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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 ..."
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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.
The weighted average constraint
 CP 2012, volume 7514 of LNCS
, 2012
"... Abstract. Weighted average expressions frequently appear in the context of allocation problems with balancing based constraints. In combinatorial optimization they are typically avoided by exploiting problems specificities or by operating on the search process. This approach fails to apply when th ..."
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Abstract. Weighted average expressions frequently appear in the context of allocation problems with balancing based constraints. In combinatorial optimization they are typically avoided by exploiting problems specificities or by operating on the search process. This approach fails to apply when the weights are decision variables and when the average value is part of a more complex expression. In this paper, we introduce a novel average constraint to provide a convenient model and efficient propagation for weighted average expressions appearing in a combinatorial model. This result is especially useful for Empirical Models extracted via Machine Learning (see [2]), which frequently count average expressions among their inputs. We provide basic and incremental filtering algorithms. The approach is tested on classical benchmarks from the OR literature and on a workload dispatching problem featuring an Empirical Model. In our experimentation the novel constraint, in particular with incremental filtering, proved to be even more efficient than traditional techniques to tackle weighted average expressions. 1
Global Constraints in Distributed CSP: Concurrent GAC and Explanations in ABT
"... Abstract. The expressiveness of Distributed CSP has been recently enhanced to include global constraints. Careful reformulation of contractible global constraints has been shown to improve efficiency. In this paper, we first show that explained global constraints further improves the efficiency in ..."
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Abstract. The expressiveness of Distributed CSP has been recently enhanced to include global constraints. Careful reformulation of contractible global constraints has been shown to improve efficiency. In this paper, we first show that explained global constraints further improves the efficiency in distributed problems, sometimes by over two orders of magnitude. We then propose maintaining GAC concurrently for any global constraint, without reformulation. We show empirically that concurrent GAC significantly reduces both message passing and computation time, achieving an order of magnitude improvement on some distributed meeting scheduling problems. 1
Global Constraints Outline
"... • Knapsack constraint • Regular constraint • Research directions ..."
On the SubexponentialTime Complexity of CSP
"... Not all NPcomplete problems share the same practical hardness with respect to exact computation. Whereas some NPcomplete problems are amenable to efficient computational methods, others are yet to show any such sign. It becomes a major challenge to develop a theoretical framework that is more fine ..."
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Not all NPcomplete problems share the same practical hardness with respect to exact computation. Whereas some NPcomplete problems are amenable to efficient computational methods, others are yet to show any such sign. It becomes a major challenge to develop a theoretical framework that is more finegrained than the theory of NPcompleteness, and that can explain the distinction between the exact complexities of various NPcomplete problems. This distinction is highly relevant for constraint satisfaction problems under natural restrictions, where various shades of hardness can be observed in practice. Acknowledging the NPhardness of such problems, one has to look beyond polynomial time computation. The theory of subexponentialtime complexity provides such a framework, and has been enjoying increasing popularity in complexity theory. An instance of the constraint satisfaction problem with n variables over a domain of d values can be solved by bruteforce in dn steps (omitting a polynomial factor). In this paper we study the existence of subexponentialtime algorithms, that is, algorithms running in do(n) steps, for various natural restrictions of the constraint satisfaction problem. We consider both the constraint satisfaction problem in which all the constraints are given extensionally as tables, and that in which all the constraints are given intensionally in the form of global constraints. We provide tight characterizations of the subexponentialtime complexity of the aforementioned problems with respect to several natural structural parameters, which allows us to draw a detailed landscape of the subexponentialtime complexity of the constraint satisfaction problem. Our analysis provides fundamental results indicating whether and when one can significantly improve on the bruteforce search approach for solving the constraint satisfaction problem. 1.
Decision diagrams for optimization
, 2014
"... Decision diagrams are compact graphical representations of Boolean functions originally introduced for applications in circuit design, simulation, and formal verification. Recently, they have been considered for a variety of purposes in optimization and operations research. These include facet enume ..."
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Decision diagrams are compact graphical representations of Boolean functions originally introduced for applications in circuit design, simulation, and formal verification. Recently, they have been considered for a variety of purposes in optimization and operations research. These include facet enumeration in integer programming, maximum flow computation in largescale networks, solution counting in combinatorics, and learning in genetic programming techniques. In this thesis we develop new methodologies based on decision diagrams to tackle discrete optimization problems. A decision diagram is viewed here as a graphical representation of the feasible solution set of a discrete problem. Since such diagrams may grow exponentially large in cases of most interest, we work with the concept of approximate decision diagrams, first introduced by Andersen et al (2007). An approximate decision diagram is a graph of parameterized size that represents instead an overapproximation or underapproximation of the feasible solution set. Thus, it can be used to obtain either bounds on the optimal solution value or primal solutions to the problem. As our first contribution, we provide a modeling framework based on dynamic programming