Optimization and Computational Fluid Dynamics - Department of ...

154 René A. Van den Braembussche
Solution quality (%)
102
101
100
99
98
97
96
95
94
93
92
91
90
89
88
87
86
85
10 0
2
5
8
11
22 25
10 1
33
Population size n
Fig. 6.4 Dependence of GA solution quality on population size for the 27 parameter test
case
Selection scheme
Different selection schemes have been proposed. One is the roulette: a system
in which the chance that an individual is selected increases proportional with
1/OF. This scheme favors the best individuals as parents. It is elitist and
has larger chances to get stuck in a local optimum.
In the tournament selection, “s” individuals are chosen randomly from
the population and the individual with the highest fitness (lowest OF) is
selected as parent. The same process is repeated to find the second parent.
The parameter s is called the tournament size and can take values between
1andN (population size). Larger values of s give more chances to the best
samples to be selected and to create offsprings. It favors a rapid, although
perhaps premature, convergence to a local optimum. Very small values of
s result in a more random selection of parents. Tests have shown that a
standard value of s = 2 gives the best results.
Population size
Fixing the total number of function evaluations at 5,000, the number of generations
t is a consequence of the population size N (N × t =5, 000). Figure
6.4 shows the solution quality at the end of the GA run in function of the
44
50
88
10 2
176
352
704
10 3