Optimization and Computational Fluid Dynamics - Department of ...

238 Marco Manzan, Enrico Nobile, Stefano Pieri and Francesco Pinto
2. Evolutionary Algorithms (EA). They are heuristic methods that use some
mechanisms inspired by biological evolution: reproduction, mutation, recombination,
natural selection and survival of the fittest. Their most important
feature is the applicability to almost all types of problems, because
they do not make any assumption about the system under study as
classical techniques do. They can be used when relation f is a completely
unknown function. In their multi-objective version, Multi-Objective Evolutionary
Algorithms (MOEA), being part of the recently cited research area
known as evolutionary multi-objective optimization (EMOO), are shown
to be capable of dealing with truly multi-objective optimizations [7].
Differential calculus is the first example of traditional programming techniques,
but there is a widely developed literature [45] on the subject. Linear
programming, quadratic programming and nonlinear programming are just
some of the examples. To perform the optimization processes described in
this chapter, evolutionary techniques have been used that are available in
the modeFRONTIER c○ optimization program [14]. modeFRONTIER c○ ,used
throughout, is a state-of-the-art optimization package that includes most instruments
relevant to data analysis and single- and multi-objective optimizations.
8.6.1 Design of Experiment
Heuristic evolutionary techniques do not make any assumption on the relation
between objectives and design variables, thus providing an analogy with
experimental dataset analysis. A good initial sampling, which allows an initial
guess on the relations between inputs and outputs, is of great relevance
in reducing optimization effort and improving results [40].
Design Of Experiments (DOE) is a methodology applicable to the design of
all information-gathering activities where variation of decisional parameters
(design variables) is present. It is a technique aimed at gaining the most
possible knowledge within a given dataset. The first statistician to consider
a formal mathematical methodology for the design of experiments was Sir
Ronald A. Fisher, in 1920.
Before the advent of DOE methodology, the traditional approach was the
so-called One Factor At a Time (OFAT). Each factor (design variable) which
would influence the system used to be moved within its interval, while keeping
the others constant. In as much as it would require a usually large number
of evaluations, such a process could be quite time consuming. By contrast,
Fischer’s approach was to consider all variables simultaneously, varying more
than one at a time, so as to obtain the most relevant information with minimum
effort. It is a powerful tool for designing and analyzing data: it eliminates
redundant observations, thus reducing time and resources in experi-