Global optimisation in process design
This thesis concerns the development of rigorous global optimisation techniques and their application to process engineering problems. Many Process Engineering optimisation problems are nonlinear. Local optimisation approaches may not provide global solutions to these problems if they are nonconvex. The global optimisation approach utilised in this work is based on interval branch and bound algorithms. The interval global optimisation approach is extended to take advantage of information about the structure of the problem and facilitate efficient solution of constrained NLPs using interval analysis. This is achieved by reformulating the interval lower bounding procedure as a convex programming problem which allows inclusion of convex constraints in the lower bounding problem. The approach is applied to a number of standard constrained test problems indicating that this algorithm retains the wide applicability of the interval methods while allowing efficient solution of constrained problems. A new approach to the construction of modular flowsheets is developed. This approach allows construction of flowsheets from linked unit models which enable the application of a number of global optimisation algorithms. The modular flowsheets are constructed with 'generic' unit operations which provide interval bounds, linear bounds, derivatives and derivative bounds using extended numerical types. The genericity means that new 'extended types' can be devised and used without rewriting the unit operations models. The new interval global optimisation algorithm is applied to the generic modular flowsheet. Using interval analysis and automatic differentiation as the arithmetic types, lower bounding linear programs are constructed and used in a branch and bound framework to globally optimise the modular flowsheet.