Generalized disjunctive programming GDP

A generalized disjunctive program (GDP) may be formulated as an MINLP, with binary variables yt replacing the logical variables Yt. The most common formulation is called the big-M approach because it uses a large positive constant denoted by M to relax or enforce the constraints. This formulation of the preceding example follows ... 

The olefin separation process involves handling a feed stream with a number of hydrocarbon components. The objective of this process is to separate each of these components at minimum cost. We consider a superstructure optimization for the olefin separation system that consists of several technologies for the separation task units and compressors, pumps, valves, heaters, coolers, heat exchangers. We model the major discrete decisions for the separation system as a generalized disjunctive programming (GDP) problem. The objective function is to minimize the annualized investment cost of the separation units and the utility cost. The GDP problem is reformulated as an MINLP problem, which is solved with the Outer Approximation (OA) algorithm that is available in DICOPT++/GAMS. The solution approach for the superstructure optimization is discussed and numerical results of an example are presented. 

GDP (Raman and Grossmann, 1994) is an extension of disjunctive programming (Balas, 1979) that provides an alternate way of modeling (MILP) and (MINLP) problems. The general formulation of a (GDP) is as follows ... 

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