Modified Harmony Methods for Slope Stability Problems - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 143

F

A

E

D '

C

B

D

Fig. 3. Correction procedures

above process, the optimization problem associated with the location of the critical
slip surface for the present formulation is outline as Eq. 7.

()

min f V

. . t xxx ≤≤ x x x ≤ ≤ − << 0.5 ζ 0.5 i = 2, ..., n

l 1 u L n + 1 U i

(7)

βββ << ⇐ ⇒ 0 << χ 1 i = 3, ..., n

2 i n + 1 i

y ≤≤ y y ⇐ ⇒ 0 << χ 1

2min 2 2max 2

It must be noticed that the trial slip surface of n +1 vertices is generated by using m
= 2 n variables.

3 Modified Harmony Search for Slope Stability Analysis

Harmony search algorithm was developed by Geem et al. [19, 20], which was concep-
tualized based on the musical process of searching for a perfect state of harmony. Mu-
sical performances seek to find pleasing harmony (a perfect state) as determined by an
aesthetic standard, just as the optimization process seeks to find a global solution as
determined by an objective function. The harmony in music is analogous to the opti-
mization solution vector, and the musician's improvisations are analogous to local
and global search schemes in optimization techniques. The HS algorithm does not re-
quire initial values for the decision variables. Furthermore, instead of a gradient
search, the HS algorithm uses a stochastic random search that is based on the har-
mony memory considering rate HMCR and the pitch adjusting rate PAR so that de-
rivative of the objective function is unnecessary during the analysis.
Harmony search algorithm (HS) is a population based search method. A harmony
memory HM of size M (usually equals 2 m ) is used to generate a new harmony which
is probably better than the optimum in the current harmony memory. The harmony
memory consists of M harmonies (slip surfaces) and the M harmonies are usually
generated randomly. Consider