MINLP algorithms

Finally, the performance of both MILP and MINLP algorithms is strongly dependent on the problem formulations (3-110) and (3-112). In particular, the efficiency of the approach is impacted by the lower bounds produced by the relaxation of the binary variables and subsequent solution of the linear program in the branch and bound tree. A number of approaches have been proposed to improve the quality of the lower bounds, including these ... 

For optimization tools linked to procedural models, note that reliable and efficient automatic differentiation tools are available that link to models written, say, in FORTRAN and C, and calculate exact first (and often second) derivatives. Examples of these include ADIFOR, ADOL-C, GRESS, Odyssee, and PADRE. When used with care, these can be applied to existing procedural models and, when linked to modern NLP and MINLP algorithms, can lead to powerful optimization capabilities. More information on these and other automatic differentiation tools can be found at http //www-unix.mcs.anl.gov/ autodiff/ADTools/. 

Skrifvars, H. S. Leyffer and T. Westerlund. Comparison of Certain MINLP Algorithms When Applied to a Model Structure Determination and Parameter Estimation Problem. Comput Chem Eng 22 1829-1835 (1998). 

Turkay, M. and I. E. Grossmann. Logic-Based MINLP Algorithms for the Optimal Synthesis of Process Networks. Comput Chem Eng 20 (8) 959-978 (1996). 

In sections 63-6.1 we discussed the generalized benders decomposition GBD and the outer approximation based algorithms (i.e., OA, OA/ER, OA/ER/AP, GOA), and we identified a number of similarities as well as key differences between the two classes of MINLP algorithms. 

This chapter introduces the fundamentals of mixed-integer nonlinear optimization. Section 6.1 presents the motivation and the application areas of MINLP models. Section 6.2 presents the mathematical description of MINLP problems, discusses the challenges and computational complexity of MINLP models, and provides an overview of the existing MINLP algorithms. 

As a result, there now exist automated implementations of MINLP algorithms which are identified as DICOPT++ (Viswanathan and Grossmann, 1990), APROS (Paules and Floudas, 1989), as well as the library OASIS (Floudas, 1990). These automated implementations make use... 

A recent development of automated implementations of MINLP algorithms, which does not rely on the GAMS modeling system, is MINOPT (Rojnuckarin and Floudas, 1994). 

The primary objectives in the design of the MINOPT system have been (i) to provide an efficient and user-friendly interface for solving MINLP problems, (ii) to allow for the other user-specified subroutines such as process simulation packages, and (iii) to provide an expandable platform that can incorporate easily additional MINLP algorithms. 

In MINLP, however, there is the additional complication that nonlinearities can often be formulated in many different, but equivalent, ways and, as expected. this can have a great impact on the performance of MINLP algorithms, particularly with respect to the nonconvexities of the nonlinear constraints. 

Our objective in this section is to provide a general overview of the basic MINLP algorithms, emphasizing their fundamental ideas and properties. 

In order to provide some insight into the computational performance of the MINLP algorithms described in the last section, we consider the following example problem ... 

Tilrkay M. and Grossmann I.E. 1996. Logic-based MINLP algorithms for the optimal sjmthesis of process networks, Comput. Chem. Eng., 20(8), 959-978. 

The integration between processes can be carried out by all the steps, or by the first and the third step or only by the last step depending on the complexity of the problems. All the steps can be carried out simultaneously and the MINLP algorithm applied with or without the first and the second step. 

The mathematical model is using the MINLP algorithm, performing the simultaneous heat integration between processes and generation of electricity. 

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