 1. Introduction Traditi...
Solving Problems with Hard and Soft Constraints Using a Stochastic Algorithm for MAXSAT
, 1995
"... Stochastic local search is an effective technique for solving certain classes of large, hard propositional satisfiability problems, including propositional encodings of problems such as circuit synthesis and graph coloring (Selman, Levesque, and Mitchell 1992; Selman, Kautz, and Cohen 1994). Many pr ..."
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Cited by 42 (3 self)
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Stochastic local search is an effective technique for solving certain classes of large, hard propositional satisfiability problems, including propositional encodings of problems such as circuit synthesis and graph coloring (Selman, Levesque, and Mitchell 1992; Selman, Kautz, and Cohen 1994). Many problems of interest to AI and operations research cannot be conveniently encoded as simple satisfiability, because they involve both hard and soft constraints  that is, any solution may have to violate some of the less important constraints. We show how both kinds of constraints can be handled by encoding problems as instances of weighted MAXSAT (finding a model that maximizes the sum of the weights of the satisfied clauses that make up a problem instance). We generalize our localsearch algorithm for satisfiability (GSAT) to handle weighted MAXSAT, and present experimental results on encodings of the Steiner tree problem, which is a wellstudied hard combinatorial search problem. On many...
Using CSP LookBack Techniques to Solve RealWorld SAT Instances
, 1997
"... We report on the performance of an enhanced version of the "DavisPutnam" (DP) proof procedure for propositional satisfiability (SAT) on large instances derived from realworld problems in planning, scheduling, and circuit diagnosis and synthesis. Our results show that incorporating CSP lookback ..."
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Cited by 40 (0 self)
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We report on the performance of an enhanced version of the "DavisPutnam" (DP) proof procedure for propositional satisfiability (SAT) on large instances derived from realworld problems in planning, scheduling, and circuit diagnosis and synthesis. Our results show that incorporating CSP lookback techniques  especially the relatively new technique of relevancebounded learning  renders easy many problems which otherwise are beyond DP's reach. Frequently they make DP, a systematic algorithm, perform as well or better than stochastic SAT algorithms such as GSAT or WSAT. We recommend that such techniques be included as options in implementations of DP, just as they are in systematic algorithms for the more general constraint satisfaction problem. Introduction While CNF propositional satisfiability (SAT) is a specific kind constraint satisfaction problem (CSP), until recently there has been little application of popular CSP lookback techniques in SAT algorithms. In previo...
Computing With Default Logic
, 1999
"... Default logic was proposed by Reiter as a knowledge representation tool. In this paper, we present our work on the Default Reasoning System, DeReS, the first comprehensive and optimized implementation of default logic. While knowledge representation remains the main application area for default l ..."
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Cited by 39 (5 self)
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Default logic was proposed by Reiter as a knowledge representation tool. In this paper, we present our work on the Default Reasoning System, DeReS, the first comprehensive and optimized implementation of default logic. While knowledge representation remains the main application area for default logic, as a source of largescale problems needed for experimentation and as a source of intuitions needed for a systematic methodology of encoding problems as default theories we use here the domain of combinatorial problems. To experimentally study the performance of DeReS we developed a benchmarking system, the TheoryBase. The TheoryBase is designed to support experimental investigations of nonmonotonic reasoning systems based on the language of default logic or logic programming. It allows the user to create parameterized collections of default theories having similar properties and growing sizes and, consequently, to study the asymptotic performance of nonmonotonic systems under i...
Experimenting with Nonmonotonic Reasoning
 IN PROCEEDINGS OF THE 12TH INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING
, 1995
"... In this paper, we describe a system, called TheoryBase, whose goal is to facilitate experimental studies of nonmonotonic reasoning systems. TheoryBase generates test default theories and logic programs. It has an identification system for generated theories, which allows us to reconstruct a logic pr ..."
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Cited by 37 (6 self)
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In this paper, we describe a system, called TheoryBase, whose goal is to facilitate experimental studies of nonmonotonic reasoning systems. TheoryBase generates test default theories and logic programs. It has an identification system for generated theories, which allows us to reconstruct a logic program or a default theory from its identifier. Hence, exchanging test cases requires only exchanging identifiers. TheoryBase can generate a large variety of examples of default theories and logic programs. We believe that its universal adoption may significantly advance experimental studies of nonmonotonic reasoning systems.
