Keywords: optimization, retaining wall, swarm intelligence, particle swarm optimization, cost optimization, optimal design.

This paper is concerned with the optimal design of reinforced concrete earth-retaining walls. In practice concrete structures are designed based on the experience of structural engineers. In many cases, the cross-sectional dimensions and material grades are first adopted by common practice. Once the structure is defined according to experience, the structure is analyzed, and the stress resultants are calculated. The design is then followed by selecting the reinforcement so as to satisfy the limit states imposed by concrete codes. This trial and error approach does not generally yield an optimum design [1].

In recent years, successful applications of the particle swarm optimization (PSO) in many optimization benchmark problems have been reported. Comparison studies demonstrated that PSO is an ideal candidate to be used in optimization tasks and has a number of advantages with respect to other algorithms. PSO is a robust algorithm and is more efficient, requiring fewer numbers of function evaluations, while leading to better or the same quality of results. In this paper PSO is proposed to optimize concrete retaining walls. PSO has already been applied in structural optimization of trusses and plane frames [2,3]. However, this algorithm has not yet used in optimal design of concrete structures.

The optimal wall design problem is obviously a constrained optimization problem. To deal with the constraints, different variants of static and dynamic penalties are used and their performances are compared. The formulation of the problem includes important design variables such as geometrical ones; and variables describing the reinforcement set-up.

The results indicate that PSO is efficient and optimal values for both cases show improvement in the weight and cost of the retaining wall. In the case of cost optimizations a decrease of 12% in concrete volume and 6% in reinforcement is observed. Corresponding values for the minimum cost case were 12% and 2% respectively. PSO has only a few adjustable parameters and the computation cost is low which makes the algorithm very attractive for structural optimization.

1

V. Yepes, J. Alcala, C. Perea, F. Gonzalez-Vidosa, "A Parametric Study of Optimum Earth-Retaining Walls by Simulated Annealing", Engineering Structures, 30, 821-830, 2008. doi:10.1016/j.engstruct.2007.05.023

2

R.E. Perez, K. Behdinan, "Particle Swarm Approach for Structural Design Optimization", Swarm Intelligence: Focus on Ant and Particle Swarm Optimization, 2007.

3

A. Kaveh, S. Talatahari, "A Hybrid Particle Swarm and Ant Colony Optimization for Design of Truss Structures", Asian Journal of Civil Engineering (Building and Housing), 9(4), 329-348, 2008.

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