Evolutionary Optimization of Passive Compensators to Improve Earthquake Resistance - Design Optimization of Active and Passive Structural Control Systems - page 254

• Parameters (Free Parameters): The free

parameters are the data that may be modi-
fied to find better values of the objective.

of the current generation. Often selection is
done by only taking the best nparent kids
as new parents.

• Parameter Range: The parameter range

limits the values of the free parameters.

• Anisotropy: Anisotropy is the interdepen-

dence between the mutations of parameters
(Figure 1b). • Individual: Individuals are the elements

of the sets of parents and kids.

• Generation: A generation is one step in the

evolutionary process given by a set of par-
ents. The production of a new set of kids
defines the genesis of a new generation.

There are many other terms used in conjunc-
tion with evolutionary or bionic optimization. As
there is no generally accepted vocabulary, users
reading papers from different authors are advised
to carefully check the definitions used. • Number of Parents per Generation:

This number should be sufficiently large
to cover some or many possible parameter
combinations.

Gradient and Evolutionary Optimization

• Number of Children per Generation:

This number covers the parameter space.
So again a large number is preferred.

Optimization of structures takes place in some
steps. First the function of a part or system has
to be defined. Next some ideas about the physical
realisation are set up and evaluated. A decision
about the basic design and the space available
yields a first proposal (Steinbuch 2004, p.195).
The following steps deal with the variation of
the parameters set during the optimization pro-
cess. This optimization is often done by gradient
or evolutionary strategies. In both cases the free
parameters used for the optimization are selected
from the total of parameters describing the initial
solution. For all of these free parameters, ranges of
acceptable values are set. Furthermore necessary
relations or constraints between the parameters
are identified to exclude impossible or infeasible
geometries, penetration of neighbouring com-
ponents, etc. Care should be taken if there are
any restrictions to be checked, e.g. the violation
of maximum stress or deflection during a mass
reduction study. After this initiation the two strate-
gies split up.
The gradient approach needs one or a small
number of good initial designs. For these initial
designs the values of the objective are deter-
mined. Furthermore the gradient of the objective
is found by differentiating the objective with the
free parameters:

• Pairing: Pairing is the selection of two in-

dividuals of the parent generation to pro-
duce one common child. Tests provide ef-
ficient strategies of pairing.

• Kill Parents: Should old parents survive to

be parents in the next generation as well?

• Crossing: How are the kids' parameters

derived from their parents' values? Figure
1a sketches some of the many ways of de-
fining the child's parameter values from
the parents' ones (Steinbuch 2010).

• Mutation: Mutation is the modification

of the parameter values of an individual.
There are infinite possibilities to do mu-
tations, so the different types of mutation
have to be checked carefully until some ex-
perience is collected. Figure 1b proposes
some of the possibilities of mutation in a
2-dimensional parameter space.

• Mutation Radius: The mutation radius

is the maximum amount that a parame-
ter may be changed in one mutation step
(Figure 1b).

• Selection: Selection is the process of de-

fining the next parent generation out of the
set of kids (including their parents or not)