Marti, P. and M. Rueher: 1995, `A Distributed Cooperating Constraints Solving System'. International Journal on AI Tools pp. 4(1--2):93--113.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....refers to the guards of constraints. This approach does not deal with the other requirements we addressed here. Many of the extensions described in [9] are already implemented in the standard Oz constraint solvers. As for the cooperation of several solvers, there exists several approaches in [11, 6, 10]. ....

P. Marti and M. Rueher. A distributed cooperating constraint solving system. International Journal on AI Tools, 4(1&2):93--113, 1995.

.... in Constraint Logic Programming [29] various extensions have been proposed, among which methods to solve socalled interval constraints [10, 8, 26, 15, 14, 5, 18, 3, 4, 28, 27] More recently several authors have studied various combinations of solvers in the case of continuous real constraints [20, 22, 13] and, in particular, combinations of techniques from computer algebra (Grobner bases) Interval Constraint methods and techniques from numerical analysis. Similar ideas for the case of 0 1 linear constraints are suggested in [2] which proposes to compute cutting planes to prune the search space ....

.... have been designed to handle similar problems such as Newton [4, 28] based on interval Newton methods and local consistency techniques, CLP(BNR) 5] implementing interval propagation methods, CoSAc [22] which combines Maple, a Grobner bases module and a linear solver, the system presented in [20] based on Grobner bases, the simplex algorithm and interval propagation methods, TKIB [14] introducing an approximation notion called tightening and the Krawckzyk operator [16, 17] In this paper, we propose to combine Grobner bases computations over subsets of the initial system, used as a ....

P. Marti and M. Rueher. A Distributed Cooperating Constraint Solving System. International Journal on Artificial Intelligence Tools, 4(1):93--113, 1995.

.... task, the interest for reusing existing solvers is obvious [17] Even more important, when dealing with problems that cannot be tackled or efficiently solved with a single solver, we definitively realize the interest of integrating several solvers, working, in general, over different domains [15, 3, 9, 16, 14]. This is called Collaboration of Solvers [11] In order to make solvers collaborate, the need for powerful strategy languages to control their integration has been well recognized [12, 13, 2] The existing approaches consider a fixed domain (linear constraints [3] non linear constraints over ....

.... called Collaboration of Solvers [11] In order to make solvers collaborate, the need for powerful strategy languages to control their integration has been well recognized [12, 13, 2] The existing approaches consider a fixed domain (linear constraints [3] non linear constraints over real numbers [14, 9, 7]) a fixed strategy, and a fixed scheme of collaboration (sequential [14, 7] asynchronous [9] In the language Bali, the collaboration is specified using control primitives. The constraint system is a parameter, but the control capabilities for specifying strategies are not fine enough [13] In ....

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P. Marti and M. Rueher. A Distributed Cooperating Constraints Solving System. International Journal of Artificial Intelligence Tools, 4(1-2):93--113, 1995.

....is much faster than our prototype implementation written in Maple. We expect that our techniques can increase the efficiency of Numerica when implemented in C. Since no preliminary modification of CSPs is required for our method, it can be combined with symbolic rewriting [4] or with other solvers [17, 18, 16] without affecting the collaboration. We plan to add some more specialized reduction functions for speeding up computation. We also envisage to use several interval extensions as in [22] We also plan to refine the selection procedure in the chaotic iteration algorithm by choosing not only the ....

P. Marti and M. Rueher. A Distributed Cooperating Constraints Solving System. International Journal on Artificial Intelligence Tools, 4(1&2):93--113, 1995.

....solvers, each one already de ned for one of the theories. Since we want to stay on the same interpretation domain, such frameworks are not well suited. Independently of these theoretical results, more practical issues have been explored for the cooperation of several solvers on a single domain [21, 5, 2, 8, 17], or on several domains [18, 20, 19] However, in such systems, extra function symbols cannot be directly handled. The problem of integrating deduction techniques into computer algebra has attracted considerable interest [24, 10, 3] and standard computer algebra systems (such as Mathematica ....

