(19f) A Sequential Approach to Global Flowsheet Optimization Using Mccormick Relaxations
In this work, we consider a method for global optimization of flowsheets that is similar to the sequential modular infeasible path method employed in local optimization in the sense that the majority of the model variables and equations are moved to external modules, while only few are left to the optimizer. While a similar approach was originally introduced using interval methods , a recent modification based on McCormick relaxations has been shown to enable significant reductions in computational time compared to equation-oriented formulations . This approach makes use of the automatic propagation of McCormick relaxations  and their subgradients through computer codes  that allow to supply tight relaxations for functions that are not explicitly handled by the optimizer, but rather act as a black box from which function values or relaxations and their subgradients can be queried as needed. Through an appropriate selection of the equations to be left to the optimizer, the applicability of the relaxation propagation is ensured. A possible alternative would be to optimize only in the degrees of freedom, which would require the relaxation of implicit functions . A simple B&B solver has been implemented that can treat external module definitions. The modules are implemented as template functions, and the propagation of relaxations is conducted using MC++ . The application of this reduced-space formulation is demonstrated for simple process flowsheets. We compare solution times of the reduced-space formulation with those of the conventional equation-oriented formulation and discuss the influence of the selection of variables and constraints left to the optimizer.
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