Logic-based outer approximation for globally optimal synthesis of process networks

Process network problems can be formulated as generalized disjunctive programs where a logic-based representation is used to deal with the discrete and continuous decisions. A new deterministic algorithm for the global optimization of process networks is presented in this work. The proposed algorithm, which does not rely on spatial branch-and-bound, is based on the logic-based outer approximation that exploits the special structure of flowsheet synthesis models. The method is capable of considering non-convexities, while guaranteeing globality in the solution of an optimal synthesis of process network problem. This is accomplished by solving iteratively reduced NLP subproblems to global optimality and MILP master problems, which are valid outer approximations of the original problem. Piecewise linear under and overestimators for bilinear and concave terms have been constructed with the property of having zero gap in a finite set of points. The global optimization of the reduced NLP may be performed either with a suitable global solver or using the inner optimization strategy that is proposed in this work. Theoretical properties are discussed as well as several alternatives for implementing the proposed algorithm. Several examples were successfully solved with this algorithm. Results show that only few iterations are required to solve them to global optimality.