194. A homotopy continuation method for flowsheet optimization
Invited abstract in session WE-7: Optimization applications III, stream Optimization applications.
Wednesday, 14:10 - 15:50Room: M:I
Authors (first author is the speaker)
| 1. | David Mogalle
|
| Optimization, Fraunhofer ITWM | |
| 2. | Tobias Seidel
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| Optimization, Fraunhofer Institute ITWM | |
| 3. | Michael Bortz
|
| Optimization, Fraunhofer ITWM | |
| 4. | Karl-Heinz Küfer
|
| Optimization, Fraunhofer ITWM |
Abstract
Distillation processes are a major part of the chemical industry. In order to find an optimal operating point for these processes, an optimization problem with a large number of variables and a large number of highly nonlinear equality constraints – the so-called MESH equations – has to be solved. To deal with the high dimensionality, one can reduce the problem into a much smaller one by solving most of the MESH equations implicitly. However, this reduction method is only guaranteed to work for feasible points of the original problem. Thus, we get an optimization problem where the remaining constraints can no longer be evaluated at every point.
To mitigate this issue, we propose a homotopy continuation method. First, we solve a simplified problem where we can guarantee the evaluation of the constraint functions on the whole domain. Then, we gradually transform our simplified problem back to the original one. The step size of this transformation is chosen in a way such that we stay in the region where evaluation of the constraints is possible. Finally, we prove that the homotopy continuation method converges under reasonable assumptions on the parameters that characterize the distillation process.
Keywords
- Optimization in industry, business and finance
Status: accepted
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