Nadel, B.: 1989, `Constraint Satisfaction Algorithms'. Computational Intelligence 5, 188--224.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....category. 3 clp(FD) in a nutshell As introduced in Logic Programming by the CHIP language, clp(FD) 6] is a constraint logic language based on nite domains, where constraint solving is done by propagation and consistency techniques originating from Constraint Satisfaction Problems [25] 11] [14]. Very close to those methods are the interval arithmetic constraints of BNR Prolog [1] The novelty of clp(FD) is the use of a unique primitive constraint which allows the user to de ne his own high level constraints. The black box approach gives way to glass box approach. 3.1 The ....

....Y = 1g has not yet been found. Indeed, in order to eciently achieve consistency, the traditional method (arc consistency) only checks that, for any constraint C involving X and Y , for each value in the domain of X there exists a value in the domain of Y satisfying C and vice versa (see [25] 11] [14] for more details) So, once arc consistency has been achieved and the domains have been reduced, an enumeration (called labeling) has to be done on the domains of the variables to yield the exact solutions. Namely, X is assigned to one value in DX , its consequences are propagated to other ....

B. A. Nadel. Constraint Satisfaction Algorithms. Computational Intelligence 5 (1989), pp 188-224.

.... given by Gaschnig [34] who described a backtracking algorithm that incorporates arc consistency; McGregor [54] who described backtracking combined with forward checking, which is a truncated form of arc consistency; Haralick and Elliott [41] who also added various look ahead methods; and Nadel [60], who discussed backtracking combined with many variations of partial arcconsistency. Gaschnig [33] has compared Waltz style look ahead backtracking with look back improvements that he introduced, such as backjumping and backmarking. Haralick and Elliot [41] have done a relatively comprehensive ....

B. A. Nadel. Constraint satisfaction algorithms. Computational Intelligence, 5:188-224, 1989.

....a ight is minimized. 3 clp(FD) in a Nutshell As introduced in Logic Programming by the CHIP language, clp(FD) 6] is a constraint logic language based on nite domains, where constraint solving is done by propagation and consistency techniques originating from Constraint Satisfaction Problems [15, 17, 10]. The novelty of clp(FD) is the use of a unique primitive constraint which allows users to de ne their own high level constraints. The black box approach gives way to glass box approach. We have developed a new constraint, the atmost interval constraint that enables the implementation of a ....

B.A. Nadel. Constraint satisfaction algorithms. Computationnal Intelligence, no 5:pp 188-224, 1989.

....is that there should be as many abstract machines as constraint domains and solvers. We chose to focus on Finite Domains (FD) as introduced in LP by the CHIP language, where constraint solving is done by propagation and consistency techniques originating from Constraint Satisfaction Problems [48, 30, 33]. Very close to those methods are the interval arithmetic constraints of BNR Prolog [4] Luckily, a recent paper [46] broke the black box monopoly by unveiling a glass box for FD constraints. The basic idea is to have a single constraint X in r, where r denotes a range (e.g. t1: t2) More ....

....constraint by which complex constraints are de ned, so for example constraints such as X = Y or X 2Y are de ned by FD constraints, instead of being built into the theory. This constraint is thought of as propagation rules, i.e. rules for describing node and arc consistency propagation (see [48, 30, 33] for more details on CSPs and consistency algorithms) We present here the basic notions underlying the FD constraint system. A domain in FD is a (non empty) nite set of natural numbers (i.e. a range) More precisely a range is a subset of f0; 1; infinityg where infinity is a particular ....

B. A. Nadel. Constraint Satisfaction Algorithms. Computational Intelligence 5 (1989), pp 188-224.

....heuristic. The same instances were translated in SAT problems with AC and PIC encoding, and then solved by BerkMin561. For ternary classes 100 instances were also generated and solved by NFCx [BMFL02] where x is 0 or 5, using GAC2001 [BR01] and dom deg dvo [BR96] without singleton propagation [Nad89]. Here again, the same instances were translated with 1 AC, 2 AC, 3 AC, mixed(1) and mixed(2) encodings, and solved by BerkMin561 . The results of our approach take also into account the translation duration, which include the time spent on reading the csp le and writing the cnf. Note that ....

B.A. Nadel. Constraint satisfaction algorithms. Computational Intelligence, 5:188224, 1989.

....Backjumping (B J) and Conflict Directed Backjumping (CBJ) have not been proven before. The orderings proved also to be a stimulus for developing more efficient backtracking algorithms. The idea of combining Backjumping and Backmarking into a new hybrid algorithm was first put forward by Nadel [8]. Such algorithm, called BMJ, was presented by Prosser It0] BMJ, however, does not retain all the power of both base algorithms in terms of consistency checks. Presser observed that on some instances of the zebra problem BMJ performs more consistency checks than BM. In the conclusion of his paper ....