P. Marti and M. Rueher. A Distributed Cooperating Constraints Solving System. International Journal on AI Tools, 4(1&2):93-113, 1995.

....several solvers collaborate to process constraints that cannot be solved (or efficiently solved) by a single solver. Informally, combination [ Nelson and Oppen, 1979; Kirchner and Ringeissen, 1994; Ringeissen, 1996 ] focuses on building a solver for the union of theories, whereas cooperation [ Marti and Rueher, 1995; Monfroy et al. 1996; Granvilliers, 1998 ] concerns data exchange between solvers devoted to a single domain. Distributed cooperative problem solving has also been studied in the field of artificial intelligence for multi agent systems [ Yokoo et al. 1992 ] in advanced knowledge processing ....

....deduction [ Homann and Calmet, 1995; Dalmas et al. 1996 ] 1 In this paper, we are concerned with the need of a general scheme for integration, and re usability of heterogeneous solvers, together with some strategies and a language for realizing their collaborations. Some systems (such as [ Marti and Rueher, 1995; Monfroy et al. 1996 ] significantly ease integration and cooperation, but they require some modifications of the system itself to add replace solvers. Moreover, these systems provide only one fixed cooperation mechanism for a unique constraint system. The ILOG library approach enables ....

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P. Marti and M. Rueher. A Distributed Cooperating Constraints Solving System. International Journal on AI Tools, 4(1&2):93--113, 1995.

....is widely recognized. The general view consists in doing several solvers collaborate in order to process constraints that cannot be solved (or efficiently solved) by a single solver. Informally combination [16, 11, 17] focuses on building a solver for the union of theories, whereas cooperation [12, 15, 7] concerns communication problems between solvers devoted to a single domain. In this case the collaborating elementary solvers share the constraints according to their specificities. Cooperative distributed problem solving has also been studied in A.I. 20, 2] in the field of knowledge ....

....knowledge processing systems [1] and for integrating symbolic mathematical tools [8] in automated deduction. Designing new solvers is usually a tedious task. Therefore it is important to focus on re usability and integration issues. Some systems (like the cooperative architecture of Marti Rueher [12] and CoSAc [15] have already been proposed for implementing the three notions of solver integration, solver cooperation and re usability. Although they significantly ease integration and cooperation, they require good knowledge of the basic level components of the systems (constraint manager, ....

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P. Marti and M. Rueher. A Distributed Cooperating Constraints Solving System. International Journal on Artificial Intelligence Tools, 4(1&2):93--113, 1995.

....future extensions. 2.2.1 Linear and Non linear Constraints Linear and non linear constraints have been distinguished in Section 2.1. While many of the earlier constraint systems dealt with linear constraints, a number of current systems such as CAL [SA89] and CLP(BNR) OB93] and architectures [MR95, Rue95, Ste93] handle non linear constraints. Interesting areas of related research are linear and non linear programming. 2.2.2 One way and Multi way Constraints One way constraints compute a function and assign the result to a variable. For example, a = b c (treated as a one way constraint) ....

P. Marti and M. Rueher. A distributed cooperating constraints solving system. Special issue of International Journal on Artificial Intelligence Tools, 4(1-2):93--113, June 1995.

.... 30] and backjumping [25, 26, 49] The fifth approach is to entirely replace propagation based techniques, which are algorithmic in nature, by the promising stochastic techniques such as the iterative repair method [45, 41] The sixth approach employs cooperation among different constraint solvers [44, 40]. The last three approaches represent partial or complete modification to the underlying constraint solving mechanism. This type of technological innovation is not easy to come up with. Propagation based constraint languages and tools are widely available. The aim of this research project is to ....

P. Marti and M. Rueher. A distributed cooperating constraints solving system. International Journal on Artificial Intelligence Tools, 4(1&2):93-- 113, 1995.

