Geology Reference
In-Depth Information
the desired number of acceptable members of the
new generation is defined. The fitness of the kids
is evaluated. From the total of new kids (possibly
including some of the parents) the new parent
generation is selected, and the cycle restarts.
Figure 1d presents some landscapes of 2D
optimization problems. There is no doubt that
gradient approaches will be superior in the case
of isolated hills; however when applied to multi-
hill problems they fail to find the global optimum.
Evolutionary strategies are able to detect the ab-
solute maximum at the prize of a large mutation
radius and many trials during many generations.
This short outline of evolutionary optimiza-
tion gives some proposals on how to perform
the process. There are many possible variants,
so a unique way to do evolutionary optimization
does not exist. Users should start with simple
but typical problems, testing the influence of the
different proposals and learning which specific
choice of input performs well for the problem
to be handled. Those users should keep in mind
that, like in nature, large populations and many
generations have to be studied before significant
improvements may be observed.
z p p
(
,
...,
p
,
p
+
p p
,
...
p
)
z
p
1
2
i
1
i
i
+
1
n
2
p
i
i
z p p
(
,
...,
p
,
p
p p
,
...
p
)
1
2
i
1
i
i
+
1
n
2
p
i
(4)
So the gradient is given by:
z
p
z
p
z
p
z
p
T
∇ =
z
,
,
, . . . . ,
1
2
3
n
(5)
We step in the direction of the gradient as
long as improvements in the objective are to be
observed. Very small or zero gradients indicate
the vicinity of a local or global maximum. There
the process stops. From the inside of the process
there is no chance to decide whether a local or
global maximum has been found. Consequently
different initial designs should be analysed. If
they represent a significant part of the solution
space, there may be realistically a chance to find
the best or global maximum or at least a very
good local maximum.
The evolutionary process starts by defining an
initial parent generation (cf. Figure 1c). This may
be done by taking some qualified initial designs,
mutations of a good initial design or by a random
process placing the parents' parameters into the
space of allowable ranges.
These parents are paired off. Each pair pro-
duces only one child by crossing the parameters
in a predefined scheme as shown in Figure 1a
(Brieger 2008). The kid's parameters are mutated
within the range given by the mutation radius and
without violating the allowed parameter ranges
(Steinbuch 2010). This step of pairing, crossing
and mutation is repeated until the number of re-
quired kids has been produced. Care should be
taken that a kid does not violate some of the re-
strictions. In this case, the kid is removed from
the population and new kids are produced until
Earthquakes as Mechanical
Impact on High Buildings
If we want to perform numerical studies of the
impact of earthquake on edifices, we have to
reduce the complex event of a real earthquake
to a reduced model using a small number of
parameters. This reduced model has to be able
to represent the most important seismic effects
acting on a specific edifice during the event in a
realistic and not too conservative way.
Interpretation of Earthquake Pulses
From the mechanical point of view, an earthquake
is a displacement controlled transient loading on
the ground around the building we are looking at
(Chopra 2000, pp. 197-206, Meskouris and Hinzen
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