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figure. Since the soil properties of layer 2 are extremely low but this layer is also ex-
tremely thin, the majority part of the critical failure surface should lie within this
zone. If the modified harmony search method is used without the domain transforma-
tion method as shown in Figure 7, a minimum safety factor of 1.486 is actually ob-
tained as shown in Figure 15. On the other hand, if the domain transformation method
is used, the minimum safety factor will be 1.037 which is shown in Figure 16. The
difference in the results is extremely significant and this problem must be carefully
considered. The present problem has a very thin domain where there is a sudden and
major change of soil properties. If there is no special treatment to this special zone, no
method can determine the minimum safety factor automatically.
8
7.5
7
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
0
1
2
3
4
5
6
7
8
9
10
11
12
Fig. 16. Failure surface with domain transformation method (factor of safety = 1.037)
6 Conclusions
The original harmony search algorithm has been found to be trapped by the local min-
ima for some large slope stability problem. The algorithm improvises only one new
harmony in each iteration and uses equal probability for choosing the harmonies
stored in HM. In views of the efficiency of the harmony search method and its limita-
tions, two modified harmony search algorithms are proposed by generating pairs of
harmonies and using different probabilities for different harmonies.
The modified harmony algorithms are found to be highly effective and efficient for
many difficult problems. From numerous internal tests, it appears that the modified
harmony methods are more effective and stable over a wide range of problems as
compared with the original harmony method, except when the problems under con-
sideration are simple with relatively few control variables.
Stochastic algorithms are approximate and not accurate algorithms. These algo-
rithms usually find a solution closest to the best one. However, they usually find it
fast and easily. Every stochastic algorithm relies on the use of some parameters for
analysis but there is no serious method in determining these kinds of parameters. It is
found that the two proposed algorithms are relatively insensitive to the use of these
parameters due to the special arrangement in generating pairs of harmonies. This
property is highly beneficial in slope stability problem.
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