S. de Givry, G. Verfaillie, and T. Schiex. Bounding the optimum of constraint optimization problems. In Proc. CP97, number 1330 in LNCS, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....18.6 4 12.0 6.64 8.12 7.00 6.90 6.65 5 15.1 5.29 6.39 5.48 6.21 5.83 6 17.7 6.39 5.36 4.61 4.66 4.81 7 19.6 6.70 8.64 9.20 9.75 8.78 Table 3: Speedup of UD MB(z) over nMB(z) Decoding. ations Research, Constraint satisfaction, heuristic search and probabilistic reasoning [ Pearl, 1988; de Givry et al. 1997; Schiex, 2000] The bucket elimination scheme [Dechter, 1999] provides a unifying framework that facilitates the development of general methods for combinatorial optimization problems. It also helps to the cross fertilization of ideas across different fields. Mini bucket elimination [Dechter ....

S. de Givry, G. Verfaillie and T. Schiex. Bounding the optimum of Constraint Optimization Problems. In Proceeding of CP'97.

....problem: the optimum of the simplified problem, either is a lower bound of the original problem, or allows computing such a bound. The simplification may be a relaxation of the constraints, such as removing or weakening some constraints. It may be a modification of the objective function [de Givry et al. 97] Studying the structure of the minimisation problem, one can deduce obvious lower bounds. For example, in the Travelling Salesman Problem, a trivial lower bound is the sum of the shortest distances starting from every city. For some combinatorial problems, there exist approximate ....

S. de Givry, G. Verfaillie and T. Schiex. Bounding the Optimum of Constraint Optimization Problems. Proc. of CP-97, p. 405-419, Linz, Austria, 1997.

....a fewer number of steps, or also that the abstracted problem can be processed by a machinery which is not available in the concrete context. There are many formal proposals to describe the process of abstracting a notion, be it a formula, or a problem [21] or even a classical [14] or a soft CSP [22]. Among these, we chose to use one based on Galois insertions [9] mainly to refer to a well know theory, with many results and properties that can be useful for our purposes. This made our approach compatible with the general theory of abstraction in [21] Then, we adapted it to work on soft ....

....semiring and abstractions between them. 11 Related work We will compare here our work to other abstraction proposals, more or less related to the concepts of constraints. 11.1 Abstracting valued CSPs The only other abstraction scheme for soft constraint problems we are aware of is the one in [22], where valued CSPs [30] are abstracted in order to produce good lower bounds for the optimal solutions. The concept of valued CSPs is similar to our notion of SCSPs. In fact, in valued CSPs, the goal is to minimize the value associated to a complete assignment. In valued CSPs, each constraint has ....

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S. de Givry, G. Verfaillie, , and T. Schiex. Bounding The Optimum of Constraint Optimization Problems. In G. Smolka, editor, Proc. CP97, pages 405-419. Springer-Verlag, LNCS 1330, 1997.

....that satisfies given constraints. CSP has been applied to many real world applications, such as scheduling [ Zweben, 1994 ] planning and product configuration [ Sabin, 1998 ] A variety of general algorithms [Tsang, 1993] Mackworth, 1977 ] Mackworth, 1985 ] Minton, 1992 ] Givry, 1997 ] have been developed for finding consistent, or less inconsistent assignments of values to predefined constraints. However, in the real world applications, the problems are sometimes incompletely defined such that problem descriptions lack some constraints or priority of the constraints [ ....

....the time complexity. In all experiments, we use binary soft constraints as the missing parts of the problems. A soft constraint assigns a score from 1 to 10 randomly for every value pair of two variables in the constraint. The soft constraints are almost similar to the criteria P 0V CSP in [Givry, 1997 ] The goodness of the solution is measured as the total amount of the scores of values pairs of the soft constraints. All of the soft constraints are unknown to the solver. Through the experiments, we generated CSPs randomly with six parameters, the number of conditional variables, P , the ....

Simon de Givry, G'erard Verfaillie, and Thomas Schiex. Bounding the Optimum of Constraint Optimization Problems. In Proceedings of the Third International Conference on Principles and Practice of Constraint Programming, 405--419, 1997.

....propagation rules for the concrete problem from propagation rules for the abstract problem. This may be useful when we don t have any (or any e#cient) propagation algorithm in the concrete setting. The only other abstraction scheme for soft constraint problems we are aware of is the one in [12], where valued CSPs [17] are abstracted in order to produce good lower bounds for the optimal solutions. The concept of valued CSPs is similar to our notion of SCSPs. In fact, in valued CSPs, the goal is to minimize the value associated to a complete assignment. In valued CSPs, each constraint ....

.... our notion of soft CSPs and that in valued CSPs are just di#erent formalizations of the same idea, since one can pass from one formalization to the other one without changing the solutions, provided that the partial order is total [3] However, our abstraction scheme is di#erent from the one in [12]. In fact, we are not only interested in finding good lower bounds for the optimum, but also in finding the exact optimal solutions in a shorter time. Moreover, we don t define ad hoc abstraction functions but we follow the classical abstraction scheme devised in [6] with Galois insertions to ....

S. de Givry, G. Verfaillie, , and T. Schiex. Bounding The Optimum of Constraint Optimization Problems. In G. Smolka, editor, Proc. CP97, pages 405--419. Springer-Verlag, LNCS 1330, 1997.