.... in Constraint Logic Programming [29] various extensions have been proposed, among which methods to solve so called interval constraints [10, 8, 26, 15, 14, 5, 18, 3, 4, 28, 27] More recently several authors have studied various combinations of solvers in the case of continuous real constraints [20, 22, 13] and, in particular, combinations of techniques from computer algebra (Grobner bases) Interval Constraint methods and techniques from numerical analysis. Similar ideas for the case of 0 1 linear constraints are suggested in [2] which proposes to compute cutting planes to prune the search space ....

.... have been designed to handle similar problems such as Newton [4, 28] based on interval Newton methods and local consistency techniques, CLP(BNR) 5] implementing interval propagation methods, CoSAc [22] which combines Maple, a Grobner bases module and a linear solver, the system presented in [20] based on Grobner bases, the simplex algorithm and interval propagation methods, TKIB [14] introducing an approximation notion called tightening and the Krawckzyk operator [16, 17] In this paper, we propose to combine Grobner bases computations over subsets of the initial system, used as a ....

P. Marti and M. Rueher. A Distributed Cooperating Constraint Solving System. International Journal on Artificial Intelligence Tools, 4(1):93--113, 1995.

....different from the original ones. Therefore, such frameworks are not well suited here since we want to stay on the same interpretation domain. Independently of these theoretical results, more practical issues have been investigated for the cooperation of several solvers on the same domain [12, 15, 3]. Furthermore, the first author has developed a system called BALI [14] for designing executing solver collaborations (i.e. solver cooperations and combinations) integrating several paradigms (as concurrency, parallelism, composition) and control instructions (as loops, conditionals, ....

P. Marti and M. Rueher. A Distributed Cooperating Constraints Solving System. International Journal on Artificial Intelligence Tools, 4(1&2):93--113, 1995.

....widely recognized. The general view consists in doing several solvers collaborate in order to process constraints that cannot be solved (or efficiently solved) by a single solver. Informally combination [1, 19, 16, 10, 17] focuses on building a solver for the union of theories, whereas cooperation [2, 12, 15] concerns communication problems between solvers devoted to a single domain. In this case the collaborating elementary solvers shared the constraints according to their specificities. Furthermore automated deduction requires more and more the integration of symbolic mathematical tools [7] for ....

....are executed. Already existing schemes for solver collaboration are of two kinds: either they are built in cooperations (i.e. the mechanisms are mixed and form a single black box solver [13] or they provide an architecture (based on a client server architecture) dedicated to a single domain [12, 15]. Although these latter are closer to BALI, they do not provide such a complete and flexible environment: both are linked to the host language; they apply to a single domain i.e. non linear polynomial constraints; they use a unique paradigm (asynchronous communication for [12] and synchronous ....

[Article contains additional citation context not shown here]

P. Marti and M. Rueher. A Distributed Cooperating Constraints Solving System. International Journal on Artificial Intelligence Tools, 4(1&2):93--113, 1995.

....forms [32, 37, 36, 3] and preconditionning [26] using diagonally dominant Jacobian matrices guarantee good convergences of interval solving. Recently, the cooperation of constraint solvers was discussed in the cc framework [38] and in the CLP context [20, 4, 31] In particular, several works [29, 6] propose to combine symbolic and interval methods for solving systems of nonlinear equations. Essentially, symbolic methods generate redundancies speedingup interval methods. However, more work can be done during the symbolic process. Let us consider the system of equations fxy Gamma x = 0; x ....

P. Marti and M. Rueher. A Distributed Cooperating Constraints Solving System. International Journal on Artificial Intelligence Tools, 4(1):93--113, 1995.

