## Proposal

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.

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 sreams to heat exchangers.

## Personnel

We were very happy to have Radu Baltean-Lugojan, Georgia Kouyialis, and Dr Dimitris Letsios collaborating on this project.

## Outcomes

We discovered that we can solve (or at least rigorously approximate) several important classes of energy efficiency problems quickly. In particular, we considered the applications of (i) designing effective heat recovery networks and (ii) blending and intermediate storage in petrochemical processes.

**Heat recovery network design**We rigorously address larger problems than ever before. We can prove mathematically that the good heuristic solutions we develop are very close to the true optimal solution. We demonstrate the utility of parallelisation by showing that running many heuristics on different cores produces the best outcome. We have made all of our code freely-available via our GitHub webpage. We have also made all of the literature test instances public and freely-available for the first time.**Blending & Intermediate Storage**We are able to address larger problems in polynomial time than anyone had previously thought possible. We also proved important mathematical structural characteristics and rigorously showed that the nonlinear optimisation problem actually has a hidden, piecewise-linear structure. Our code is freely-available.

During the grant itself, we’ve presented this work to academic experts in both computer science and process systems engineering:

- I gave a seminar at the University of Manchester School of Chemical Engineering & Analytical Science (02/2018)
- Georgia won the 1st Poster Prize at the UK/Ireland Annual Meeting of the Society for Industrial & Applied Mathematics (01/2018)
- Georgia won the 2nd Poster Prize at the Centre for Process Systems Engineering Industrial Consortium Meeting (12/2017)
- I gave an invited presentation at the AIChE Annual Meeting in memory of Professor C A Floudas (10/2017)
- Georgia won the 1st Poster Prize at the 2nd PSE@ResearchDayUK (06/2017)
- Dimitris won the 2nd Presentation Prize at the Department of Computing Research Associate Symposium (06/2017)

## Where do we go from here?

We’re really excited about the outcomes and we’re looking to share the results more broadly. I will present the EPSRC First Grant results to the process systems engineering community during my keynote at the 2018 European Symposium for Computer-Aided Process Engineering.

For the computer science community, we have offered a useful path into energy efficiency applications by making all case studies freely-available online. We’ve made it possible to contribute to designing heat recovery networks with solely a background in computer science or mathematical optimisation.