Parallelising Mixed-Integer Optimisation: Energy Efficiency Applications

最优决策的数学模型通常需要非线性和离散分量。这些混合整数非线性规划（MINLP）构成了一类重要的优化问题，具有迫切的社会需求。例如，MINLP对于优化大型工业工厂的能源使用、将可再生能源整合到能源网络、生物和生物医学设计以及无数其他应用都是必要的。第一个MINLP算法和软件是由应用工程师设计的。虽然这些努力最初被证明是非常有用的，但科学家、工程师和从业者已经意识到，要充分发挥MINLP的潜力，需要技术上的转型。作为MINLP重要性的一个例子，考虑到许多工业过程涉及加热和冷却液体。随着目前减少二氧化碳排放的重点，例如2008年英国气候变化法案，再利用多余的过程热量变得越来越重要，一个主要挑战是通过热量集成提高工业工厂的效率。换热器网络（HEN）的综合是一个混合整数非线性优化问题（MINLP）。使用优化框架可以节省大量的能源和成本。2009年，韩国炼油公司S-Oil估计，使用商业优化软件包AspenTech Energy Analyzer，一个工厂每年可节省2800万英镑。但这些并不是唯一的收获。换热器网络综合是一个具有许多局部最优解的非凸非线性优化问题；我们估计通过开发更好的优化算法可以额外节省10%。混合整数非线性规划的确定性全局优化（MINLP）可以有效地设计节能网络，但目前针对这类问题的MINLP技术受到非凸非线性传热函数和路由流到换热器的许多同构可能性的限制。并行化很有吸引力，但是naïve当前并行化策略的设计也不合适，因为有效的树探索需要广泛的节点间通信。本提案旨在为MINLP分支切断算法开发新的节点间通信策略，以有效解决工业相关的能效优化问题。这一建议与在英国能源部门工作的68万人员密切相关。该提案属于EPSRC工程和制造未来主题；MINLP与工业设计问题高度相关。两个相关的子主题是可持续工业系统与能源效率的相关研究领域（EPSRC研究行动：增长）和制造信息学与运筹学的数学方面的相关研究领域（EPSRC研究行动：维持）。该提案也与EPSRC合作优先事项密切相关；这个团队包括PI、PDRA、一位数学家、一家软件公司和一个过程工程师联盟。自2012年移居英国以来，PI因其在MINLP方面的贡献而受到国际关注，并于2013年和2014年获得两篇论文奖；这项EPSRC第一笔拨款将使她成为一名在优化理论和实践方面有着可靠记录的研究人员。

Mathematical models for optimal decisions often require both nonlinear and discrete components. These mixed-integer nonlinear programs (MINLP) form an important class of optimisation problems of pressing societal need. For example, MINLP is necessary for optimising the energy use of large industrial plants, for integrating renewable sources into energy networks, for biological and biomedical design, and for countless other applications. The first MINLP algorithms and software were designed by application engineers. While these efforts initially proved very useful, scientists, engineers, and practitioners have realised that a transformational shift in technology will be required for MINLP to achieve its full potential.As an example of the importance of MINLP, consider that many industrial processes involve heating and cooling liquids. With the present day focus on reducing CO2 emissions, e.g. the UK Climate Change Act 2008, reusing excess process heat becomes ever more important and a major challenge is increasing industrial plant efficiency via heat integration. Heat exchanger network (HEN) synthesis is most naturally formulated as a mixed-integer nonlinear optimisation problem (MINLP). Using an optimisation framework can result in tremendous energy and cost savings. In 2009, the South Korean refining company S-Oil estimated £28M annual savings at a single plant using a commercial optimisation package, AspenTech Energy Analyzer. But these are not the only gains available. Heat exchanger network synthesis is a nonconvex nonlinear optimisation problem with many local optima; we estimate additional possible savings on the order of 10% via developing better optimisation algorithms.Deterministic global optimisation of mixed integer nonlinear programs (MINLP) may effectively design energy efficient networks, but current MINLP technology for this problem class is limited by nonconvex nonlinear heat transfer functions and the many isomorphic possibilities of routing streams to heat exchangers. Parallelisation is attractive, but the naïve design of current parallelisation strategies is also inappropriate because effective tree exploration requires extensive inter-node communication. This proposal aims to develop novel internode communication strategies for MINLP branch-and-cut algorithms with a target of effectively addressing industrially-relevant energy efficiency optimisation problems.This proposal is highly relevant to the 680k people working in the UK energy sector. This proposal falls under the EPSRC Engineering and Manufacturing the Future themes; MINLP is highly relevant to industrial design problems. The two related sub-themes are Sustainable Industrial Systems with a related research area of Energy Efficiency (EPSRC Research Action: Grow) and also Manufacturing Informatics with a related research area of Mathematical Aspects of Operational Research (EPSRC Research Action: Maintain). This proposal is also tightly linked to the EPSRC Working Together priority; the team includes the PI, the PDRA, a mathematician, a software company, and a consortium of process engineers. Since moving to the UK in 2012, the PI has attracted international attention for her MINLP contributions as evidenced by her 2 paper awards in 2013 and 2014; this EPSRC First Grant will establish her as researcher with a reliable track record of linking optimisation theory and practice.