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18
Heuristics for dynamically adapting propagation
 In ECAI2008
, 2008
"... Building adaptive constraint solvers is a major challenge in constraint programming. An important line of research towards this goal is concerned with ways to dynamically adapt the level of local consistency applied during search. A related problem that is receiving a lot of attention is the design ..."
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Cited by 9 (3 self)
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Building adaptive constraint solvers is a major challenge in constraint programming. An important line of research towards this goal is concerned with ways to dynamically adapt the level of local consistency applied during search. A related problem that is receiving a lot of attention is the design of adaptive branching heuristics. The recently proposed adaptive variable ordering heuristics of Boussemart et al. use information derived from domain wipeouts to identify highly active constraints and focus search on hard parts of the problem resulting in important saves in search effort. In this paper we show how information about domain wipeouts and value deletions gathered during search can be exploited, not only to perform variable selection, but also to dynamically adapt the level of constraint propagation achieved on the constraints of the problem. First we demonstrate that when an adaptive heuristic is used, value deletions and domain wipeouts caused by individual constraints largely occur in clusters of consecutive or nearby constraint revisions. Based on this observation, we develop a number of simple heuristics that allow us to dynamically switch between enforcing a weak, and cheap local consistency, and a strong but more expensive one, depending on the activity of individual constraints. As a case study we experiment with binary problems using AC as the weak consistency and maxRPC as the strong one. Results from various domains demonstrate the usefulness of the proposed heuristics. 1
Exploiting constraint weights for revision ordering in Arc Consistency Algorithms
 In Submitted to the ECAI08 Workshop on Modeling and Solving Problems with Constraints
, 2008
"... Abstract. Coarse grained arc consistency algorithms, like AC3, operate by maintaining a list of arcs (or variables) that records the revisions that are still to be performed. It is well known that the performance of such algorithms is affected by the order in which revisions are carried out. As a r ..."
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Cited by 7 (3 self)
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Abstract. Coarse grained arc consistency algorithms, like AC3, operate by maintaining a list of arcs (or variables) that records the revisions that are still to be performed. It is well known that the performance of such algorithms is affected by the order in which revisions are carried out. As a result, several heuristics for ordering the elements of the revision list have been proposed. These heuristics exploit information about the original and the current state of the problem, such as domain sizes, variable degrees, and allowed combinations of values, to reduce the number of constraint checks and list operations aiming at speeding up arc consistency computation. Recently, Boussemart et al. proposed novel variable ordering heuristics that exploit information about failures gathered throughout search and recorded in the form of constraint weights. Such heuristics are now considered as the most efficient general purpose variable ordering heuristic for CSPs. In this paper we show how information about constraint weights can be exploited to efficiently order the revision list when AC is applied during search. We propose a number of simple revision ordering heuristics based on constraint weights for arc, variable, and constraint oriented implementations of coarse grained arc consistency algorithms, and compare them to the most efficient existing revision ordering heuristic. Importantly, the new heuristics can not only reduce the numbers of constraints checks and list operations, but also cut down the size of the explored search tree. Results from various structured and random problems demonstrate that some of the proposed heuristics can offer significant speedups. 1
Value Ordering for Quantified CSPs
"... We investigate the use of value ordering in backtracking search for Quantified Constraint Satisfaction problems (QCSPs). We consider two approaches for ordering heuristics. The first approach is solutionfocused and is inspired by adversarial search: on existential variables we prefer values that ..."
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Cited by 5 (2 self)
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We investigate the use of value ordering in backtracking search for Quantified Constraint Satisfaction problems (QCSPs). We consider two approaches for ordering heuristics. The first approach is solutionfocused and is inspired by adversarial search: on existential variables we prefer values that maximise the chances of leading to a solution, while on universal variables we prefer values that minimise those chances. The second approach is verificationfocused, where we prefer values that are easier to verify whether or not they lead to a solution. In particular, we give instantiations of this approach using QCSPSolve’s purevalue rule [1]. We show that on dense 3block problems, using QCSPSolve, the solutionfocused adversarial heuristics are up to 50 % faster than lexicographic ordering, while on sparse loose interleaved problems, the verificationfocused purevalue heuristics are up to 50 % faster. Both types are up to 50 % faster on dense interleaved problems, with one purevalue heuristic approaching an order of magnitude improvement.
