Parallelising Mixed-Integer Optimisation: Energy Efficiency Applications

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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.