Mixed-integer programming

Grossmann, I. E., Mixed Integer Programming Approach for the Synthesis of Integrated Process Flowsheets, Camp. Chem. Eng., 9 463, 1985. 

Kakhu, A. L, and Flower, J. R., Synthesi ng Heat-Integrated Distillation Systems Using Mixed Integer Programming, Trans. IChemE ChERD, 66 241, 1988. 

Mixed-integer programming contains integer variables with the values of either 0 or 1. These variables represent a stmcture or substmcture. A special constraint about the stmctures states that of a set of (stmcture) integer variables only one of them can have a value of 1 expressed in a statement the sum of the values of (alternate) variables is equal to 1. In this manner, the arbitrary relations between stmctures can be expressed mathematically and then the optimal solution is found with the help of a computer program. (52). 

Using mixed-integer programming, find the minimum number of mass exchangers the benzene recovery example described in Section 3.7 (Example 3.1). 

Engineered Mixed-Integer Programming in Chemical Batch Scheduling"... 

A very popular scheduling framework is based on mixed-integer programming. Herein, the scheduling problem is modeled in terms of variables and algebraic inequalities and solved by mathematical optimization techniques. In opposition to this well-established framework, a different approach is advocated in the paper by Alur and Dill [8] on timed automata (TA). 

The Excel Solver. Microsoft Excel, beginning with version 3.0 in 1991, incorporates an NLP solver that operates on the values and formulas of a spreadsheet model. Versions 4.0 and later include an LP solver and mixed-integer programming (MIP) capability for both linear and nonlinear problems. The user specifies a set of cell addresses to be independently adjusted (the decision variables), a set of formula cells whose values are to be constrained (the constraints), and a formula cell designated as the optimization objective. The solver uses the spreadsheet interpreter to evaluate the constraint and objective functions, and approximates derivatives, using finite differences. The NLP solution engine for the Excel Solver is GRG2 (see Section 8.7). 

Branch and bound (BB) is a class of methods for linear and nonlinear mixed-integer programming. If carried to completion, it is guaranteed to find an optimal solution to linear and convex nonlinear problems. It is the most popular approach and is currently used in virtually all commercial MILP software (see Chapter 7). 

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