MS 96-004a Abstract

A Parallel Algorithm for the Global Minimization of Gibbs Free Energy

S.Berner, K.I.M. McKinnon and C. Millar

Technical Report MS 96-004a

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 over 90% are obtained using up to 14 processors. The algorithm copes well with varying workstation loads and has low communication overheads. A method of assessing the performance of a parallel algorithm on a shared heterogeneous network of workstations is developed.

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

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Previous version MS 96-004 Submitted to Annals of Operations research, May 1996.
Current version resubmitted, Nov 1996.
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