Results 1  10
of
34
A Global Constraint for Total Weighted Completion Time for Cumulative Resources
, 2008
"... The criterion of total weighted completion time occurs as a subproblem of combinatorial optimization problems in such diverse areas as scheduling, container loading and storage assignment in warehouses. These applications often necessitate considering a rich set of requirements and preferences, whi ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
The criterion of total weighted completion time occurs as a subproblem of combinatorial optimization problems in such diverse areas as scheduling, container loading and storage assignment in warehouses. These applications often necessitate considering a rich set of requirements and preferences, which makes constraint programming (CP) an effective modeling and solving approach. On the other hand, basic CP techniques can be inefficient in solving models that require inference over sum type expressions. In this paper, we address increasing the solution efficiency of constraintbased approaches to cumulative resource scheduling with the above criterion. Extending previous results for unary capacity resources, we define the COMPLETIONm global constraint for propagating the total weighted completion time of activities that require the same cumulative resource. We present empirical results in two different problem domains: scheduling a single cumulative resource, and container loading with constraints on the location of the center of gravity. In both domains, the proposed constraint propagation algorithm outperforms existing propagation techniques.
Kernels for Global Constraints
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... Bessière et al. (AAAI’08) showed that several intractable global constraints can be efficiently propagated when certain natural problem parameters are small. In particular, the complete propagation of a global constraint is fixedparameter tractable in k – the number of holes in domains – whenever b ..."
Abstract

Cited by 8 (6 self)
 Add to MetaCart
Bessière et al. (AAAI’08) showed that several intractable global constraints can be efficiently propagated when certain natural problem parameters are small. In particular, the complete propagation of a global constraint is fixedparameter tractable in k – the number of holes in domains – whenever bound consistency can be enforced in polynomial time; this applies to the global constraints ATMOSTNVALUE and EXTENDED GLOBAL CARDINALITY (EGC). In this paper we extend this line of research and introduce the concept of reduction to a problem kernel, a key concept of parameterized complexity, to the field of global constraints. In particular, we show that the consistency problem for ATMOSTNVALUE constraints admits a linear time reduction to an equivalent instance on O(k2) variables and domain values. This small kernel can be used to speed up the complete propagation of NVALUE constraints. We contrast this result by showing that the consistency problem for EGC constraints does not admit a reduction to a polynomial problem kernel unless the polynomial hierarchy collapses.
An Analysis of Slow Convergence in Interval Propagation
"... Abstract. When performing interval propagation on integer variables with a large range, slowconvergence phenomena are often observed: it becomes difficult to reach the fixpoint of the propagation. This problem is practically important, as it hinders the use of propagation techniques for problems wi ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
(Show Context)
Abstract. When performing interval propagation on integer variables with a large range, slowconvergence phenomena are often observed: it becomes difficult to reach the fixpoint of the propagation. This problem is practically important, as it hinders the use of propagation techniques for problems with large numerical ranges, and notably problems arising in program verification. A number of attempts to cope with this issue have been investigated, yet all of the proposed techniques only guarantee a fast convergence on specific instances. An important question is therefore whether slow convergence is intrinsic to propagation methods, or whether an improved propagation algorithm may exist that would avoid this problem. This paper proposes the first analysis of the slow convergence problem under the light of complexity results. It answers the question, by a negative result: if we allow propagators that are general enough, computing the fixpoint of constraint propagation is shown to be intractable. Slow convergence is therefore unavoidable unless P=NP. The result holds for the propagators of a basic class of constraints. 1
Tractable Cases of the Extended Global Cardinality Constraint
, 2008
"... We study the consistency problem for extended global cardinality (EGC) constraints. An EGC constraint consists of a set X of variables, a set D of values, a domain D(x) ⊆ D for each variable x, anda“cardinality set ” K(d) of nonnegative integers for each value d. The problem is to instantiate each ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
We study the consistency problem for extended global cardinality (EGC) constraints. An EGC constraint consists of a set X of variables, a set D of values, a domain D(x) ⊆ D for each variable x, anda“cardinality set ” K(d) of nonnegative integers for each value d. The problem is to instantiate each variable x with a value in D(x) such that for each value d, the number of variables instantiated with d belongs to the cardinality set K(d). It is known that this problem is NPcomplete in general, but solvable in polynomial time if all cardinality sets are intervals. First we pinpoint connections between EGC constraints and general factors in graphs. This allows us to extend the known polynomialtime case to certain noninterval cardinality sets. Second we consider EGC constraints under restrictions in terms of the treewidth of the value graph (the bipartite graph representing variablevalue pairs) and the cardinalitywidth (the largest integer occurring in the cardinality sets). We show that EGC constraints can be solved in polynomial time for instances of bounded treewidth, where the order of the polynomial depends on the treewidth. We show that (subject to the complexity theoretic assumption FPT � = W[1]) this dependency cannot be avoided without imposing additional restrictions. If, however, also the cardinalitywidth is bounded, this dependency gets removed and EGC constraints can be solved in linear time.
