Mixed-integer nonlinear programming simultaneous

The best way to approach the retrofit synthesis of the heat-exchanger network is to model all five tasks simultaneously. A mixed-integer nonlinear programming model is usually formulated to accomplish this goal. 

Flowsheet optimization is also regarded as a key task in the structural optimization of a flowsheet. As a described in the introduction, structural optimization for process design can be formulated as a mixed integer nonlinear program (MINLP). This then allows for addition or replacement of existing units, and consideration of a number of design options simultaneously. In these formulations individual units are turned on and off over the course of the optimization, as suggested by the MINLP master problem. 

One of the most popular methods of synthesis is hierarchical approach (Douglas, 1988). The other common method of synthesis is mixed integer nonlinear programming (MINLP). MINLP is also used to perform synthesis and system optimization simultaneously (Duran and Grossmann, 1986). The simultaneous design and optimization method has three steps (a) build a superstructure (b) generate the MINLP model of the superstructure (c) find the optimal structure and operation with a proper tool. 

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