....constraints for a general CSP. The third approach is to replace propagation based techniques, which are algorithmic in nature, entirely by the promising stochastic techniques such as the iterative repair method [18, 15] The fourth approach employs cooperation among different constraint solvers [17]. The last two approaches call for technological innovations, which are usually difficult to come up with. Propagation based constraint languages and tools are widely available. The aim of this research project is to adopt existing technology and devise a general and systematic methodology for ....

P. Marti and M. Rueher. A distributed cooperating constraints solving system. International Journal on Artificial Intelligence Tools, 4(1&2):93--113, 1995.

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Marti, P. and M. Rueher: 1995, `A Distributed Cooperating Constraints Solving System'. International Journal on AI Tools pp. 4(1--2):93--113.

....slow convergence always entails a cyclic phenomenon. Of course, in this case the slow convergence phenomenon can be removed by simplifying the linear system with a linear solver. Cooperation between an interval narrowing solver and a linear solver is especially worthwhile in this latter case [1, 31, 7, 26, 32]. For arbitrary 4 non linear systems, slow convergence very often leads to a cyclic phenomenon too. As arbitrary non linear systems cannot be tackled with a symbolic solver, automatic cycle simplification is the only way to accelerate convergence in many real applications. 1.3. Layout of the ....

P. Marti and M. Rueher. A distributed cooperating constraints solving system. IJAIT (International Journal on Artificial Intelligence Tools) , 4(1-2), 93--113, June 1995.

....slow convergence always entails a cyclic phenomenon. Of course, in this case the slow convergence phenomenon can be removed by simplifying the linear system with a linear solver. Cooperation between the interval narrowing solver and a linear solver is especially worthwhile in this latter case [6, 22, 18]. For arbitrary non linear systems, slow convergence very often leads to a cyclic phenomenon. As arbitrary non linear systems cannot be tackled with a symbolic solver, automatic cycle simplification is the only way to accelerate convergence in the majority of real applications. 1.3 Organization ....

P. Marti and M. Rueher, `A distributed cooperating constraints solving system ', Special issue of IJAIT (International Journal on Artificial Intelligence Tools), 4(1-2), 93--113, (June 1995).

....= 2; x Gamma y = 1g. 2 M. Rueher and C. Solnon The motivation of cooperating approaches is to tackle such mixed systems of constraints over the reals by combining solvers based on different algorithms. Many systems combining a LP solver and an INsolver have been proposed during the last years [3, 8, 5, 14, 5, 6]. The purpose of this paper is to introduce and to study a novel cooperating architecture based on the following features: Pi A concurrent architecture; Pi An active use of the LP solver. 1.1. Concurrent Architecture Cooperating solvers are usually based on the scheme suggested by Hong [11] ....

P. Marti and M. Rueher. A Distributed Cooperating Constraints Solving System Special issue of IJAIT (International Journal on Artificial Intelligence Tools), 4(1-2):93--113, June 1995.

....nous ont montr# qu une combinaison d algorithmes symboliques et Figure 2: Visualisation des processus et des messages sous sdrc d algorithmes num#riques pouvait s av#rer tr#s fructueuse. Pour permettre une r#utilisation de solveurs existants nous avons d# ni un mod#le de coop#ration, sdrc [22, 31], bas# sur la notion d acteurs communiquant de mani#re asynchrone via des messages iaskj et itellj. Les dioe#rents agents de SDRC sont ex#cut#s via une machine parall#le virtuelle (PVM) qui assure la gestion des processus et le passage des messages. La coop#ration entre les solveurs est illustr#e, ....

P. Marti and M. Rueher. A distributed cooperating constraints solving system. Special issue of the International Journal on Artiøcial Intelligence Tools (World Scientiøc), vol. 4, number 1-2, 93113, 1995.

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Marti, P., and Rueher, M. A Distributed Cooperating Constraints Solving System. International Journal on Arti cial Intelligence Tools 4, 1&2 (1995), 93-113.

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P. Marti and M. Rueher. A distributed cooperating constraint solving system. International Journal on AI Tools, 4(1&2):93--113, 1995.

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