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a limitation of the mass to 1%−2% of the mass
of a single floor and the stiffness to 10% of the
transversal stiffness of the beam elements seems
promising as starting values. Figure 3e already
proposes using small damping values.
The initial values of the mutation radius
should be so large that the parameters of the kids
produced by the parents cover an essential part
of the total parameter space. On the other hand, a
mutation radius which is too large transforms the
evolutionary search to a purely random process.
A mutation radius which is too small reduces the
evolutionary strategy to a local gradient search.
Starting with a mutation radius of 25%−50% of
the parameter range may help during the initial
studies indicating which values to use during the
following analysis.
The selection of the number of parents, kids
and generations should be done after some pre-
liminary studies of the specific problem. Initial
guesses may be the following:
of the not-so-good kids as new parents as well.
For studies with relatively small numbers of free
parameters as in our problem, parents surviving a
long time proved to be accelerating the progress.
Process of Evolutionary Optimization
Evolutionary optimization studies are relatively
tolerant and forgive many errors. As long as the
mutation radius is not too small, progress will be
visible. But like in nature, populations must be
sufficiently large and many generations are re-
quired before essential progress can be observed.
So impatient users or projects where results are
required within some hours are not adequate for
evolutionary optimization.
To simplify the process of rerunning and evalu-
ation of similar studies, an overlay process creating
many jobs and interpreting the most important data
could be helpful. If there are qualified ideas on
where to locate the best solutions, many parallel
studies with slightly different initial data should
be performed. Today computing power is available
and there is no need to survey the processes. So
some nights could be used to run studies on all
available computers.
Figure 5c compares the values of the fitness
function of the 3 best and the worst parents vs.
the generation number. Figure 5d compares the
edifice's top deflection vs. time for a structure
without and one with a compensation system.
Obviously the proposal derived by the analysis
outlined is able to reduce the transient impact
during the seismic attack.
The example of the changing fitness function
(Figure 4c) should be kept in mind once more.
If there is a region where the objective assumes
acceptable values, why shouldn't we search this
region for proposals which optimize other goals?
We may transform the damage intensity from the
objective to a constraint. Now the search continues
for all parameter sets that do not cause a violation
of the damage limit to a new objective, for example
the minimisation of the compensators mass or
•
Let the number of parents be twice the
number of free parameters.
•
Let the number of kids be twice the num-
ber of parents.
•
Let the number of generations be in the
range of the number of kids.
These starting values together with an appropri-
ate mutation radius will provide ideas on how to
proceed. In our compensator optimization study
with 10 floors and 3 compensators, the use of 10
parents, 20 kids and 20-40 generations worked
well in the initial jobs. Later we increased the data
to 20 parents, 50 kids and 100-500 generations.
Many different ways to select the new parents
out of a set of kids and perhaps even the old parents
exist. It is often a good idea to let some of the best
parents survive for at least a limited number of
generations. The new parent generation may then
be defined by the best of parents and kids of the last
generation. It can be useful to expand the region
of the parameter space searched by taking some
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