OPTFEKO calculates upon termination of an optimisation,
a sensitivity analysis of the goal function with relation to each parameter.
The sensitivity analysis is calculated using the particle swarm optimisation (PSO),
generic algorithm (GA) or Simplex method, if sufficient information is available.
The calculated sensitivity values are indicated on the screen output, and stored in
the text .log file. If no sensitivity analysis is performed,
the reason is indicated on the screen output, but no indication is written to the
text .log file.
Figure 1 shows an example
goal function f that varies as a function of the parameter x. The sensitivity
with relation to the parameter x can be described by the following
equation:
with equal to 1
Solving the equation, however, gives a near zero value
when the solution space is well converged. We therefore rather compute the second
derivative from which the sensitivity parameter can be computed through
integration
to finally give the sensitivity with relation to
x as
A sensitivity analysis will only be performed if at least 2N +1 samples are
available for a problem with N parameters and these samples should all be
within a 5% radius of the optimum. If the samples under consideration are scattered
outside of a 5% radius of the optimum, the stored data is considered insufficient
for proper sensitivity analysis. It should also be realised that as this computation
makes use of already computed samples only, the accuracy of the reported sensitivity
number depends on how well the algorithm has converged.