2245
A smart adaptive multivariable search algorithm applied to slope stability
in locating the global optima
Un algorithme adaptatif multivariable de recherche d’optimum global appliqué
à la stabilité des pentes
Saha A.
Irrigation & Waterways Department, Govt. of West Bengal, Kolkata, India
ABSTRACT: The paper addresses the topic of single objective optimisation of a three dimensional real-world problem and introduces
a hybrid technique of an iterative random population search within a geometrically shrinking hypercube and a sort of simplified
Design of Experiments (DOE). A ‘population’ of design variables are generated and augmented with the multivariable objective
function, and the design variables pertaining to the local optima are perturbed by a factor (
k) sequentially in both positive and
negative directions to create 2(2
N
-1) offspring in the neighbourhood of local optima to hopefully produce some better progeny. The
‘fittest’ perturbed offspring decides a new contracted search interval for the consecutive generation according to a geometric decay
rule commensurate with the generation number. A ‘simple hill-climbing’ strategy in Artificial Intelligence context is followed
subsequently and the loop is continued to produce fresh generations of refined offspring till the outcome converges to the global
optimum. The method is applied in searching the critical slip-surface of a vulnerable soil-slope and it was revealed that the optimum
found by this method is superior to that found by traditional and non-traditional (genetic algorithms) optimization techniques while
using much less computational resources.
RÉSUMÉ: L'article traite de l'optimisation à une seule fonction objectif pour un problème réel tridimensionnel et introduit une
technique hybride de recherche itérative à partir d’une population aléatoire au sein d’un hyper cube de taille décroissante, selon une
méthode simplifiée de plan d’expérience. Une "population" de variables de design est générée, et étendue grâce à la fonction objectif
multi variable. Les variables de design correspondant à l’optimum local sont alors perturbées par une facteur (
k) de manière
séquentielle dans les directions à la fois positives et négatives pour créer 2(2
N
-1) individus de génération suivante dans le voisinage de
cet optimum, dans l'espoir de produire une meilleure génération. La génération perturbée la plus satisfaisante selon l’objectif définit
un nouvel intervalle de recherche, de taille réduite pour la génération suivante, selon une règle de décroissance géométrique en rapport
avec le rang de génération. Une stratégie simple de plus grande pente dans un contexte d'intelligence artificielle est suivie pas à pas et
une boucle produit de nouvelles générations améliorées jusqu'à ce que le résultat converge vers l'optimum global, indépendant de la
population initiale. La méthode est appliquée à la recherche de la surface de glissement critique d'un sol en pente vulnérable. Il a été
constaté que l'optimum trouvé par cette méthode est plus critique que celui donné par les méthodes traditionnelles et non
traditionnelles (algorithmes génétiques) et de plus, cette méthode est moins exigeante en terme de capacité de calcul.
KEYWORDS: hybrid technique, random population search, optimization algorithm, slope stability.
1 INTRODUCTION
The stability of slopes has received wide attention due to its
practical importance in the design of excavations,
embankments, and dams. There are numerous methods
available for stability analysis and the majority of analyses
performed in practice still use traditional limit equilibrium
approaches. By the advent of computers, the use of optimization
techniques in locating the critical slip surface has been a major
topic for the researchers. Duncan (1996) presented a
comprehensive review of both limit equilibrium and finite-
element analysis of slopes. Malkawi et al (2001) developed an
effective approach for locating the critical circular slip surface
based on Monte-Carlo techniques. Non-traditional optimization
algorithms simulating processes drawn from nature like genetic
algorithm (GA) and simulated annealing (SA) have proved to be
efficient in locating the global optima. GA mimics the
principles of Darwin’s natural selection and survival of the
fittest rule, in which an optimum solution evolves through a
series of generations of population and has the super ability of
global convergence and parallel searching. SA is the stochastic
evolution of thermodynamic state of slow cooling of molten
metals to achieve a crystalline absolute minimum energy state,
where a perpetual decreasing sequence of temperature controls
the reproduction rate, which is very efficient in neighborhood
search. Li et al (2009), Author (2011) proposed hybrid global
search procedures combining GA with SA. While summarizing
the state of the art techniques for evolutionary algorithm (EA)
parameter tuning, T. Beielstein (2003) exclaims that “
real world
optimization problems allow only a few preliminary
experiments to find good EA settings. As the commonly used
‘one factor at a time approach’ is considered as inefficient and
ineffective, we recommend DOE methods
”. The present paper
introduces a new Soft Computing algorithm- a hybrid technique
of an iterative
random population based search embedded with
simulated annealing (SA) features within a geometrically
shrinking hypercube coupled with simplified Design of
Experiments (DOE)
.
2 APMA-A NOVEL OPTIMIZING TOOL
A smart adaptive population based multivariable function
optimization algorithm proposed herein, and referred to as
APMA hereinafter, is a simple yet robust optimization
procedure basically of heuristic nature. Before plunging into
details, a fitness function is defined to maintain uniformity over
various problem domains and to map the ‘goodness’ of the
objective function (here FOS) value to a fitness value. The
fitness of an individual is calculated as the worst objective
function objective function (FOS) value of the whole population
subtracted from the individual’s objective function value.
Hence, this fitness function is computed for the individual as
F
i
= max.{f(x)
i
|
j = 1, 2, …, n
}− f(x)
i
. Where; ‘n’ is the population
