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Tailoring solverindependent constraint models: A case study with essence’ and minion
 In Proceedings of the 7th International Symposium on Abstraction, Reformulation and Approximation
, 2007
"... Abstract. In order to apply constraint programming to a particular domain, the problem must first be modelled as a constraint satisfaction problem. There are typically many alternative models of a given problem, and formulating an effective model requires a great deal of expertise. To reduce this bo ..."
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Abstract. In order to apply constraint programming to a particular domain, the problem must first be modelled as a constraint satisfaction problem. There are typically many alternative models of a given problem, and formulating an effective model requires a great deal of expertise. To reduce this bottleneck, the Essence language allows the specification of a problem abstractly, i.e. without making modelling decisions. This specification is refined automatically by the Conjure system to a solverindependent constraint modelling language Essence ′. However, there is still significant work involved in translating an Essence ′ model for use with a particular constraint solver. This paper discusses this ‘tailoring’ process with reference to the constraint solver Minion. 1
The challenge of generating spatially balanced scientific experiment designs
 In: CPAIOR’04
, 2004
"... The development of the theory and construction of combinatorial designs originated with the work of Euler on Latin squares. A Latin square on symbols is an matrix ( is the order of the Latin square), in which each symbol occurs precisely once in each row and in each column. Several interesting resea ..."
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Cited by 14 (1 self)
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The development of the theory and construction of combinatorial designs originated with the work of Euler on Latin squares. A Latin square on symbols is an matrix ( is the order of the Latin square), in which each symbol occurs precisely once in each row and in each column. Several interesting research questions posed by Euler with respect to Latin squares, namely regarding orthogonality properties, were only solved in 1959 [3]. Many other questions concerning Latin squares constructions still remain open today. From the perspective of the Constraint Programing (CP), Artificial Intelligence (AI), and Operations Research (OR) communities, combinatorial design problems are interesting since they possess rich structural properties that are also observed in realworld applications such as scheduling, timetabling, and error correcting codes. Thus, the area of combinatorial designs has been a good source of challenge problems for these research communities. In fact, the study of combinatorial design problem instances has pushed the development of new search methods both in terms of systematic and stochastic procedures. For example, the question of the existence and nonexistence of certain
Duality in Permutation State Spaces and the Dual Search Algorithm
, 2007
"... Geometrical symmetries are commonly exploited to improve the efficiency of search algorithms. A new type of symmetry in permutation state spaces, duality, is introduced. Each state has a dual state. Both states share important attributes such as their distance to the goal. Given a state S, it is sho ..."
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Cited by 13 (10 self)
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Geometrical symmetries are commonly exploited to improve the efficiency of search algorithms. A new type of symmetry in permutation state spaces, duality, is introduced. Each state has a dual state. Both states share important attributes such as their distance to the goal. Given a state S, it is shown that an admissible heuristic of the dual state of S is an admissible heuristic for S. This provides opportunities for additional heuristic evaluations. An exact definition of the class of problems where duality exists is provided. A new search algorithm, dual search, is presented which switches between the original state and the dual state when it seems likely that the switch will improve the chance of reaching the goal faster. The decision of when to switch is very important and several policies for doing this are investigated. Experimental results show significant improvements for a number of applications, for using the dual state’s heuristic evaluation and/or dual search.
Transforming and refining abstract constraint specifications
 In Proceedings of the Sixth Symposium on Abstraction, Reformulation and Approximation, volume 3607 of Lecture Notes in Computer Science
, 2005
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Value ordering for finding all solutions
 In Intl. Joint Conf. on Artificial Intelligence (IJCAI
, 2005
"... In finding all solutions to a constraint satisfaction problem, or proving that there are none, with a search algorithm that backtracks chronologically and forms kway branches, the order in which the values are assigned is immaterial. However, we show that if the values of a variable are assigned in ..."
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Cited by 10 (0 self)
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In finding all solutions to a constraint satisfaction problem, or proving that there are none, with a search algorithm that backtracks chronologically and forms kway branches, the order in which the values are assigned is immaterial. However, we show that if the values of a variable are assigned instead via a sequence of binary choice points, and the removal of the value just tried from the domain of the variable is propagated before another value is selected, the value ordering can affect the search effort. We show that this depends on the problem constraints; for some types of constraints, we show that the savings in search effort can be significant, given a good value ordering. 1
Modeling choices in quasigroup completion: SAT vs. CSP
 In AAAI
, 2004
"... Abstract We perform a systematic comparison of SAT and CSP models for a challenging combinatorial problem, quasigroup completion (QCP). Our empirical results clearly indicate the superiority of the 3D SAT encoding ..."
