24-08-2016, 11:47 AM
This paper presents an effective optimization method for nonlinear constrained optimization of retaining structures. A
newly developed heuristic global optimization algorithm called gravitational search algorithm (GSA) is introduced and
applied for the optimization of retaining structures. The optimization procedure controls all geotechnical and structural
design constraints while reducing the overall cost of the retaining wall. To verify the efficiency of the proposed method,
two design examples of retaining structures are illustrated. To further validate the effectiveness and robustness of the
GSA, these examples are solved using two other heuristic algorithms namely particle swarm optimization and genetic
algorithm. The comparison between the results of the new method and selected other algorithms indicate that, the
proposed method could provide solutions of high quality, accuracy and efficiency and outperforms other methods for
optimum design of retaining structure.
Introduction
Earth retaining structures constitute an integral part of
the infrastructure and reinforced concrete retaining walls
as earth structures are frequently constructed for a variety
of applications, most commonly for bridge abutments,
road, transportation systems, lifelines and other
constructed facilities. Retaining structures design should
address at least three basic requirements: geotechnical
requirements, structural requirements and economic.
Traditional methods for design of retaining structures are
based on trial and error approach, in which a trial design
is proposed and is checked against the geotechnical and
structural requirements, which is followed by revision of
the trial design, if necessary. Moreover, there is no
guarantee that final design is economical. In the case of
retaining structure optimization, all requirements are
considered simultaneously and there is a guarantee that
the final design is optimized economically. During the
past decades, limited studies have been undertaken to
develop methodologies for the optimization of retaining
structures (Saribas & Erbatur, 1996; Ceranic et al., 2001;
Sivakumar Babu & Munwar Basha, 2008; Khajehzadeh et
al., 2011). Therefore, such an effort has been made here.
Optimization problems may be addressed using either
deterministic or heuristic methods. For deterministic
algorithms, the objective function must be differentiable or
continuous, or the reasonable region must be convex.
Conversely, the heuristic methods not require the
differentiability and continuity of objective functions. Be
different with other heuristic optimization algorithm based
on swarm behaviors, such as genetic algorithm (GA) and
particle swarm optimization (PSO), gravitational search
algorithm (GSA) is a newly developed heuristic
optimization method based on the law of gravity and
mass interactions (Rashedi et al., 2009). GSA is
characterized as a simple concept that is both easy to
implement and computationally efficient. The method has
been confirmed higher performance in solving various
nonlinear functions, compared with some well-know
search methods (Rashedi et al., 2009).
In this study, the gravitational search algorithm is
proposed to determine the optimum design of reinforced
concrete retaining structures. The objective function
considered is taken as the cost of the structure, and
design is based on ACI 318-05. This function is
minimized subjected to design constraints. A computer
program called retaining structure optimization using
gravitational search algorithm (RSO-GSA) was developed
by MATLAB. A numerical example is presented in order
to illustrate the performance of the present algorithm.
Gravitational search algorithm
Gravitational search algorithm (GSA) is a newly
developed stochastic search algorithm based on the law
of gravity and mass interactions (Rashedi et al., 2009). In
this approach, the search agents are a collection of
masses which interact with each other based on the
Newtonian gravity and the laws of motion, in which the
method is completely different from other well-known
population-based optimization method inspired by the
swarm behaviors. In GSA, agents are considered as
objects and their performance are measured by their
masses. All of the objects attract each other by the gravity
force, while this force causes a global movement of all
objects towards the objects with heavier masses
(Rashedi et al., 2009). The heavy masses correspond to
good solutions of the problem. In other words, each mass
presents a solution, and the algorithm is navigated by
properly adjusting the gravitational and inertia masses.
By lapse of time, the masses will be attracted by the
heaviest mass which it presents an optimum solution in
the search space.