Modified Harmony Methods for Slope Stability Problems - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 139

Optimization search for the non-circular failure surface (large number of control
variables) has been considered by various classical methods (mainly gradient type
method) by Baker and Gaber [2], Nguyen [3], Celestino and Duncan [4], Arai and
Tagyo [5], Baker [6], Yamagami and Jiang [7], Chen and Shao [8]. These classical
methods are all limited by the presence of local minimum as the local minimum close
to the initial trial will be obtained using these methods.
In view of the limitations of the classical optimization methods, the current ap-
proach is the adoption of the stochastic global optimization methods for the present
problem. These algorithms usually find a solution which is close to the best one with
good efficiency. Greco [9] and Malkawi et al. [10] adopted Monte Carlo technique for
searching the critical slip surface with success for some cases, but there is no preci-
sion control on the accuracy of the global minimum. Zolfaghari et al. [11] adopted the
genetic algorithm while Bolton et al. [12] used the leap-frog optimization technique to
evaluate the minimum factor of safety. The above methods are based on the use of
static bounds to the control variables where the solution domain for each control vari-
able is fixed and pre-determined by engineering experience. Cheng [13, 14] has de-
veloped a procedure, which transformed the various constraints and requirements of a
kinematically acceptable failure mechanism to the evaluation of the upper and lower
bounds of the control variables and employed a simulated annealing algorithm to
determine the critical slip surface. The control variables are defined with dynamic
domains where the bounds are controlled by the requirement of a kinematically
acceptable failure mechanism and are changing during the solution. Through such ap-
proach, there is no need to define the fixed solution domain for each control variable
by engineering experience. The approach by Cheng [13] is actually equivalent to the
enforcement of convex shape by limiting the upper and lower bounds of the control
variables sequentially, and this approach should be applicable to other disciplines
which require a convex shape (but not necessarily a convex function). On the other
hand, by removing some of the constraints of the lower bounds, the approach can also
be adopted to non-convex shapes.
Among the modern stochastic global optimization methods that have evolved in
recent years, there have been applications in geotechnical engineering using the ge-
netic algorithm, simulated annealing, tabu search, ant-colony optimization, particle
swarm optimization (PSO), leap-frog algorithm, and harmony search (HM) [11-16].
Cheng et al. [16] have carried out a detailed comparisons between six major types of
stochastic global optimization methods, and the sensitivity of these methods under
different optimization parameters have been investigated. Later, fish swarm algorithm
and a modified harmony search algorithm were also applied to the slope stability
problem [17, 18].
Some of the special problems for a robust and versatile optimization algorithm for
slope stability analysis which may not be present in common optimization problems
include:

(1) Discontinuity in some solution domain because the generated slip surface

may be kinematically inadmissible or no factor of safety can be determined
(no converged solution).

(2) Presence of many local minima which has been demonstrated by Chen and

Shao [8].