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37
Breaking row and column symmetries in matrix models
 Proceedings of Eighth International Conference on Principles and Practice of Constraint Programming (CPO2
, 2002
"... Abstract. We identify an important class of symmetries in constraint programming, arising from matrices of decision variables where rows and columns can be swapped. Whilst lexicographically ordering the rows (columns) breaks all the row (column) symmetries, lexicographically ordering both the rows ..."
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Cited by 115 (37 self)
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Abstract. We identify an important class of symmetries in constraint programming, arising from matrices of decision variables where rows and columns can be swapped. Whilst lexicographically ordering the rows (columns) breaks all the row (column) symmetries, lexicographically ordering both the rows and the columns fails to break all the compositions of the row and column symmetries. Nevertheless, our experimental results show that this is effective at dealing with these compositions of symmetries. We extend these results to cope with symmetries in any number of dimensions, with partial symmetries, and with symmetric values. Finally, we identify special cases where all compositions of the row and column symmetries can be eliminated by the addition of only a linear number of symmetrybreaking constraints. 1
Global Constraints for Lexicographic Orderings
, 2002
"... We propose some global constraints for lexicographic orderings on vectors of variables. These constraints are very useful for breaking a certain kind of symmetry arising in matrices of decision variables. We show ..."
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Cited by 83 (35 self)
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We propose some global constraints for lexicographic orderings on vectors of variables. These constraints are very useful for breaking a certain kind of symmetry arising in matrices of decision variables. We show
A fast and simple algorithm for bounds consistency of the alldifferent constraint
 IN PROCEEDINGS OF THE 18TH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2003
"... In constraint programming one models a problem by stating constraints on acceptable solutions. The constraint model is then usually solved by interleaving backtracking search and constraint propagation. Previous studies have demonstrated that designing special purpose constraint propagators for comm ..."
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Cited by 42 (9 self)
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In constraint programming one models a problem by stating constraints on acceptable solutions. The constraint model is then usually solved by interleaving backtracking search and constraint propagation. Previous studies have demonstrated that designing special purpose constraint propagators for commonly occurring constraints can significantly improve the efficiency of a constraint programming approach. In this paper we present a fast, simple algorithm for bounds consistency propagation of the alldifferent constraint. The algorithm has the same worst case behavior as the previous best algorithm but is much faster in practice. Using a variety of benchmark and random problems, we show that our algorithm outperforms existing bounds consistency algorithms and also outperforms—on problems with an easily identifiable property—stateoftheart commercial implementations of propagators for stronger forms of local consistency.
Function Variables for Constraint Programming
, 2003
"... We introduce function variables to constraint programs (CP), variables whose values are one of (exponentially many) possible functions between two sets. Such variables are useful for modelling problems from domains such as configuration, planning, scheduling, etc. We show that a function variable ca ..."
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Cited by 40 (5 self)
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We introduce function variables to constraint programs (CP), variables whose values are one of (exponentially many) possible functions between two sets. Such variables are useful for modelling problems from domains such as configuration, planning, scheduling, etc. We show that a function variable can be mapped into different representations in terms of integer and set variables, and illustrate how to map constraints stated on a function variable into constraints on integer and set variables. As a result, a constraint model expressed using function variables allows for the generation of alternate CP models. Furthermore, we present an extensive theoretical comparison of models of problems involving injective functions supported by asymptotic and empirical studies. Finally, we present and evaluate a practical modelling tool that is based on a highlevel language that supports function variables. The tool helps users explore different alternate CP models starting from a function model that is easy to develop, understand, and maintain.
Permutation Problems and Channelling Constraints
 TR 26, APES Group
, 2001
"... When writing a constraint program, we have to decide what to make the decision variable, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. For example, with permutation problems, we can choose between a primal and a dual ..."
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Cited by 39 (2 self)
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When writing a constraint program, we have to decide what to make the decision variable, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. For example, with permutation problems, we can choose between a primal and a dual representation. In the dual representation, dual variables stand for the primal values, whilst dual values stand for the primal variables. By means of channelling constraints, a combined model can have both primal and dual variables. In this paper, we perform an extensive theoretical and empirical study of these different models. Our results will aid constraint programmers to choose a model for a permutation problem. They also illustrate a general methodology for comparing different constraint models.
