Comparative Study on Multi-Objective Genetic Algorithms for Seismic Response Controls of Structures - Design Optimization of Active and Passive Structural Control Systems - page 346

Figure 7. Determining the number of individu-
als to create between selected Pareto-optimal
individuals (Cha et al. 2011a)

and the fourth and later individuals, only if the
number of new individuals in specific section is
bigger than 4, are generated using random values
bounded between the decoded variables. The cre-
ated values are encoded based on binary and this
new gene instance is inserted at specific location
of the representative individuals as shown in
Figure 8. The flag values are used and the larger
flag valued gene instances is selected for to insert
the new gene instance when there are more than
one gene instances that express the same story
information.
As a final step, the newly created individuals
are added to individuals which are created by
standard genetic operation to create new child
population for the next generation. The benefit of
using the proposed GMGA to obtain a set of near-
optimal control device and sensor layout designs
for larger, more complex problems is investi-
gated in this research effort.

k = k +1

where v is number of design variable parameters
encoded in a IRR individual, t is the number of
Pareto-optimal front sections determined between
every two individuals lying on the front (Figure
7 identifies 7 sections along the Pareto-optimal
front), j is number of individuals bounding the
Pareto-optimal front sections ( j = 2 for problems
with two objectives and j = 3 for problems with
three-objectives), and k is the number of new
individuals to be created in each section, s , deter-
mined using Eq. 10, P s k v

EXAMPLE

Optimal Formulation

In this chapter, a multi-objective optimization
problem is formulated in terms of the distribu-
tion of both device and sensor and interstory drift
responses of structures. The maximum drift is a
normalized measure (Barroso 1999, Barroso et
al. 2002)

n ( , , ) is the new param-
eter value for the v -th parameter in the k -th new
individual in the s -th section of the Pareto-optimal
front, and P v i

c

d t
h

( )

c ( , ) is the v -th current parameter
value, which may be determined by the gene
instance with the highest flag value if there are
duplicate story gene instances in the current in-
dividual.
The gene instances of the first new individual
are generated using average value of the variables.
The second one is created by maximum values of
the variables, the third using the minimum values,

i

J

1 =

max max , (15)

t i ,

i

J 2 = Summation of the number of control devices and sensors,