The simplex method and fuzzy set membership functions to optimize analytical methods - Method approach and a case study from gas chromatography
Öberg, T., Warman, K.
Presentation vid Federation of Analytical Chemistry and Spectroscopy Societies meeting, Providence, Rhode Island, USA, 26-30 oktober, 1997.
Abstract
Objective functions in combination with the simplex method have been used for multicriteria optimization in analytical chemistry. We have evaluated a slightly different approach using fuzzy set membership functions (desirability functions) and a suitable aggregating technique.
Simplex optimization and fuzzy set membership functions makes it possible to work more economically and interactively compared to a traditional design of experiments strategy. Only the minimum amount of necessary trials are performed in the direction of improvement.
We will describe the calculation routines we have used, and discuss functional requirements for a calculation tool. We will also show how these ideas subsequently has been implemented in a user-friendly Windows software.
The application of multicriteria optimization is illustrated with a case study on the determination of PCB with HRGC/ECD. In routine chromatographic separations, it is of crucial importance to keep the total run time short, without jeopardizing necessary chromatographic resolution. A simplex optimization of the separation conditions is a straightforward solution to this common problem.
Four control variables were used in this study:
Three different response variables were used to characterize the outcome. Two of them were chromatographic resolution R1 and R2; the first between two peaks in the beginning of the chromatogram, the second between two peaks in the late part of the chromatogram. The third response variable was the total run time.
In this study the total run time was shortened from 45 to 25 minutes, in 11 trials, without any loss of resolution.
|
English homepage