It is hard to obtain derivative functions for branched modules in polycondensation process optimization problems with current differentiation approaches

such as symbolic differentiation

extended automatic differentiation (XAD)

etc .In this paper

symbolic automatic differentiation (SAD) and numerical automatic differentiation (NAD)

the two components of XAD

are integrated in a flexible way to solve this problem.The resulting derivative evaluation approach

named as hybrid automatic differentiation (HAD)

is used to solve a polycondensation optimization problem.In the polycondensation model

a flash distillation process model is adopted to calculate the concentration of volatile species in the reaction mass

which is a typical branched module.So the specific module is taken apart from the main model and each of the two parts is managed in a different way.Accordingly

the derivative function obtained by HAD contains two parts:one is a NAD tool to compute the derivatives of the flash distillation process module

the other is a series of symbolic derivatives generated by SAD for derivative evaluation of the main model.Numerical results demonstrate that the HAD based optimization can significantly reduce the solution time

and is of great importance for on-line process optimization.