A Mixed-Integer Nonlinear Programming Algorithm for Process Systems Synthesis z The problem of synthesizing processing systems via simultaneous structural and parameter optimization is addressed in this paper. Based on a superstructure representation for embedding alternative configurations, a general mixed-integer nonlinear programming (MINLP) framework is presented for the synthesis problem. An efficient outer- approximation algorithm is described for the solution of the underlying optimization problem, which is characterized by linear binary variables and continuous variables that appear in nonlinear functions. The pro- posed algorithm is based on a bounding sequence that requires the analysis of few system configurations, and the solution of a master problem that identifies new candidate structures. Application of the pro- posed algorithm is illustrated with the optimal synthesis of gas pipe- lines. SCOPE Synthesis is perhaps the cornerstone of the process design activity since it addresses the fundamental problem of structuring a processing scheme so as to satisfy given goals and/or needs. This relatively new research area in chemical engineering has received considerable attention in the literature; see Nishida et al. (1981) for a review. Theoretical as well as applica- tions-related work in this area is currently the subject of major efforts. The main approaches that have emerged for tackling process synthesis problems are the use of heuristics, thermodynamic targets, and algo- rithmic methods that are based on optimization tech- niques (Stephanopoulos, 1981). As indicated by Gross- mann (1985), the first two approaches have been used quite extensively with some important successes de- spite their obvious limitations, such as the fact of not being able to assert the quality of the solution, the assumption on dominance of energy costs, and the restricted application to specific subproblems. Algo- rithmic methods, on the other hand, offer a more gen- eral and systematic approach since they explicitly ac- zyxwvu Correspondence concerning this paper should be addressed to 1. E. Grossmann. M. A. Duran’s currenl address is Universidad Autonoma Metropolitans-lztapalapa. zyxwvutsrq A*. Postal 55-534.09340 MexicoCity. M. A. Duran and I. E. Grossmann Department of Chemical Engineering Carnegie-Mellon University Pittsburgh, PA 15213 count for the economic trade-offs and interactions in the synthesis of arbitrary processing systems. Further- more, because of their nature these methods can accommodate the other two approaches and are bet- ter suited for automatic synthesis of systems, as has recently been shown in the mixed-integer linear pro- gramming (MILP) framework proposed by Papoulias and Grossmann (1983a,b,c). These authors developed MILP formulations for utility systems, heat recovery networks, and integrated total processing systems. An important limitation of these formulations is that nonlin- earities cannot be handled explicitly as they require the discretization of those variables that give rise to nonlinear functions. Thus, there is a need to develop efficient optimization procedures that can handle dis- crete and continuous variables in nonlinear models for the synthesis of process systems. This paper addresses the problem of developing an efficient solution procedure for algorithmic methods for the synthesis of process systems. Based on the model- ing of a superstructure of alternatives as a mixed- integer nonlinear programming (MINLP) program in which the binary variables appear linearly and the con- tinuous variables are involved in nonlinear functions, an 592 April 1986 Vol. 32, No. 4 AIChE Journal