S.Berner, K.I.M. McKinnon and C. Millar
Technical Report MS 96-004 and ECOSSE report 1996-07
Abstract
A chemical mixture under conditions of constant temperature and pressure
may split into different phases. The number of phases and the composition
of each may be determined by globally minimizing the Gibbs free energy
of the system. This can be done by iterating between an easy local
minimization problem with a high number of variables and a difficult
global search and verification problem in a small number of variables.
The global problem can be solved by a branch and bound method using
bounds from interval analysis. When implemented in parallel, the
method has lower communication requirements than other related branch
and bound approaches for general global minimization. We present a
parallel implementation on a network cluster of workstations that
exploits this characteristic. On difficult instances, utilizations
of about 90% are obtained using up to 14 processors. The
algorithm copes well with varying workstation loads and has low
communication overheads.
Key words: Global optimization, interval-analysis, parallel programming, branch and bound, Gibbs free energy, phase equilibrium, primal-dual methods.
amsmos: 90C90, 90C99, 65Y05, 68Q22, 80-08, 80A10, 80A15