Constraint programs with one or more matrices of decision variables are commonly and naturally used to model real-world problems.

. Many real-life problems can be represented as constraint satisfaction problems (CSPs) and then be solved using constraint solvers, in which labelling heuristics are used to ne-tune 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, family-specic 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

. We propose a reformulation algorithm as well as a set of reformulation rules for models of constraint satisfaction problems written in our high-level 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 esra-to-esra reformulation rules achieve models that integrate primal variables with dual variables and infer the appropriate channelling constraints. 1

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 real-life application domains, we demonstrate the generality and utility of such matrix modelling. 1

Introduction Many real-life 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 forward-checking, 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