Mixed-integer nonlinear programming optimization

Ponsich, A. and Azzaro-Pantel, C. (2007) Mixed-integer nonlinear programming optimization strategies for batch plant design problems. Industrial Engineering Chemistry Research, 46 (3), 854-863. 

Stichlmair J. and Prey T. (2001). Mixed-Integer Nonlinear Programming optimization of reactive distillation processes. Industrial and Engineering Chemistry Research 40 (25), 5978-5982. 2.9.1.1, 3.3, 3.3.1... 

One of the approaches that can be used in design is to carry out structural and parameter optimization of a superstructure. The structural optimization required can be carried out using mixed integer linear programming in the case of a linear problem or mixed integer nonlinear programming in the case of a nonlinear problem. Stochastic optimization can also be very effective for structural optimization problems. 

Kalitventzeff, B. Mixed Integer Nonlinear Programming and its Application to the Management of Utility Networks. Eng Optim 18 183-207 (1991). 

Bauer, M. H. and J. Stichlmair. Design and Economic Optimization of Azeotropic Distillation Process Using Mixed-Integer Nonlinear Programming. Comput Chem Eng 22 1271-1286 (1998). 

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. 

A wide range of nonlinear optimization problems involve integer or discrete variables in addition to the continuous variables. These classes of optimization problems arise from a variety of applications and are denoted as Mixed-Integer Nonlinear Programming MINLP problems. 

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. 

McKinney, D. C., and Lin, M. D. (1995). "Approximate mixed-integer nonlinear programming methods for optimal aquifer remediation design." Water Resour. Res., 31(3), 731-740. 

A process-synthesis problem can be formulated as a combination of tasks whose goal is the optimization of an economic objective function subject to constraints. Two types of mathematical techniques are the most used mixed-integer linear programming (MILP), and mixed-integer nonlinear programming (MINLP). 

Kocis, G. R., A Mixed-Integer Nonlinear Programming Approach to Structural Flowsheet Optimization. Ph.D. thesis, Carnegie Mellon University, Pittsburgh, 1988. 

Mixed integer nonlinear programming Multi-criteria optimization... 

M. Tawarmalani, V. Sahinidis, Global Optimization in Continuous and Mixed-Integer Nonlinear Programming Theory, Algorithms, Software, and Applications, Kluwer, Boston, 2001. 

Kocis, G. R., and Grossmann, I. E. Global Optimization of Nonconvex Mixed-Integer Nonlinear Programming (MINLP) Problems in Process Synthesis, Ind. Eng. Chem. Res. 27,1407 (1988). 

One approach to making discrete design decisions is to pose a mixed-integer nonlinear program (MINLP) and apply a suitable optimization method to the selection of discrete design parameters. We have not adopted this approach for the following reasons. 

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