Optimization and Computational Fluid Dynamics - Department of ...

8 Multi-objective Optimization in Convective Heat Transfer 239
ments, and giving a clearer understanding of the influence of design variables.
Three main aspects must be considered when choosing a DOE:
1. The number of design variables (i.e., domain space dimension);
2. The effort of a single experiment;
3. The expected complexity of the objective function.
The modeFRONTIER package includes several algorithms for the DOE selection
[14]. In this work, we have mainly used full factorial and Sobol ones.
Full Factorial
Full factorial (FF) algorithm sample each variable span for n values called
levels and evaluates every possible combination. The number of total experiments
is
k�
N =
(8.40)
i=1
where ni is the number of levels for the i-th variable and k is the number of
design variables. Full factorial provides a very good sampling of the variables
domain space, giving complete information on the influence of each parameter
on the system. The higher the number of levels, the better the information.
However, this algorithm bears an important drawback, namely that the
number of samples increase exponentially with the number of variables. This
makes the use of FF unaffordable in many practical circumstances.
Sobol
Sobol algorithm creates sequences of n points that fill the n-dimensional space
more uniformly than a random sequence does. These types of sequences are
called quasi-random sequences. This term is misleading since there is nothing
random in this algorithm. The data in this type of sequence are chosen as to
avoid each other, filling in a uniform way the design space. This is illustrated
in Fig. 8.7(b).
8.7 Optimization Algorithms
Optimization algorithms investigate the behavior of a system, seeking for
design variable combinations that give optimal performances. In terms of
objective function values, an optimal performance means the attainment of
extrema. Extrema are points in which the value of the function is either minimum
or maximum. Generally speaking, a function might present more than
ni