Technical Issues - Workbook Tutorial III - Constraints

Optimization in the FilmStar Workbook includes an objective (merit function) which is the quantity to be minimized. In addition the NOL (NASA developed Numerical Optimization Library) allows n constraints. While most designs do not require constraints it behooves FilmStar users to understand its possibilities so as to recognize cases where it is beneficial or even crucial.

The object is to design a four layer AR coating where the first two and the last two layers have equal thickness and total thickness is less than 225 nm. We now add two new defined names: Constraint ($G$5:$H$7) and Design ($E$11). Any number of constraints can be added; note that Constraint utilizes two columns. The first column is the function defining the constraint and the second column is constraint type: equality or inequality, linear or nonlinear. See Help (DESIGN Reference.. FilmStar Workbook.. Defined Names) for details. While the difference between equality and inequality is clear, the difference between constraint types is not. In this case there is no difference for column H values =1 (nonlinear) or =2 (linear).

Bbar_Wb.zip includes Workbook Bbar_wb.xls and FILM Archive Bbar_Wb.faw (BBAR initial design converted to physical thickness). Open the FILM Archive, activate the Workbook and open Bbar_Wb.xls. Click Optimize.. Optimize <Ctrl+O> in the Workbook. If everything works as planned  you get this:

Explanation: Macro command LayersCopy copies the design to the clipboard during each optimization iteration. The design is then automatically pasted into the Workbook starting at the cell with defined name Design. This capability makes it possible to design coatings which include film thickness as constraints. When studying the example, please activate the edit bar Edit.. Show Edit Bar <F7> so you can view functions such as those in $F$12:$F$15.

How does the final design compare with BBAR optimized without constraints? Rather than remove the constraints permanently, set DataType=32 to ignore them. Results are shown below; as expected the unconstrained design suffers somewhat. Would increasing total thickness improve performance? That is left to the reader to discover!

Users sometimes inquire about NOL Parameters. Unfortunately the choice of parameters depends on the problem and there is little guidance that can be given except experiment with different Optimizer and 1-D Search settings. Some combinations lead nowhere while others offer quick solutions. Scaling appears to be important for constrained Workbook problems. Note that Update Graph and Merit Exponent do not apply to Workbook optimization.

A second example is discussed on a separate page: Optimizing Two Designs Simultaneously.