A new practical approach for differentiation

named hybrid differentiation algorithm

is presented to improve the efficiency of chemical process system optimization. In this approach

the original function is partitioned into two kinds of modules:simple module and complicated module. On the one hand

automatic differentiation is used to analyze the structure of the simple modules and represent them as rooted direct trees. Then symbolic differentiation is used to obtain the symbolic derivatives of the trees

by which derivative evaluation of the simple modules can be carried out. On the other hand

finite difference is adopted to differentiate the complicated modules. Accumulation of derivatives

the critical technique of hybrid differentiation

is discussed and two approaches are developed. Numerical experiment with a distillation column optimization problem demonstrates that the efficiency of optimization is significantly improved by using hybrid differentiation.