Mixed-integer nonlinear programming MINLP modeling

The specific problem characteristics are modeled most appropriately by a combination of concepts from various general modeling frameworks leading to a mixed-integer nonlinear programming (MINLP) model. 

The above formulation is a mixed-integer nonlinear programming MINLP model and has the following characteristics. The binary variables appear linearly and separably from the continuous variables in both the objective and constraints, by defining a new set of variables Wj = tij/Tu and including the bilinear constraints WiTu = Uj- The continuous variables nitBi,Tu,Wi appear nonlinearly. In particular, we have bilinear terms of riiBi in the objective and constraints, bilinear terms of niT i and WiTu in the constraints. The rest of the continuous variables Vj, (V fc)ra, Vfjk appear linearly in the objective function and constraints. 

The general mathematical model of the superstructure presented in step 2 of the outline, and indicated as (7.1), has a mixed set of 0 - 1 and continuous variables and as a result is a mixed-integer optimization model. If any of the objective function and constraints is nonlinear, then (7.1) is classified as mixed- integer nonlinear programming MINLP 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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