Improved algorithms for the global cardinality constraint
 In Proceedings CP’04
, 2004
"... Abstract. We study the global cardinality constraint (gcc) and propose an O(n ..."
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Cited by 36 (3 self)
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Abstract. We study the global cardinality constraint (gcc) and propose an O(n
Stochastic Constraint Programming: A ScenarioBased Approach
 SUBMISSION TO CONSTRAINTS
"... To model combinatorial decision problems involving uncertainty and probability, we introduce scenario based stochastic constraint programming. Stochastic constraint programs contain both decision variables, which we can set, and stochastic variables, which follow a discrete probability distribution. ..."
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Cited by 30 (4 self)
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To model combinatorial decision problems involving uncertainty and probability, we introduce scenario based stochastic constraint programming. Stochastic constraint programs contain both decision variables, which we can set, and stochastic variables, which follow a discrete probability distribution. We provide a semantics for stochastic constraint programs based on scenario trees. Using this semantics, we can compile stochastic constraint programs down into conventional (nonstochastic) constraint programs. This allows us to exploit the full power of existing constraint solvers. We have implemented this framework for decision making under uncertainty in stochastic OPL, a language which is based on the OPL constraint modelling language [Hentenryck et al., 1999]. To illustrate the potential of this framework, we model a wide range of problems in areas as diverse as portfolio diversification, agricultural planning and production/inventory management.
An Efficient Bounds Consistency Algorithm for the Global Cardinality Constraint
 PROCEEDINGS CP
, 2003
"... Previous studies have demonstrated that designing special purpose constraint propagators can significantly improve the efficiency of a constraint programming approach. In this paper we present an efficient algorithm for bounds consistency propagation of the generalized cardinality constraint (gcc). ..."
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Cited by 24 (4 self)
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Previous studies have demonstrated that designing special purpose constraint propagators can significantly improve the efficiency of a constraint programming approach. In this paper we present an efficient algorithm for bounds consistency propagation of the generalized cardinality constraint (gcc). Using a variety of benchmark and random problems, we show that our bounds consistency algorithm is competitive with and can dramatically outperform existing stateoftheart commercial implementations of constraint propagators for the gcc. We also present a new algorithm for domain consistency propagation of the gcc which improves on the worstcase performance of the best previous algorithm for problems that occur often in applications.
GLOBAL CONSTRAINTS AND FILTERING ALGORITHMS
"... Constraint programming (CP) is mainly based on filtering algorithms; their association with global constraints is one of the main strengths of CP. This chapter is an overview of these two techniques. Some of the most frequently used global constraints are presented. In addition, the filtering algor ..."
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Cited by 22 (1 self)
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Constraint programming (CP) is mainly based on filtering algorithms; their association with global constraints is one of the main strengths of CP. This chapter is an overview of these two techniques. Some of the most frequently used global constraints are presented. In addition, the filtering algorithms establishing arc consistency for two useful constraints, the alldiff and the global cardinality constraints, are fully detailed. Filtering algorithms are also considered from a theoretical point of view: three different ways to design filtering algorithms are described and the quality of the filtering algorithms studied so far is discussed. A categorization is then proposed. Overconstrained problems are also mentioned and global soft constraints are introduced.
Search and Strategies in OPL
, 2000
"... OPL is a modeling language for mathematical programming and combinatorial optimization. It is the first language to combine highlevel algebraic and set notations from mathematical modeling languages with a rich constraint language and the ability to specify search procedures and strategies that are ..."
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Cited by 19 (2 self)
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OPL is a modeling language for mathematical programming and combinatorial optimization. It is the first language to combine highlevel algebraic and set notations from mathematical modeling languages with a rich constraint language and the ability to specify search procedures and strategies that are the essence of constraint programming. This paper describes the facilities available in OPL to specify search procedures. It describes the abstractions of OPL to specify both the search tree (search) and how to explore it (strategies). The paper also illustrates how to use these highlevel constructs to implement traditional search procedures in constraint programming and scheduling.