....We propose a modification to the hybrids, and then include these algorithms in our hi erarchies. Backmarking (BM) imposes a marking scheme on the Chronological Backtracking algorithm in order to eliminate some redundant consistency checks. The scheme is based on the following two observations [8]: a) If at the most recent node where a given instantia tion was checked the instantiation failed against some past instantiation that has not yet changed, then it will fail against it again. Therefore, all consistency checks involving it may be avoided. b) If, at the most recent node where a ....

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B. Nadel. Constraint satisfaction algorithms. Cornput. Intell., 5:188-224, 1989.

....algorithms that maintain a local consistency property at each node in their search tree. Various types of local consistency have been defined, and algorithms developed for enforcing them (e. g, 5, 13, 14] Algorithms that maintain a local consistency property during backtracking search (e.g. [8, 10, 15, 16, 20]) can detect dead ends sooner and thus have the potential of significantly reducing the size of the tree they have to search. Such algorithms have demonstrated significant empirical advantages and are the algorithms of choice in practice. Hence, they are the most relevant objects of study. We ....

....The forward checking algorithm (FC) 10, 15, 25] enforces arc consistency only on the constraints which have exactly one uninstantiated variable. By comparison, on a problem that is not empty after enforcing arc consistency, the maintaining arc consistency or really full lookahead algorithms [8, 16, 20], as their names suggest, enforce full arc consistency on the induced CSP. 2.2 Dual and hidden transformations The dual and hidden transformations are two general methods for converting a nonbinary CSP into an equivalent binary CSP. The dual transformation comes from the relational database ....

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B. A. Nadel. Constraint satisfaction algorithms. Computational Intelligence, 5:188--224, 1989.

....algorithms that maintain a local consistency property at each node in their search tree. Various types of local consistency have been defined, and algorithms developed for enforcing them (e. g, 5, 13, 14] Algorithms that maintain a local consistency property during backtracking search (e.g. [8, 10, 15, 16, 20]) can detect dead ends sooner and thus have the potential of significantly reducing the size of the tree they have to search. Such algorithms have demonstrated significant empirical advantages and are the algorithms of choice in practice. Hence, they are the most relevant objects of study. We ....

....The forward checking algorithm (FC) 10, 15, 25] enforces arc consistency only on the constraints which have exactly one uninstantiated variable. By comparison, on a problem that is not empty after enforcing arc consistency, the maintaining arc consistency or really full lookahead algorithms [8, 16, 20], as their names suggest, enforce full arc consistency on the induced CSP. 2.2 Dual and hidden transformations The dual and hidden transformations are two general methods for converting a nonbinary CSP into an equivalent binary CSP. The dual transformation comes from the relational database ....

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B. A. Nadel. Constraint satisfaction algorithms. Computational Intelligence, 5:188--224, 1989.

....the constraint on the quality of a solution. 2. 2 Using Constraint Types Constraint based reasoning owes a large portion of its success to systems like CHIP [Dincbas et al. 1988] and ILOG Solver [Puget, 1994] that integrate powerful inferences on global constraints into backtracking algorithms [Nadel, 1989] . Because of the well founded semantics of hard constraints [Mackworth, 1992] PROLOG like languages denote constraints by built in predicates. Constraint propagation is used to improve unification [Diaz and Codognet, 1993] of these predicates. When using soft constraints, the situation is a bit ....

B. A. Nadel. Constraint satisfaction algorithms. Computational Intelligence, 5:188--224, 1989.

....The traditional way of solving a CSP is to assign a value to one variable and then see if the assignment violates any constraints involving this variable and other previously instantiated variables. If there is a violation, another value is chosen; otherwise we go to the next unassigned variable [4]. If we exhaust the domain of a variable without success, then we can backtrack to a previously instantiated variable and change its value. Several methods rely on multiple agents to solve a CSP. The Distributed Constraint Satisfaction Problem (DCSP) is defined as in [6] In DCSP the variables of ....

....4. Check the constraints with one or two missing variables; set their change flag if an inconsistency is found. 5. Give the partial solution back to the pool. Agent 1 Owned variables: x 0 x 2 , x 3 Constraints: x 3 x 2 10, x 0 x 1 6, x 1 x 1 12 Partial Solution 1: [1,3,4,2,2] Partial Solution 2: 7,2,6,1,3] Partial Solution 3: 3,7,3,1,4] Agent 2 Owned variables: x 0 , x 1 Constraints: x 0 x 2 7 The results of running the SCSPS.java program to solve randomly generated CSPs are given in [2] where we witnessed very good scalability. 4. Solving the Traveling ....

