On the optimum choice of decision variables for equation-oriented global optimization

In design problems, where the set of variables is larger than the set of equations, the difference corresponds to the degrees of freedom available to the designer. The use of equation-oriented simulators is particularly useful for the global optimization of nonconvex problems, such as those that usually describe chemical processes. This paper shows that, by coupling a combinatorial optimizer with a tearing/partitioning algorithm, the simulation step of an optimization problem can be posed as a combinatorial optimization problem, with the objective of minimizing the cost of the simulation step. The functional form in which the variables appear in the equations can easily be taken into account as constraints to the optimization problem. The concept is described in detail for several examples found in the chemical engineering literature, showing that the proposed method may be a useful preprocessing tool for the global optimization of nonconvex NLP or MINLP problems, where SQP-based methods may not be adequate.