Experimental evaluation of modern variable selection strategies in Constraint Satisfaction Problems
"... Constraint programming is a powerful technique for solving combinatorial search problems that draws on a wide range of methods from artificial intelligence and computer science. Constraint solvers search the solution space either systematically, as with backtracking or branch and bound algorithms, o ..."
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Cited by 3 (1 self)
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Constraint programming is a powerful technique for solving combinatorial search problems that draws on a wide range of methods from artificial intelligence and computer science. Constraint solvers search the solution space either systematically, as with backtracking or branch and bound algorithms, or use forms of local search which may be incomplete. Systematic methods typically interleave search and inference. A key factor that can dramatically reduce the search space is the criterion under which we decide which variable will be the next to be instantiated. Numerous heuristics have been proposed for this purpose in the literature. Recent years have seen the emergence of new and powerful methods for choosing variables during CSP search. Some of these methods exploit information about failures gathered throughout search and recorded in the form of constraint weights, while others measure the importance/impact of variable assignments for reducing the search space. In this paper we experimentally evaluate the most recent and powerful variable ordering heuristics, and new variants of them, over a wide range of academic, random and real world problems. Results demonstrate that heuristics based on failures are in general faster. To be precise, heuristic dom/wdeg and its variants are the dominant heuristics in most instances tried. 1
On conflictdriven variable ordering heuristucs
 In Proceedings of the ERCIM workshop  CSCLP
, 2008
"... Abstract. It is well known that the order in which variables are instantiated by a backtracking search algorithm can make an enormous difference to the search effort in solving CSPs. Among the plethora of heuristics that have been proposed in the literature to efficiently order variables during sear ..."
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Abstract. It is well known that the order in which variables are instantiated by a backtracking search algorithm can make an enormous difference to the search effort in solving CSPs. Among the plethora of heuristics that have been proposed in the literature to efficiently order variables during search, a significant recently proposed class uses the learningfromfailure approach. Prime examples of such heuristics are the wdeg and dom/wdeg heuristics of Boussemart et al. which store and exploit information about failures in the form of constraint weights. The efficiency of all the proposed conflictdirected heuristics is due to their ability to learn though conflicts encountered during search. As a result, they can guide search towards hard parts of the problem and identify contentious constraints. Such heuristics are now considered as the most efficient general purpose variable ordering heuristic for CSPs. In this paper we show how information about constraint weights can be used in order to create several new variants of the wdeg and dom/wdeg heuristics. The proposed conflictdriven variable ordering heuristics have been tested over a wide range of benchmarks. Experimental results show that they are quite competitive compared to existing ones and in some cases they can increase efficiency. 1
A portable and efficient implementation of global constraints: the tree constraint case
"... Abstract. Global constraints represent invaluable modeling tools for Constraint Programming (CP). Efficiently solving recurrent subproblems is a key point for CP successes. However, global constraints mainly remain strongly attached to a given constraint solver. Indeed, they heavily rely on internal ..."
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Abstract. Global constraints represent invaluable modeling tools for Constraint Programming (CP). Efficiently solving recurrent subproblems is a key point for CP successes. However, global constraints mainly remain strongly attached to a given constraint solver. Indeed, they heavily rely on internal mechanisms in order to be as efficient as possible. In this paper, we emphasize the interest of decoupling global constraint implementations from the underlying solver. We show, on a tree constraint, that even more decoupling it by providing fully dynamic algorithms enhances efficiency and, which is much more important, allow an efficient portability of the constraint. We illustrate this for the Choco and Gecode solvers. 1
Incorporating Variance in ImpactBased Search
"... Abstract. We present a simple modification to the idea of impactbased search which has proven highly effective for several applications. Impacts measure the average reduction in search space due to propagation after a variable assignment has been committed. Rather than considering the mean reductio ..."
