Civil Engineering Reference
In-Depth Information
More specifically, individuals in a population compete for surviving in such a way
that the best individuals remain in new generations, while the worst ones usually
disappear. From an optimisation point of view, it means that GA work with a popu-
lation of individuals (
n-uplas
of the unknown parameters
, which you can apply to
solve the optimisation problem) exploring in parallel new areas in the search space,
and thus, reducing the probability of being trapped in a local minimum (Rodríguez
and Berenguel
2002
). The GA optimisation process is described by Algorithm 2.
Ψ
Algorithm 1
GA optimisation process (Matlab
2012
)
Instant t = 0;
Create an initial population,
P
0
.
while
(None of the stopping criteria are satisfied)
do
Create a new population,
P
t
+
1
, from the individuals in the current population
P
t
. To do that, it
is necessary to perform the following steps:
1. Obtain a score,
S
t
,
j
for each individual in the current population,
P
t
by computing its fitness
value.
2. Perform a selection of individuals from the current population,
P
t
, called
parents
,asa
function of their score, i.e. a selection of potential solutions for the optimisation problem.
3. Select the individuals from the current population,
P
t
with best score that are chosen as
Elite individuals
. These individuals are directly passed to the new Population
P
t
+
1
.
4. Create
children
from the
parents
by means of genetic operations:
mutations
and
crossovers
.
5. Create a new population,
P
t
+
1
, from replacing the current population
P
t
with the children
obtained in the previous step.
6. t = t + 1;
end while
As mentioned previously, the GA optimisation technique is used to obtain the
final values of the unknown parameters (
) of the developed room model. Hence,
the GA provides optimal values of the variables shown in Table
4.12
by minimising
a fitness function,
J
Ψ
(
x
)
, presented in Sect.
4.3.2.1
.
4.3.2.1 Optimisation Problem: The Fitness Function
The optimisation problem consists in optimising a fitness function. In standard opti-
misation algorithms, it is known as the objective function. In the case of study of this
work, the fitness function is defined by a least squares criterion, see Eq.
4.45
.
N
2
J
(
x
)
=
min
1
|
x
(
i
)
− ˆ
x
(
i
,Ψ)
|
i
=
N
3
2
=
min
1
|
x
k
(
i
)
−ˆ
x
k
(
i
,Ψ)
|
(4.45)
i
=
1
k
=
