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modelling desirability
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of Multi-Criteria-Optimisation
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Practical optimisation issues
Turned the original problem into a response surface problem to
use gradient based search algorithms.
But: Multiple local optima of
different heights may occur! (Often ignored in literature!)
If
dim(X) > 1, then manyfolds can occur as regions
of optimum desirability.
Factor space can even fall apart in disjunct
regions of non-zero desirability.
Simple, but expensive way out:
performing a grid search in factor space. (used in STAVEX)
Unimodality has
to be assured before performing the optimisation step.
Desirability of type (-1, 0, 0.5, 1, 1), Y= -X2 +1, plotted against X
Desirability of type (-1, 0, 4, 0.5, 0.5), Y = X12 + X22, plotted against factor space.
Dipl.-Stat. Detlef Steuer
1999-10-04