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An Integrated Approach to Integer and Nonlinear Optimization
Sven Leyffer
University of Dundee
Hosted by Stephen Wright
10:30AM, Wednesday, February 24, 1999
Building 221, A-216
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| Abstract |
Mixed integer nonlinear programming problems (MINLPs) arise in a wide
variety of industrial applications such as batch plant design, synthesis of processing
systems, optimal positioning of a new product, distillation column design, trim loss
minimization in the paper industry and optimization of nuclear reactor core reload
patterns.
All applications have in common that some of the variables are restricted to be integer
(e.g. the number of batches or trays in a column) or binary (e.g., the existence of a
piece of equipment or of a cut in the paper cutting problem). In addition, these problems
also involve some nonlinear relationships modeling the underlying physics of the
application.
Classical methods for the solution of MINLP problems decompose the problem by separating
the nonlinear part from the integer part. This approach is largely due to the existence of
packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear
Programming problems.In this talk, a new integrated approach to solving MINLP problems
is considered. This new algorithm is based on branch-and-bound, but does not require the
NLP problem at each node to be solved to optimality. Instead, branching is allowed after
each iteration of the NLP solver. In this way, the nonlinear part of the MINLP problem is
solved while searching the tree.
A numerical comparison of the new method with nonlinear branch-and-bound is presented and
a factor of about 3 improvement over branch-and-bound is observed. |