Lparse Programs Revisited: Semantics and Representation of Aggregates
"... Abstract. Lparse programs are logic programs with weight constraints as implemented in the SMODELS system, which constitute an important class of logic programs with constraint atoms. To effectively apply lparse programs to problem solving, a clear understanding of its semantics and representation p ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
(Show Context)
Abstract. Lparse programs are logic programs with weight constraints as implemented in the SMODELS system, which constitute an important class of logic programs with constraint atoms. To effectively apply lparse programs to problem solving, a clear understanding of its semantics and representation power is indispensable. In this paper, we study the semantics of lparse programs, called the lparse semantics. We show that for a large class of programs, called strongly satisfiable programs, the lparse semantics agrees with the semantics based on conditional satisfaction. However, when the two semantics disagree, a stable model admitted by the lparse semantics may be circularly justified. We then present a transformation, by which an lparse program can be transformed to a strongly satisfiable one, so that no circular models may be generated under the current implementation of SMODELS. This leads to an investigation of a methodological issue, namely the possibility of compact representation of aggregate programs by lparse programs. We present some experimental results to compare this approach with the ones where aggregates are more explicitly handled. 1
Improved Filtering for Weighted Circuit Constraints
"... We study the weighted circuit constraint in the context of constraint programming. It appears as a substructure in many practical applications, particularly routing problems. We propose a domain filtering algorithm for the weighted circuit constraint that is based on the 1tree relaxation of Held a ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
We study the weighted circuit constraint in the context of constraint programming. It appears as a substructure in many practical applications, particularly routing problems. We propose a domain filtering algorithm for the weighted circuit constraint that is based on the 1tree relaxation of Held and Karp. In addition, we study domain filtering based on an additive bounding procedure that combines the 1tree relaxation with the assignment problem relaxation. Experimental results on Traveling Salesman Problem instances demonstrate that our filtering algorithms can dramatically reduce the problem size. In particular, the search tree size and solving time can be reduced by several orders of magnitude, compared to existing constraint programming approaches. Moreover, for mediumsize problem instances, our method is competitive with the stateoftheart specialpurpose TSP solver Concorde.
Propagating separable equalities in an MDD store
"... Abstract. We present a propagator that achieves MDD consistency for a separable equality over an MDD (multivalued decision diagram) store in pseudopolynomial time. We integrate the propagator into a constraint solver based on an MDD store introduced in [1]. Our experiments show that the new propaga ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We present a propagator that achieves MDD consistency for a separable equality over an MDD (multivalued decision diagram) store in pseudopolynomial time. We integrate the propagator into a constraint solver based on an MDD store introduced in [1]. Our experiments show that the new propagator provides substantial computational advantage over propagation of two inequality constraints, and that the advantage increases when the maximum width of the MDD store increases. In [1] we proposed a widthlimited multivalued decision diagram (MDD) as a general constraint store for constraint programming. We demonstrated the potential of MDDbased constraint solving by developing MDDpropagators for alldiff and inequality constraints. In this paper, we describe an MDDpropagator for the separable equality constraint that uses a pseudopolynomial algorithm to achieve MDD consistency. We show the computational advantage of the new propagator over the existing approach of modeling equalities with two inequality propagators.
Global constraints in distributed constraint satisfaction and optimization. The Computer Journal
, 2014
"... Global constraints are an essential component in the efficiency of centralized constraint programming. We propose to include global constraints in distributed constraint satisfaction problem (DisCSP) and distributed constraint optimization problem (DCOP). We detail how this inclusion can be done, co ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
Global constraints are an essential component in the efficiency of centralized constraint programming. We propose to include global constraints in distributed constraint satisfaction problem (DisCSP) and distributed constraint optimization problem (DCOP). We detail how this inclusion can be done, considering different representations for global constraints (direct, nested, binary). We explore the relation of global constraints with local consistency (both in the hard and soft cases), in particular, for generalized arc consistency (GAC). We provide experimental evidence of the benefits of global constraints on several benchmarks, both for distributed constraint satisfaction and for distributed constraint optimization.
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 ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
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
Limits of preprocessing
 In Proceedings of the TwentyFifth Conference on Artificial Intelligence, AAAI 2011
, 2011
"... We present a first theoretical analysis of the power of polynomialtime preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability, Nonmonotonic and Bayesian Reasoning. We show that, subject to a ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
We present a first theoretical analysis of the power of polynomialtime preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability, Nonmonotonic and Bayesian Reasoning. We show that, subject to a complexity theoretic assumption, none of the considered problems can be reduced by polynomialtime preprocessing to a problem kernel whose size is polynomial in a structural problem parameter of the input, such as induced width or backdoor size. Our results provide a firm theoretical boundary for the performance of polynomialtime preprocessing algorithms for the considered problems.