....fuzzy, or optimized, or probabilistic, or even classical hard constraints. For valued constraints, we do not have yet full CLP languages working with them, but we have many techniques to achieve good lower bounds for their optimal solutions, which in most real cases seem to be good enough [50, 28]. Constraint query languages. As noted above, constraints are just relations, thus it is obvious that many researchers have investigated the relationship between CLP technology and Databases (DB) In this area of research, there are mainly two ways in which constraints and databases have ....

S. de Givry, G. Verfaille, , and T. Schiex. Bounding The Optimum of Constraint Optimization Problems. In G. Smolka, editor, Proc. CP97, pages 405--419. Springer-Verlag, LNCS 1330, 1997.

....18.6 4 12.0 6.64 8.12 7.00 6.90 6.65 5 15.1 5.29 6.39 5.48 6.21 5.83 6 17.7 6.39 5.36 4.61 4.66 4.81 7 19.6 6.70 8.64 9.20 9.75 8.78 Table 3: Speedup of UD MB(z) over nMB(z) Decoding. ations Research, Constraint satisfaction, heuristic search and probabilistic reasoning [ Pearl, 1988; de Givry et al. 1997; Schiex, 2000] The bucket elimination scheme [Dechter, 1999] provides a unifying framework that facilitates the development of general methods for combinatorial optimization problems. It also helps to the cross fertilization of ideas across different fields. Mini bucket elimination [Dechter ....

S. de Givry, G. Verfaillie and T. Schiex. Bounding the optimum of Constraint Optimization Problems. In Proceeding of CP'97.

....propagation rules for the concrete problem from propagation rules for the abstract problem. This may be useful when we don t have any (or any efficient) propagation algorithm in the concrete setting. The only other abstraction scheme for soft constraint problems we are aware of is the one in [12], where valued CSPs [17] are abstracted in order to produce good lower bounds for the optimal solutions. The concept of valued CSPs is similar to our notion of SCSPs. In fact, in valued CSPs, the goal is to minimize the value associated to a complete assignment. In valued CSPs, each constraint has ....

.... our notion of soft CSPs and that in valued CSPs are just different formalizations of the same idea, since one can pass from one formalization to the other one without changing the solutions, provided that the partial order is total [3] However, our abstraction scheme is different from the one in [12]. In fact, we are not only interested in finding good lower bounds for the optimum, but also in finding the exact optimal solutions in a shorter time. Moreover, we don t define ad hoc abstraction functions but we follow the classical abstraction scheme devised in [6] with Galois insertions to ....

S. de Givry, G. Verfaille, , and T. Schiex. Bounding The Optimum of Constraint Optimization Problems. In G. Smolka, editor, Proc. CP97, pages 405--419. Springer-Verlag, LNCS 1330, 1997.

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S. de Givry, G. Verfaillie, and T. Schiex (1997) Bounding the Optimum of Constraint Optimization Problems. In Proc. of the 3rd International Conference on Principles and Practice of Constraint Programming (CP-97), Schloss Hagenberg, Austria.

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S. de Givry, G. Verfaillie and T. Schiex (1997). Bounding the optimum of constraint optimization problems. Proc. of the Third International Conference on Principles and Practice of Constraint Programming, pages 405--419, Schloss Hagenberg, Austria.

....completely a simplified problem: the optimum of the simplified problem, either is a lower bound of the original problem, or allows such a bound to be computed. Such a simplification is currently obtained by removing some constraints or by removing some forbidden tuples in some constraints. In [3], it is obtained by modifying the violation aggregation function to be minimized. 3.2 Objective simplification Another method to obtain a problem lower bound consists in aiming at a simpler objective, like Local Consistency. For example, Directed Arc Consistency preprocessing [20] produces a ....

.... the first considered variables are the least constrained; note that choosing the inverse order leads to worse results: solving subproblems is strongly penalized by a bad variable ordering; This optimum has been proven by producing a lower bound, equal to the best upper bound found (see [3]) 500 1000 1500 2000 2500 bound cpu time (in seconds) CELAR6 instance 0 500 1000 1500 2000 2500 bound cpu time (in seconds) CELAR6 instance idrds ior Fig. 12. Radio Link Frequency Assignment Problem the similar behavior of rbf, id, ior, and ia was unexpected; it may be due to the ....

S. de Givry, G. Verfaillie, and T. Schiex. Bounding the Optimum of Constraint Optimization Problems. In Proc. of the 3rd International Conference on Principles and Practice of Constraint Programming (CP-97), Schloss Hagenberg, Austria, 1997.

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S. de Givry, G. Verfaillie, and T. Schiex. Bounding the optimum of constraint optimization problems. In Proc. CP97, number 1330 in LNCS, 1997.

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S. de Givry, G. Verfaillie, and T. Schiex. Bounding the optimum of constraint optimization problems. In Proc. of Constraint Programming CP97, number 1330 in LNCS, 1997.

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S. de Givry, G. Verfaillie, and T. Schiex. Bounding the optimum of constraint optimization problems. In Proc. of Constraint Programming CP97, number 1330 in LNCS, 1997.

No context found.

S. de Givry, G. Verfaillie, and T. Schiex. Bounding the optimum of constraint optimization problem. In Proc. of CP'97, Schloss Hagenberg, Austria, 1997.

No context found.

S. De Givry, G. Verfaillie, and T. Schiex, Bounding the optimum of constraint optimization problems, Proceedings of the 3rd International Conference on Principles and Practice of Constraint Programming (CP-97), 1997.

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de Givry, S. ; Verfaillie, G. ; et Schiex, T. 1997. Bounding the optimum of constraint optimization problems. Dans Proc. of CP'97. 19

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