Black box problem
A mathematical model implemented in an Excel workbook is provided. You may find the file
“Blackbox.xlsm” on Canvas. The model may be classified as a black box where the user provides two
input variables, x1 and x2, and receives an output f1. The Excel workbook is shown in figure 1.
Figure 1. Excel workbook.
The provided Excel workbook calls an executable DLL called SDD.dll. DLLs (dynamic-link libraries) are
portable libraries that can be created by one application and used by another. The SDD.dll is available
on Canvas. For the execution to work properly SDD.dll should be put in the local folder “C:\temp”.
Hence we have an unknown function:
f1 (x1 , x2 )
Your task is to minimize that function considering the following set constraint:
− 0,05  x1  0,05
− 0,05  x2  0,05
The optimization of this unknown system should be based on polynomial metamodel, i.e. a response
surface model, created in Matlab.
The Excel model is executed each time the value of x2, i.e. the value in cell B3, is changed. Once
model execution is completed, the result, f1, is written in cell B5. One function call takes almost 3
hours. Hence some sort of automated experiment is appropriate. A suggestion could be to use the
DOE process component in Isight to conduct experiments. The results of these experiments can then
be exported to Matlab for generation of metamodel and finally optimization.
Johan Wall | BLEKINGE TEKNISKA HÖGSKOLA