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
