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ISGSR 2011 - Vogt, Schuppener, Straub & Bräu (eds) - © 2011 Bundesanstalt für Wasserbau ISBN 978-3-939230-01-4

Optimization of Reinforced Concrete Retaining Walls Using Ant Colony Method
M. Ghazavi
Faculty of Civil Engineering, K. N. T. University of Technology, Tehran, Iran

S. Bazzazian Bonab

Department of Geotechnical Engineering, Islamic Azad University, Arak, Iran

ABSTRACT:Optimization of concrete retaining walls is an important task in geotechnical and structural engineering. Classical optimization search methods are rudimentarily based on direct search methods. Direct search methods belong to a class of optimization methods that do not compute derivatives. However, these algorithms suffer from both trapping in local minima and increasing run time. In order to reducethe possibility of suffering from this problem, the heuristic approaches are more favored among the scientists. This paper applies a methodology to arrive at optimal design of concrete retaining wall using ant colony optimization (ACO) algorithm that is a general search technique for the solution of difficult combinatorial problems with its theoretical roots based on the foraging behavior of ants.The algorithm is used to find the minimum weight and cost for concrete retaining walls. Coulomb lateral earth pressure theory is used to derive the lateral total thrust on the wall. The results are compared with other available optimization scheme applied by other researchers. The results clearly indicate that ACO yields the solutions for all benchmarks due to its capability to explore and exploitthe solution space effectively. As a result, it can be used for optimizing the reinforced concrete retaining walls. Keywords: Ant Colony, Education, Optimization, Concrete Retaining Wall, Swarm Intelligent.

1 INTRODUCTION Concrete retaining walls are most widely used structures in civil engineering practice. Such walls are commonly used to support earth, coal, ore piles, and water.Optimization of retaining walls is necessary due to economical consideration. Current optimization structural softwares for retaining wall design often lack the ability to find out optimal design because of their deterministic nature, while those employing stochastic methods are not tailored specifically for retaining walls and massive concrete structures. Classic optimization search methods arerudimentarily based on direct search methods. Direct search methods belong to a class of optimization methods that do not compute derivatives. Examples of direct search method are the Nelder Mead Simplex method, Hooke and Jeeves’s pattern search, the box method, and Dennis and Torczon’s parallel direct search algorithm employing a multi-sided simplex. However, these algorithms suffer from both trapping inlocal minima and increasing running time. In this paper, a methodology is presented to arrive at optimal design of concrete retaining wall using Ant Colony Optimization (ACO) algorithm that is a general search technique for the solution of difficult combinatorial problems with its theoretical roots based on the foraging behavior of ants. ACO is based on the indirect communication of a colony ofsimple agents, called artificial ants, mediated by artificial pheromone trails. The pheromone trails in ACO serve as distributed numerical information, which the ants use to probabilistically construct solutions to the problem being solved. Optimum design of retaining walls has been the subject of a number of studies. Saribas and Erbatur presented a detailed study on optimum design of reinforcedconcrete cantilever retaining walls using cost and weight of walls as objective functions. In their study, they controlled overturning failure, sliding failure, shear and moment capacities of toe slab, heel slab, and stem of wall as constraints [1]. Ceranic and Fryer proposed an optimization algorithm based on Simulated Annealing, which can compute the mini297

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