Earthquake Engineering Research - HKU Libraries - The University ...

133
1st Generation
dGenerate individuals randomly !
generations
[ Evaluation of fitness )
I Preserve the elite solutions j
Selection
O
D
parent
child
.0 a
..-Parent-]
/
0
•Parent .2
F
Parent-3
\.
0"
gQ-^arent _2
a-'
%r'DD
0-Sn
.©"'
..•Parent- !
Parent-3
Q
/ ••.
f*B\
/%£ )D
••' Q
•'* n
(£"""
Parent- 1
••*"'"
Type-1 Type-2 Type-3
Fzg. 4 Outline of Crossover in Real Coded GA
..-••"" Parent-
Crossover and Mutation J modified Newton methods (DFP, BFGS, etc.) can not be
applicable. In this study, we adopt GA (Genetic algorithms)
Optimum solution
which attracts attention as practical global optimization
methods.
Fig.3 Flowchart of Genetic Algorithm
Traditionally, binary codes have been used to represent
the design variables including real number parameters, and
the crossover operation is performed by the exchange of a
part of the binary bit. However, some researchers are using
the GA with real coded crossover operators (Tsutsui et al,1997) and reported the advantage of their
methods. Among them, the unimodal normal distribution crossover (UNDX) is reported to show good
performance in optimizing problems (Kita, et al, 1999).
Basically, the outline of real coded GA which is shown in Fig.3 is same as that of binary coded GA,
except crossover operator and mutation. There are several models proposed for real coded crossover
operator with Gaussian noise. The concepts of the crossover operator which are used in this paper are
illustrated in Fig.4 (Yoshida, 2000). In the case of Type-1, the children are derived by following
equation.
g_ A+P 2 Pi-P* here, a * N(0,l) (2)
V
2 2
c, p l and p 2 are vectors in design parameter space, c is a child made from parents p l and p 2 . The
parents are randomly selected in proportion to their fitness, which is the inverse of safety factor in this
slope stability study. The children are generated in one-dimensional subspace of the parameter space in
Type-1. In Type-2, n dimensional perturbation is given to Type-1 children, consequently Type-2
children are generated in n dimensional space, when there are n design variables. The magnitude of the
perturbation is defined based on the distance from Parent-3 to the line with Parent-1 and 2. In Type-3,
the children are generated in 2-dimensional subspace made by three parents as shown in Fig.4. In all
types, the generated children are in the neighbourhood of the gravity center of their parents.
Perturbation v is added to each design variable as mutation. In this study, Cauchy distribution is
used.
NUMERICAL EXAMPLES
Models and Characteristics of Dynamic Response
Two types of slope model are used for the numerical calculations. FEM model of them are shown
in Fig.5. The height and width of the slope are indicated in Fig.6. The number of node and element of
Type-1 model is 8848 and 7557, while those of Type-2 are 11336 and 9883. The sides and base of the