In this chapter, two of the most commonly used types of software for optimization, BINGSS and PARROT, are described.

Common features

Handling bad starting coefficients

The definition of the “error” (vi in Eq. (2.52)) is based on the “calculated value” (Fi(Cj, xki)), which is often defined by an equilibrium calculation with two or more phases. The initial set of adjustable coefficients may result in improper Gibbs-energy functions, with which this equilibrium cannot be calculated. As an example, in Fig. 7.1 such a situation is shown for a two-phase equilibrium, liquid + bcc. There Gbcc at all compositions is larger than Gliquid and the construction of a common tangent is impossible, so also no equilibrium can be calculated numerically.

The experimental information is either “at temperature T1 there is a two-phase equilibrium, liquid + bcc, for which the composition of the bcc phase was measured as (xbcc = x′)” or “in a single-phase bcc sample of composition x′ on heating the first liquid appears at temperature T1” (see Fig. 4.4).

In the least-squares calculation for Eq. (2.52) no “calculated value” (Fi(Cj, xki)) can be provided as long as the starting values for the Gibbs-energy descriptions of liquid and bcc phases behave as in Fig. 7.1. To find better starting values by trial and error is not easy and is time-consuming. Therefore it is desirable to have a method whereby this problem is avoided and that can start even with a very bad initial set of adjustable coefficients.