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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.
Automated reformulation of specifications by safe delay of constraints
 Proceedings of the 2nd International Workshop on Modelling and Reformulating Constraint Satisfaction Problems
, 2003
"... In this paper we propose a form of reasoning on specifications of combinatorial problems, with the goal of reformulating them so that they are more efficiently solvable. The reformulation technique highlights constraints that can be safely “delayed”, and solved afterwards. Our main contribution is t ..."
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Cited by 19 (8 self)
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In this paper we propose a form of reasoning on specifications of combinatorial problems, with the goal of reformulating them so that they are more efficiently solvable. The reformulation technique highlights constraints that can be safely “delayed”, and solved afterwards. Our main contribution is the characterization (with soundness proof) of safedelay constraints with respect to a criterion on the specification, thus obtaining a mechanism for the automated reformulation of specifications applicable to a great variety of problems, e.g., graph coloring and jobshop scheduling. This is an advancement with respect to the forms of reasoning done by stateoftheartsystems, which typically just detect linearity of specifications. Another contribution is a preliminary experimentation on the effectiveness of the proposed technique, which reveals promising time savings.
Exploiting functional dependencies in declarative problem specifications
 In Proceedings of the Ninth European Conference on Logics in Artificial Intelligence (JELIA 2004
, 2004
"... Abstract. In this paper we tackle the issue of the automatic recognition of functional dependencies among guessed predicates in constraint problem specifications. Functional dependencies arise frequently in pure declarative specifications, because of the intermediate results that need to be computed ..."
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Cited by 16 (11 self)
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Abstract. In this paper we tackle the issue of the automatic recognition of functional dependencies among guessed predicates in constraint problem specifications. Functional dependencies arise frequently in pure declarative specifications, because of the intermediate results that need to be computed in order to express some of the constraints, or due to precise modelling choices, e.g., to provide multiple viewpoints of the search space in order to increase propagation. In either way, the recognition of dependencies greatly helps solvers, letting them avoid spending search on unfruitful branches, while maintaining the highest degree of declarativeness. By modelling constraint problem specifications as secondorder formulae, we provide a characterization of functional dependencies in terms of semantic properties of firstorder ones. Additionally, we show how suitable search procedures can be automatically synthesized in order to exploit recognized dependencies. We present opl examples of various problems, from bioinformatics, planning and resource allocation fields, and show how in many cases opl greatly benefits from the addition of such search procedures. 1
Matrix Modelling: Exploiting Common Patterns in Constraint Programming
 Proceedings of the International Workshop on Reformulating Constraint Satisfaction Problems
, 2002
"... Constraint programs with one or more matrices of decision variables are commonly and naturally used to model realworld problems. ..."
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Cited by 13 (8 self)
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Constraint programs with one or more matrices of decision variables are commonly and naturally used to model realworld problems.
Towards Inferring Labelling Heuristics for CSP Application Domains
 In Proceedings of KI'01
, 2001
"... . Many reallife problems can be represented as constraint satisfaction problems (CSPs) and then be solved using constraint solvers, in which labelling heuristics are used to netune the performance of the underlying search algorithm. However, few guidelines have been proposed for the applicatio ..."
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Cited by 8 (1 self)
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. Many reallife problems can be represented as constraint satisfaction problems (CSPs) and then be solved using constraint solvers, in which labelling heuristics are used to netune the performance of the underlying search algorithm. However, few guidelines have been proposed for the application domains of these heuristics. If a mapping between application domains and heuristics is known to the solver, then modellers can  if they wish so  be relieved from guring out which heuristic to indicate or implement. Instead of inferring the application domains of (known) heuristics, we advocate inferring (known or new) heuristics for application domains. Our approach is to rst formalise a CSP application domain as a family of models, so as to exhibit the generic constraint store for all models in that family. Second, familyspecic labelling heuristics are inferred by analysing the interaction of a given search algorithm with this generic constraint store. We illustrate our approach on a domain of subset problems. 1
Automatable HighLevel Integration of Constraint Programs
"... . We propose a reformulation algorithm as well as a set of reformulation rules for models of constraint satisfaction problems written in our highlevel constraint programming language esra, which is more expressive than opl and is compiled into opl. For the class of mapping problems, the reformu ..."
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Cited by 1 (1 self)
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. We propose a reformulation algorithm as well as a set of reformulation rules for models of constraint satisfaction problems written in our highlevel constraint programming language esra, which is more expressive than opl and is compiled into opl. For the class of mapping problems, the reformulation algorithm achieves models that integrate a constraint programming formulation and an integer programming formulation while the esratoesra reformulation rules achieve models that integrate primal variables with dual variables and infer the appropriate channelling constraints. 1
Preproceedings of the International Symposium on Logic Based Program Synthesis and Transformation
, 2003
"... This volume contains preliminary versions of papers presented at LOPSTR 2003, ..."
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This volume contains preliminary versions of papers presented at LOPSTR 2003,
HighLevel Modelling and Reformulation of Constraint Satisfaction Problems
"... Introduction The modelling process of constraint satisfaction problems (CSPs) as constraint programs requires sophisticated reasoning skills and involves crucial decisions on which variable and value representations to choose, on which constraint formulation to state, and on which solution methods ..."
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Introduction The modelling process of constraint satisfaction problems (CSPs) as constraint programs requires sophisticated reasoning skills and involves crucial decisions on which variable and value representations to choose, on which constraint formulation to state, and on which solution methods to employ. Furthermore, the tight interaction between representation, constraint formulation, and solution methods adds another degree of complexity to the modelling task. For instance, the choice of the constraint formulation is strongly affected by the choice of the representation of variables and values, and by the choice of the solution methods. In addition, the performance of solution methods is sensitive to the problem instances. Thus, modelling combinatorial optimisation problems so as to solve them in more efficient ways is a major challenge for constraint programming (CP). To address the modellingtime
Labelling Heuristics for CSP Application Domains
"... Introduction Many reallife problems are constraint satisfaction problems (CSPs), which can be programmed as constraint models and then be solved using constraint solvers, such as clp(fd) [2] and opl [14]. Constraint solvers are equipped with a search algorithm, such as forwardchecking, and labell ..."
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Introduction Many reallife problems are constraint satisfaction problems (CSPs), which can be programmed as constraint models and then be solved using constraint solvers, such as clp(fd) [2] and opl [14]. Constraint solvers are equipped with a search algorithm, such as forwardchecking, and labelling heuristics, one of which is the default. To enhance the performance of constraint models, a lot of research has been made in recent years to develop new labelling heuristics, which concern the choice of the next variable to branch on during the search and the choice of the value to be assigned to that variable. These heuristics signicantly reduce the search space [12]. However, little is said about the application domains of these heuristics, so modellers nd it dicult to decide when to apply a particular heuristic, and when not. Indeed, it is not a trivial task to infer the applicat
Matrix Modelling
 In: Proc. of the CP01 Workshop on Modelling and Problem Formulation. International Conference on the Principles and Practice of Constraint Programming
, 2001
"... We argue that constraint programs with one or more matrices of decision variables provide numerous benefits, as they share many patterns for which general methods can be devised, such as for symmetry breaking. On a wide range of reallife application domains, we demonstrate the generality and u ..."
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We argue that constraint programs with one or more matrices of decision variables provide numerous benefits, as they share many patterns for which general methods can be devised, such as for symmetry breaking. On a wide range of reallife application domains, we demonstrate the generality and utility of such matrix modelling. 1