When solving a combinatorial problem, the formulation or model of the problem is critical to the efficiency of the solver. Automating the modelling process has long been of interest because of the expertise and time required to produce an effective model of a given problem. We describe a method to automatically produce constraint models from a problem specification written in the abstract constraint specification language Essence. Our approach is to incrementally refine the specification into a concrete model by applying a chosen refinement rule at each step. Any non-trivial specification may be refined in multiple ways, creating a space of models to choose from.

The handling of symmetries is a particularly important aspect of automated modelling. Many combinatorial optimisation problems contain symmetry, which can lead to redundant search. If a partial assignment is shown to be invalid, we are wasting time if we ever consider a symmetric equivalent of it. A particularly important class of symmetries are those introduced by the constraint modelling process: modelling symmetries. We show how modelling symmetries may be broken automatically as they enter a model during refinement, obviating the need for an expensive symmetry detection step following model formulation.

Our approach is implemented in a system called Conjure. We compare the models produced by Conjure to constraint models from the literature that are known to be effective. Our empirical results confirm that Conjure can reproduce successfully the kernels of the constraint models of 42 benchmark problems found in the literature.

在解决组合问题时，问题的公式或模型对于求解器的效率至关重要。由于生成给定问题的有效模型所需的专业知识和时间，自动化建模过程长期以来一直受到关注。我们描述了一种从用抽象约束规范语言Essence编写的问题规范自动生成约束模型的方法。我们的方法是通过在每一步应用选定的细化规则，将规范逐步细化为具体模型。任何重要的规范都可以通过多种方式进行细化，从而创造出可供选择的模型空间。

对称性的处理是自动化建模的一个特别重要的方面。许多组合优化问题包含对称性，这会导致冗余搜索。如果部分分配被证明是无效的，那么如果我们考虑它的对称等价物，我们就是在浪费时间。一类特别重要的对称性是由约束建模过程引入的对称性：建模对称性。我们展示了建模对称性如何在细化过程中进入模型时自动被破坏，从而避免了在模型制定之后需要昂贵的对称性检测步骤。

我们的方法在一个名为Conjure的系统中实现。我们将Conjure生成的模型与已知有效的文献中的约束模型进行比较。我们的实证结果证实，Conjure可以成功再现文献中发现的 42 个基准问题的约束模型的内核。