Modelling and Optimisation with Graphs

使用图形进行建模和优化

基本信息

批准号：
EP/P026842/1
负责人：
Jessica Anne Enright
金额：
$ 85.77万
依托单位：
University of Glasgow
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2017
资助国家：
英国
起止时间：
2017 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FP026842%2F1
关键词：
Modelling Optimisation Graphs

项目摘要

Optimisation technologies are used to deliver parcels and groceries cheaply and efficiently, to decide who gets a kidney transplant, to identify candidate chemicals for new drugs, to explain the building blocks of life, and to understand disease transmission in livestock. Graphs are the natural way of describing relationships, compatibilities, transport networks, chemical molecules, instructions and interactions in computer programs, and structured patterns; in particular, many important questions ask, in effect, whether certain graphs contain another subgraph, or can be covered by a collection of subgraphs. This project addresses optimisation problems which involve subgraphs, either with other constraints, or with a complex objective. Problem of this nature are common---we will be working with four real-world application areas involving disease transmission in livestock, matching kidney donors to recipients, metabolomics, and computational algebra.Currently, dealing with these kinds of problems is complex, time-consuming, and requires a specialist. One option would be to select a particular constraint programming (CP), mixed integer programming (MIP), or boolean satisfiability (SAT) solver. These solvers require a problem to be modelled in terms of variables which have domains of values, and constraints between variables; the solver then finds a way of giving each variable a value from its domain, whilst satisfying all the constraints (or the best such way, as defined by some objective function). Different solver technologies have different restrictions upon the types of variables and constraints allowed---for example, SAT solvers support only boolean (true / false) variables and simple logical constraints. None of these technologies support graphs directly, and so the modeller would also have to come up with a way of encoding the graph part of the problem in a way that is compatible with the other constraints and the objective. Unfortunately, even the most experienced modellers are unlikely to make the best choice of solver and encoding on the first attempt, and even after a long development process, current optimisation technologies give performance several orders of magnitude worse than dedicated algorithms when dealing with subgraph problems.Another alternative would be to implement a simple algorithm manually---but this is time-consuming and error-prone, and without a huge development effort the performance is again unlikely to be sufficient except for very small inputs. To address this, one might try to adapt a state-of-the-art algorithm from the literature to handle side constraints, but this has an even larger development cost: the theories underlying recently published algorithms are specific to certain variants of subgraph problems (e.g. induced or non-induced, sparse or dense, with particular injectivity and labelling rules, ...) and are not immediately compatible with arbitrary side constraints. Also, publicly available implementations of these algorithms are tailored to support scientific investigation, rather than being engineered for use in a production environment.The aim of this project is to address the difficulties in solving graph-based optimisation problems from two directions. At the high level, we will provide modelling support for working with graphs directly: being able to express graph problems in a high level optimisation modelling language will make models easier to produce, understand, teach, and verify, and will make optimisation and subgraph technologies accessible to a wider academic and industrial audience. At the low level, we will improve solver support for graph-based and hybrid models: co-operation between general purpose optimisation solvers and dedicated subgraph algorithms will deliver better performance and scalability than any one technique can on its own, and will introduce new opportunities for automatic reformulation and constraint inference.

优化技术用于廉价有效地提供包裹和杂货，以决定谁进行肾脏移植，以识别新药的候选化学物质，以解释生命的基本障碍，并了解牲畜中的疾病传播。图是描述关系，兼容性，运输网络，化学分子，计算机程序中的指示和相互作用的自然方法，以及结构化模式；特别是，许多重要的问题实际上问，某些图是否包含另一个子图，还是可以被一系列子图覆盖。该项目解决了涉及子图的优化问题，具有其他约束或具有复杂目标的优化问题。这种性质的问题很普遍 - 我们将与四个现实世界中的应用领域合作，涉及牲畜中的疾病传播，将肾脏捐赠者与接受者，代谢组学和计算代数相匹配。目前，处理这类问题是复杂的，耗时的，耗时的，需要专家。一种选择是选择特定的约束编程（CP），混合整数编程（MIP）或布尔值满意度（SAT）求解器。这些求解器需要以具有值域的变量和变量之间的约束来对问题进行建模。然后，求解器找到了一种从其域中给出每个变量一个值的方法，同时满足了所有约束（或最好的方式，如某些目标函数所定义）。不同的求解器技术对允许的变量和约束的类型有不同的限制 - 例如，SAT求解器仅支持布尔值（true / false）变量和简单的逻辑约束。这些技术都没有直接支持图形，因此建模器还必须提出一种以与其他约束和目标兼容的方式编码问题的图形部分的方法。不幸的是，即使是最有经验的模块货币机也不太可能在第一次尝试中做出最佳选择和编码，即使经过漫长的开发过程，当前的优化技术也会使绩效比专门的算法要差几个数量级，而在处理次级问题时，在处理次级问题时，在不进行算法的情况下，这是一个既定的效果，但在不及时的范围内进行了巨大的努力，并且可以努力地努力，并且不及时努力，并且算不上了一个算法，并且不及时努力，并且不及时努力，并且可以努力努力，并且可以努力努力，并且可以努力努力，并且可以努力努力，并且可以努力努力，并且可以努力努力，并且可以努力努力，并且可以努力努力，并且可以努力努力，并且可以努力努力，并且是算法的，并且效果不佳，并且可以努力努力。除了非常小的输入外，还足够。为了解决这个问题，人们可能会试图适应文献中最先进的算法来处理侧面约束，但这具有更大的发展成本：最近发表的算法的理论是特定于某些子段问题的某些变体（例如，诱导的，稀疏或密集的，均匀的，不可限制的，不立即繁殖的，并且不立即繁殖，又是...同样，这些算法的公开实现是为支持科学研究而定制的，而不是在生产环境中使用。该项目的目的是解决从两个方向解决基于图的优化问题的困难。在高水平上，我们将直接为使用图表提供建模支持：能够在高级优化建模语言中表达图形问题，这将使模型更易于生产，理解，教学，教学和验证，并将使更广泛的学术和工业受众访问优化和子图技术。在低水平上，我们将改善对基于图的和混合模型的求解器支持：通用优化求解器和专用子图算法之间的合作将比任何一种技术本身提供更好的性能和可伸缩性，并将为自动重新印度和约束推理带来新的机会。