Optimization and Computational Fluid Dynamics - Department of ...

242 Marco Manzan, Enrico Nobile, Stefano Pieri and Francesco Pinto
1 2 3 4 5 6
A B C D E F
1 2 3 4 5 6
Design i
o n
=⇒
(a) Mutation
)
=⇒
(b) Crossover
Design 2
Fig. 8.10 Evolutionary operators of a GA
1 2 3 H 5 6
( A B 3 4 5 6
New Design i
(c) Directional Crossover
1 2 C D E F
Design 1
data can be represented graphically as in Fig. 8.9. The relations (8.41) allows
the determination of a design set – those joined by a dashed line – which is
called Pareto front or Pareto optimal set and whose dimension is equal to
n − 1. In this example n = 2, and the front is a line.
8.7.1 Genetic Algorithm
Genetic algorithm (GA) is the most popular type of EA. The basic idea
underlying the method comes from the behavior of living organisms in nature.
An initial set of individuals, called initial population, undergoes a natural
selection process. So each individual can be seen as a DNA string. Parental
populations give birth to offsprings. GAs work on individuals as coded bit
strings, thus they need discrete variable intervals. The new generations are
created following a series of genetic rules:
• Selection. Selection operator randomly shifts a defined number of individuals
to the next generation, keeping them unchanged. The probability
for an individual to undergo a process of selection is weighed on the fitness 1
value of each design. The better the fitness, the higher the probability to
be selected for the new population.
1 fitness is the measure of how a design variable set fits the goal of an optimization. Its
quantitative definition depends on the chosen algorithm.