A Constraint Modelling Pipeline

今天，在许多情况下，我们面临着越来越大和复杂的决策，许多不同的考虑因素以复杂的方式相互交织。考虑一个工作人员花名册问题，以分配工作人员轮班，同时尊重所需的轮班模式和人员配备水平，物质和人力资源，以及工作人员的工作偏好。决策过程往往因需要优化目标而变得更加复杂，例如利润最大化或浪费最小化。很自然地，将这些问题视为一组决策变量，每个变量代表必须做出的选择，以解决手头的问题（例如，星期五夜班由哪位工作人员值班），以及一组约束条件，说明允许的可变分配组合（例如，不能将工作人员分配到紧接夜班之后的白班）。一个解决方案是对满足所有约束条件的每个变量赋值。许多决策和优化形式主义都采用这种一般形式。在所有这些形式主义中，问题的模型对于解决问题的效率至关重要。在这个意义上，模型是选择来表示给定问题的决策变量和约束的集合。通常有许多可能的模型，并且制定有效的模型是非常困难的。因此，自动化建模是一个关键的挑战。在过去的十年中，在约束编程的背景下，我们采取了一种新的方法来解决这一挑战。用户编写一个问题规范的抽象约束规范语言的“约束”，捕捉的抽象层次之上的问题的结构，在建模决策。我们的建模管道，我们提出的研究的基础上，自动生成一个模型，从这个规范。这消除了对用户约束建模专业知识的需要，也保留了指定问题的结构，使系统可以轻松地探索替代模型，并利用属性，如对称性。我们的管道生成的约束模型质量相当于一个称职的人类约束程序员，因此代表了一个重要的里程碑，走向全自动化建模。然而，仍然存在重大挑战。第一个是生成人类专家能够胜任的质量模型。考虑到这些问题固有的困难，以及模型在减轻困难方面的重要性，提高生成模型的质量至关重要。第二个是扩大范围的输出模型超出了约束编程formalis.The实质性的挑战，我们在这个建议中解决的是要克服这两个限制，以产生一个强大的，通用的自动化建模和求解系统的唯一目标范围内的解决形式主义从一个单一的抽象约束规范。我们现有的管道是理想的扩展到其他形式主义。这一变化的影响将是巨大的：组合搜索问题是无处不在的公共和私营部门，以及学术界。我们将更快地为这些问题提供更好的解决方案，提高效率并降低成本。

In numerous contexts today we are faced with making decisions of increasing size and complexity, where many different considerations interlock in complex ways. Consider a staff rostering problem to assign staff to shifts while respecting required shift patterns and staffing levels, physical and staff resources, and staff working preferences. The decision-making process is often further complicated by the need also to optimise an objective, such as to maximise profit or to minimise waste.It is natural to characterise such problems as a set of decision variables, each representing a choice that must be made in order to solve the problem at hand (e.g. which staff member is on duty for the Friday night shift), and a set of constraints describing allowed combinations of variable assignments (e.g. a staff member cannot be assigned to a day shift immediately following a night shift). A solution is an assignment of a value to each variable satisfying all constraints.Many decision-making and optimisation formalisms take this general form. In all of these formalisms the model of the problem is crucial to the efficiency with which it can be solved. A model in this sense is the set of decision variables and constraints chosen to represent a given problem. There are typically many possible models and formulating an effective model is notoriously difficult. Therefore automating modelling is a key challenge.Over the last decade, in the context of Constraint Programming we have taken a novel approach to addressing this challenge. The user writes a problem specification in the abstract constraint specification language 'Essence', capturing the structure of the problem above the level of abstraction at which modelling decisions are made. Our modelling pipeline, on which our proposed research is based, automatically generates a model from this specification. This removes the need for user constraint modelling expertise, and also preserves the structure of the specified problem, allowing the system easily to explore alternative models and to exploit properties such as symmetry.Our pipeline generates constraint models equivalent in quality to those of a competent human constraint programmer, and so represents a significant milestone towards fully automated modelling. Important challenges do, however, remain. The first is to generate models of the quality that human experts are capable. Given the inherent difficulty of these problems, and the importance of the model in mitigating that difficulty, raising the quality of the generated models is crucial. The second is to expand the range of output models beyond the constraint programming formalism.The substantial challenge we address in this proposal is to overcome these two limitations to produce a powerful, general automated modelling and solving system unique in targeting a range of solving formalisms from a single abstract constraint specification. Our existing pipeline is ideal for extension to other formalisms.The impact of this change will be substantial: combinatorial search problems are ubiquitous across the public and private sectors, and academia. We will deliver better solutions to these problems more rapidly, increasing efficiency and reducing cost.