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Cited by 10 (1 self)
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Abstract We perform a systematic comparison of SAT and CSP models for a challenging combinatorial problem, quasigroup completion (QCP). Our empirical results clearly indicate the superiority of the 3D SAT encoding
Caching search states in permutation problems
 In van Beek [19
"... Abstract. When the search for a solution to a constraint satisfaction problem backtracks, it is not usually worthwhile to remember the assignment that failed, because the same assignment will not occur again. However, we show that for some problems recording assignments is useful, because other assi ..."
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Abstract. When the search for a solution to a constraint satisfaction problem backtracks, it is not usually worthwhile to remember the assignment that failed, because the same assignment will not occur again. However, we show that for some problems recording assignments is useful, because other assignments can lead to the same state of the search. We demonstrate this in two classes of permutation problem, a satisfaction problem and an optimization problem. Caching states visited has proved effective in reducing both search effort and runtime for difficult instances of each class, and the space requirements are manageable. 1
Removing propagation redundant constraints in redundant modeling. (to appear)
 ACM Transactions on Computational Logic,
, 2007
"... A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with various degrees of constraint propagation for pruning the search space. One common technique to improve the execution efficiency is to add redundant constraints, which are constraints logicall ..."
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Cited by 8 (4 self)
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A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with various degrees of constraint propagation for pruning the search space. One common technique to improve the execution efficiency is to add redundant constraints, which are constraints logically implied by others in the problem model. However, some redundant constraints are propagation redundant and hence do not contribute additional propagation information to the constraint solver. Redundant constraints arise naturally in the process of redundant modeling where two models of the same problem are connected and combined through channeling constraints. In this paper, we give general theorems for proving propagation redundancy of one constraint with respect to channeling constraints and constraints in the other model. We illustrate, on problems from CSPlib (http://www.csplib.org), how detecting and removing propagation redundant constraints in redundant modeling can speed up search by several order of magnitudes. Choi, C., Lee, J., and Stuckey, P. 2007. Removing propagation redundant constraints in redundant modeling.
Modelling Equidistant Frequency Permutation Arrays: An Application of Constraints to Mathematics
"... Abstract Equidistant Frequency Permutation Arrays are combinatorial objects of interest in coding theory. A frequency permutation array is a type of constant composition code in which each symbol occurs the same number of times in each codeword. The problem is to find a set of codewords such that an ..."
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Abstract Equidistant Frequency Permutation Arrays are combinatorial objects of interest in coding theory. A frequency permutation array is a type of constant composition code in which each symbol occurs the same number of times in each codeword. The problem is to find a set of codewords such that any pair of codewords are a given uniform Hamming distance apart. The equidistant case is of special interest given the result that any optimal constant composition code is equidistant. This paper presents, compares and combines a number of different constraint formulations of this problem class, including a new method of representing permutations with constraints. Using these constraint models, we are able to establish several new results, which are contributing directly to mathematical research in this area. 3 1
Extensible Automated Constraint Modelling
"... In constraint solving, a critical bottleneck is the formulation of an effective constraint model of a given problem. The CONJURE system described in this paper, a substantial step forward over prototype versions of CONJURE previously reported, makes a valuable contribution to the automation of const ..."
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Cited by 5 (4 self)
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In constraint solving, a critical bottleneck is the formulation of an effective constraint model of a given problem. The CONJURE system described in this paper, a substantial step forward over prototype versions of CONJURE previously reported, makes a valuable contribution to the automation of constraint modelling by automatically producing constraint models from their specifications in the abstract constraint specification language ESSENCE. A set of rules is used to refine an abstract specification into a concrete constraint model. We demonstrate that this set of rules is readily extensible to increase the space of possible constraint models CONJURE can produce. Our empirical results confirm that CONJURE can reproduce successfully the kernels of the constraint models of 32 benchmark problems found in the literature.