Mixed Integer Non linear Programming MINLP

To assure sequence feasibility, a mixed-integer non-linear program (MINLP) is formulated for the ELSP-BP and sELSP-BP. Table 3.6 contains the required set of parameters and variables. 

Abstract. In the present paper the problem of reuse water networks (RWN) have been modeled and optimized by the application of a modified Particle Swarm Optimization (PSO) algorithm. A proposed modified PSO method lead with both discrete and continuous variables in Mixed Integer Non-Linear Programming (MINLP) formulation that represent the water allocation problems. Pinch Analysis concepts are used jointly with the improved PSO method. Two literature problems considering mono and multicomponent problems were solved with the developed systematic and results has shown excellent performance in the optimality of reuse water network synthesis based on the criterion of minimization of annual total cost. 

Kocis, G.R. and Grossmann, I.E. (1988) Global optimisation of nonconvex mixed-integer non linear programming (MINLP) problems in process synthesis. Industrial Engineering Chemistry Research, 27 (8), 1407-1421. 

The gasoline blend problem is formulated as a Mixed Integer Non-Linear Programming (MINLP) problem, where the fuel composition is to be optimised, subject to product attributes (target properties) and process specifications. Considering the multiple types of eonstraint equations, the general gasoline blend problem is formulated as ... 

Binary variables are used to represent the occurrence of molecular structural groups (e.g. -CH3, -CHO, -OH. ..) found in the group contribution correlations. This allows molecules to be generated according to a set of structural and chemical feasibility constraints. In addition, a variety of pure component physical and environmental property prediction equations, non-ideal multi-component vapour-liquid equilibrium equations (UNIFAC), process operational constraints and an aggregated process model form part of the overall procedure. Finally, the solvent identification task is solved as a mixed integer non-linear programming (MINLP) problem (Buxton et ai, 1999). 

In a paper machine heat recovery system (HRS) the exhaust air streams of the paper machine dryer section are utilised for heating different cold streams. Condensation of the air moisture causes strong non-linearities in the system, notably the heat flow rates per °C and the heat transfer coefficients in the exchangers. A mixed integer non-linear programming (MINLP) model has been developed that takes into account these non-linearities (Soderman et al., 1999). Additionally the heat transfer area prices can be given as concave price curves in the model and the climate of the mill location can be taken into account with a multiple period formulation. 

Independent of the nature of the plant, either multiproduct or multipurpose, the most-used mathematical approaches are MILP (Mixed-Integer Linear Programming) or MINLP (Mixed-Integer Non-Linear Programming). The predominant objective function is based on an economic criterion. 

The TMP design optimization is a MINLP (mixed-integer non-linear programming) problem since it has both a discrete, A Ref, and a continuous, Fu,nk, design parameter. The operational optimization subproblem has integer decision variables (number of active refiners in time) affecting the continuous state of intermediate tank volume through process dynamics. The tank volume is constrained to stay between a minimum and a maximum volume. 

The formulation of the batch plant retrofit problem generally involves either deterministic methods based on mathematical programming such as LP (Linear Programming), NLP (Non-Linear Programming), MILP or MINLP or stochastic ones such as evolutionary algorithms. The non-linearity aspect may result from the nature of the constraints and/or the objective function. The mixed feature means that continuous and integer variables are involved in the formulation. 

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