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(3)
Soil parameters, ground condition, and external loads can vary over a wide
range so that the choices of the optimization parameters are difficult to be
established.
(4)
The number of control variables can be very large and solution time can be
long if a refined analysis is required or the size of the solution domain is
large.
In view of the limitations of the classical optimization methods in slope stability
analysis, several stochastic global optimization methods were developed mainly from
pattern recognition, electronic production or control engineering. Also, the signal
processing system is under consideration by the author. Some of the new global opti-
mization methods such as that based on the genetic algorithm [11, 12] and the simu-
lated annealing method [13, 16] have been used successfully in many problems, but
the author has shown that these methods are less efficient when the number of control
variables is large. For the harmony search method, the author has found that the origi-
nal harmony search method can be trapped easily by the presence of local minima if
the number of control variables is large and the objective function is discontinuous
within the solution domain. Because of the limitation in the basic harmony search
method, two improved harmony search algorithms (NHS1 and NHS2) are proposed in
this chapter. NHS1 and NHS2 have been found to be effective and efficient for gen-
eral problems, and four relatively difficult examples were investigated to demonstrate
the effectiveness of the proposed method. To deal with the case of a narrow zone
where there is a rapid change in the design parameters, the author proposes the use of
a domain transformation method (equivalent to a weighted random number) which is
coupled with the present modified harmony search method, and this approach can be
useful in geotechnical as well as other types of problems.
2 Generation of Trial Failure Surfaces
In global optimization analysis for a slope stability problem, there are two major is-
sues to be considered: generation of failure surfaces and the determination of mini-
mum factor of safety. The slip surface generation method used in this chapter [15, 16]
is applicable to both concave and convex slip surface for slope stability problem. The
procedures for generating arbitrary slip surface is shown in Figure 1, where the
ground surface is represented by
y=y
g
(x)
, bedrock is represented by
y=R(x)
. The trial
slip surface in the figure is composed of
n
+1 vertices with coordinates of (
x
i
, y
i
), in
which
i
varies between 1 and
n
+1, thus there will be
n
vertical slices with slice angle
α
i
, in which
i
varies between 1 and
n
. The vertices
V
1
and
V
n+1
are the exit and en-
trance points of the slip surface respectively, and the lower and upper bounds for
these two vertices can be prescribed by the engineers easily. Usually, the x- and y-
ordinates of these vertices are taken as the variables. The x-coordinates of
V
2
to
V
n
can
be obtained by even spacing as given by Eq. 1 while the upper and lower bounds to
the y-ordinates
y
i,max
and
y
i,min
can be calculated by using Eq. 2.
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