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. 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.