Optimization and Computational Fluid Dynamics - Department of ...

240 Marco Manzan, Enrico Nobile, Stefano Pieri and Francesco Pinto
(a) random sampling (b) Sobol sampling
Fig. 8.7 Random sampling vs. Sobol (quasi-random) sampling
local maximum
Fig. 8.8 Multiple extrema points
global maximum
one extreme point, called local extrema, see Fig. 8.8. It is of great importance
for an algorithm to be capable of finding the global extremum of an
objective with the minimum effort. There are three main characteristics that
distinguish and classify the efficiency of an optimization algorithm:
• Robustness. Robustness is the capability of reaching a global optimum
point without being stuck in local extrema, or blocked for lack of useful
data. This is the most important feature in measuring the efficiency of an
optimization technique. The more an algorithm is robust, the higher the
chance to reach a global optimum or sub-optimum, i.e., a point close to
the global optimum.
• Accuracy. Accuracy is the ability of an algorithm to reach the actual
extrema, either global or local, around its proximity. Usually, accuracy
and robustness are conflicting attributes, so that robust algorithms are
not accurate and vice versa.
• Convergence rate. Convergence rate is a measure of the effort an algorithm
has to carry on to reach its goal. Again, robust algorithms are
usually slow. However, fast but not robust ones might not reach the goal
at all.
In this work, evolutionary techniques have been used that are usually robust
but neither accurate nor fast. However, as already stressed, their most
important attribute as well as reason for their popularity is the applicability