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Abstract. We present a simple modification to the idea of impactbased search which has proven highly effective for several applications. Impacts measure the average reduction in search space due to propagation after a variable assignment has been committed. Rather than considering the mean reduction only, we consider the idea of incorporating the variance in reduction. Experimental results show that using variance can result in improved search performance. Keywords: Search Strategies, Impactbased Search, Robust Search 1
Sat and hybrid models of the car sequencing problem
 In CPAIOR
, 2014
"... Abstract. We compare both pure SAT and hybrid CP/SAT models for solving car sequencing problems, and close 13 out of the 23 large open instances in CSPLib. Three features of these models are crucial to improving the state of the art in this domain. For quickly finding solutions, advanced CP heurist ..."
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Abstract. We compare both pure SAT and hybrid CP/SAT models for solving car sequencing problems, and close 13 out of the 23 large open instances in CSPLib. Three features of these models are crucial to improving the state of the art in this domain. For quickly finding solutions, advanced CP heuristics are important and good propagation (either by a specialized propagator or by a sophisticated SAT encoding that simulates one) is necessary. For proving infeasibility, clause learning in the SAT solver is critical. Our models contain a number of novelties. In our hybrid models, for example, we develop a linear time mechanism for explaining failure and pruning the ATMOSTSEQCARD constraint. In our SAT models, we give powerful encodings for the same constraint. Our research demonstrates the strength and complementarity of SAT and hybrid methods for solving difficult sequencing problems.
Evaluating and improving modern variable and revision ordering strategies for CSPs
 Fundamenta Informaticae
"... A key factor that can dramatically reduce the search space during constraint solving is the criterion under which the variable to be instantiated next is selected. For this purpose numerous heuristics have been proposed. Some of the best of such heuristics exploit information about failures gathere ..."
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A key factor that can dramatically reduce the search space during constraint solving is the criterion under which the variable to be instantiated next is selected. For this purpose numerous heuristics have been proposed. Some of the best of such heuristics exploit information about failures gathered throughout search and recorded in the form of constraint weights, while others measure the importance of variable assignments in reducing the search space. In this work we experimentally evaluate the most recent and powerful variable ordering heuristics, and new variants of them, over a wide range of benchmarks. Results demonstrate that heuristics based on failures are in general more efficient. Based on this, we then derive new revision ordering heuristics that exploit recorded failures to efficiently order the propagation list when arc consistency is maintained during search. Interestingly, in addition to reducing the number of constraint checks and list operations, these heuristics are also able to cut down the size of the explored search tree.
Operations Research Methods in Constraint Programming
"... A number of operations research (OR) methods have found their way into constraint programming (CP). This development is entirely natural, since OR and CP have similar goals. OR is essentially a variation on the scientific practice of mathematical modeling. It describes phenomena in a formal language ..."
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A number of operations research (OR) methods have found their way into constraint programming (CP). This development is entirely natural, since OR and CP have similar goals. OR is essentially a variation on the scientific practice of mathematical modeling. It describes phenomena in a formal language that allows one to deduce consequences in a rigorous way. Unlike a typical scientific model, however, an OR model has a prescriptive as well as a descriptive purpose. It represents a human activity with some freedom of choice, rather than a natural process. The laws of nature become constraints that the activity must observe, and the goal is to maximize some objective subject to the constraints. CP’s constraintoriented approach to problem solving poses a prescriptive modeling task very similar to that of OR. CP historically has been less concerned with finding optimal than feasible solutions, but this is a superficial difference. It is to be expected, therefore, that OR methods would find application in solving CP models. There remains a fundamental difference, however, in the way that CP and OR understand constraints. CP typically sees a constraint as a procedure, or at least as invoking a procedure, that operates on the solution space, normally by reducing variable domains.