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B. A. Nadel, "Constraint satisfaction algorithms", Computational Intelligence, No. 5, 1989.

....The traditional way of solving a CSP is to assign a value to one variable and then see if the assignment violates any constraints involving this variable and other previously instantiated variables. If there is a violation, another value is chosen; otherwise we go to the next unassigned variable [3]. If we exhaust the domain of a variable without success, then we can backtrack to a previously instantiated variable and change its value. 3.2 Related Work Several methods rely on multiple agents to solve a CSP. The Distributed Constraint Satisfaction Problem (DCSP) is defined as in [6] In ....

....The agents continue like this until the workpool s counter for the number of checked out partial solutions reaches the limit. At this point no more partial solutions are given out and the agents stop executing. The main processing loop in each agent is shown in figure 4. Partial Solution 1: [1,3,4,2,2] Partial Solution 2: 7,2,6,1,3] Partial Solution 3: 3,7,3,1,4] Fig. 4. The algorithm followed by each agent in SCSPS.java. Table 1 contains the results of several runs of the program to solve six problems using 1, 5, 10 and 20 agents. 30 runs were attempted for each row. There were 21 ....

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B. A. Nadel, "Constraint satisfaction algorithms", Computational Intelligence, No. 5, 1989.

....Backmarking addresses another drawback of backtracking. Consistency checks are performed without keeping the information, which of them were already performed at an earlier stage. Backmarking imposes a marking scheme [Gas77] This marking scheme is based on two observations, again identi ed in [Nad89] 1. If, at the most recent node where a given instantiation was checked, the instantiation failed against some past instantiation that has not yet changed, then it will fail against it again. 2. If, at the most recent node where a given instantiation was checked, the instantiation succeeded ....

B. A. Nadel. Constraint satisfaction algorithms. Computational Intelligence, 5:188-224, 1989.

....some parameters in common. There has developed a considerable body of literature on the processing of constraint networks. This literature tends to fall into two broad classes. In the first kind of paper, which is where the term CSP is used, constraint networks are assumed to have finite domains [10, 13, 16, 21, 23, 25], the relationships imposed by constraints are expressed extensionally, and the CSPs are NP complete. Although the CSPs in this literature can be solved by backtracking search, the exponential computational cost of such search algorithms has led to the development of preprocessing algorithms [12, ....

Nadel, B. (1989) Constraint Satisfaction Algorithms. Computational Intelligence, 5 (4), 188-224.

....of different pruning strategies for each constraint. These pruning strategies include forward checking, partial lookahead and full lookahead [Hen89] but also contain many other pruning behaviours in between forward checking and lookahead. The existence of such pruning strategies was suggested in [Nad89]. In [VDS94] these pruning strategies were presented and discussed. Another feature of the finite domain language is a powerful enumeration primitive [Van94] consistency techniques (removal of inconsistent values) are not enough to solve a finite domain problem. Most problems also need ....

Bernard A. Nadel. Constraint satisfaction algorithms. Computational Intelligence, 5(4):188--224, November 1989.

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Nadel, B.: 1989, `Constraint Satisfaction Algorithms'. Computational Intelligence 5, 188--224.

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B.A. Nadel. Constraint satisfaction algorithms. Computational Intelligence, 5:188--224, 1989.

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B.A. Nadel. Constraint satisfaction algorithms. Computational Intelligence, 5:188-- 224, 1989.

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B.A. Nadel. Constraint satisfaction algorithms. Computational Intelligence, 5:188 224, 1989.

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B.E. Nadel. Constraint satisfaction algorithms. Computational Intelligence, 5(4):188--224, 1989.

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B.A. Nadel, Constraint Satisfaction Algorithms, Computational Intelligence 5(4): 188-224, 1989

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B. A. Nadel (1989). Constraint satisfaction algorithms. Comput. Intell. 5(4): 188--224.

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B.A. Nadel. Constraint satisfaction algorithms. Computational Intelligence, 5:188-224, 1989.

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B.A. Nadel. Constraint satisfaction algorithms. Computational Intelligence, 5:188 224, 1989.

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B.E. Nadel. Constraint satisfaction algorithms. Computational Intelligence, 5(4):188--224, 1989.

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B. A. Nadel. Constraint Satisfaction Algorithms. Computational Intelligence 5 (1989), pp 188-224.

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