Compiling Problem Specifications into SAT
, 2001
"... We present a compiler that translates a problem specification into a propositional satisfiability test (SAT). Problems are specified in a logicbased language, called npspec, which allows the definition of complex problems in a highly declarative way, and whose expressive power is such to captu ..."
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Cited by 36 (10 self)
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We present a compiler that translates a problem specification into a propositional satisfiability test (SAT). Problems are specified in a logicbased language, called npspec, which allows the definition of complex problems in a highly declarative way, and whose expressive power is such to capture exactly all problems which belong to the complexity class NP. The target SAT instance is solved using any of the various stateoftheart solvers available from the community. The system obtained is an executable specification language for all NP problems which shows interesting computational properties. The performances of the system have been tested on a few classical problems, namely graph coloring, Hamiltonian cycle, and jobshop scheduling. c flSpringerVerlag. To appear on the Proceedings of the European Symposium On Programming (ESOP 2001) Genova, Italy, April 26, 2001 Lecture Notes in Computer Science, SpringerVerlag, 2001. ftp://ftp.dis.uniroma1.it/pub/ai/papers/cadoscha01.ps.gz 1
SATenstein: Automatically Building Local Search SAT Solvers From Components
"... Designing highperformance algorithms for computationally hard problems is a difficult and often timeconsuming task. In this work, we demonstrate that this task can be automated in the context of stochastic local search (SLS) solvers for the propositional satisfiability problem (SAT). We first intr ..."
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Cited by 32 (9 self)
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Designing highperformance algorithms for computationally hard problems is a difficult and often timeconsuming task. In this work, we demonstrate that this task can be automated in the context of stochastic local search (SLS) solvers for the propositional satisfiability problem (SAT). We first introduce a generalised, highly parameterised solver framework, dubbed SATenstein, that includes components gleaned from or inspired by existing highperformance SLS algorithms for SAT. The parameters of SATenstein control the selection of components used in any specific instantiation and the behaviour of these components. SATenstein can be configured to instantiate a broad range of existing highperformance SLSbased SAT solvers, and also billions of novel algorithms. We used an automated algorithm configuration procedure to find instantiations of SATenstein that perform well on several wellknown, challenging distributions of SAT instances. Overall, we consistently obtained significant improvements over the previously bestperforming SLS algorithms, despite expending minimal manual effort. 1 1
Propagation via Lazy Clause Generation
"... Finite domain propagation solvers effectively represent the possible values of variables by a set of choices which can be naturally modelled as Boolean variables. In this paper we describe how to mimic a finite domain propagation engine, by mapping propagators into clauses in a SAT solver. This imm ..."
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Cited by 31 (19 self)
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Finite domain propagation solvers effectively represent the possible values of variables by a set of choices which can be naturally modelled as Boolean variables. In this paper we describe how to mimic a finite domain propagation engine, by mapping propagators into clauses in a SAT solver. This immediately results in strong nogoods for finite domain propagation. But a naive static translation is impractical except in limited cases. We show how to convert propagators to lazy clause generators for a SAT solver. The resulting system introduces flexibility in modelling since variables are modelled dually in the propagation engine and the SAT solver, and we explore various approaches to the dual modelling. We show that the resulting system solves many finite domain problems significantly faster than other techniques.
Random 3SAT: The Plot Thickens
 IN PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING
, 2000
"... This paper presents an experimental investigation of the following questions: how does the averagecase complexity of random 3SAT, understood as a function of the order (number of variables) for xed density (ratio of number of clauses to order) instances, depend on the density? Is there a phase tra ..."
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Cited by 28 (2 self)
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This paper presents an experimental investigation of the following questions: how does the averagecase complexity of random 3SAT, understood as a function of the order (number of variables) for xed density (ratio of number of clauses to order) instances, depend on the density? Is there a phase transition in which the complexity shifts from polynomial to exponential in the order? Is the transition dependent or independent of the solver? Our experiment design uses three complete SAT solvers embodying dierent algorithms: GRASP, CPLEX, and CUDD. We observe new phase transitions for all three solvers, where the median running time shifts from polynomial in the order to exponential. The location of the phase transition appears to be solverdependent. While GRASP and CUDD shift from polynomial to exponential complexity at a density of about 3.8, CUDD exhibits this transition between densities of 0.1 and 0.5. This experimental result underscores the dependence between the solver and the complexity phase transition, and challenges the widely held belief that random 3SAT exhibits a phase transition in computational complexity very close to the crossover point.