Keywords: structural optimization, metaheuristics, genetic algorithms, particle swarm optimization, ant colony optimization.

In recent years a number of metaheuristic search techniques [1] have been widely used in developing structural optimization algorithms. This paper attempts to provide a bird's-eye literature survey of the developments and applications of the most popular metaheuristic methods for structural optimization problems. Three metaheuristics are considered: genetic algorithms (GAs), particle swarm optimization (PSO) and ant colony optimization (ACO). In the first section, the origin of the name metaheuristic is explained and some techniques belonging to this class are cited.

In the first part of the second section, the basic principles of genetic algorithms (GAs) [2] are presented and seven papers concerning optimization (sizing, geometry and topology) of benchmarks of planar and space trusses are reviewed. The second part of this section is dedicated to the applications of the GAs to the topology optimization; three papers are presented.

In the section three, the particle swarm optimization (PSO) algorithm [3] is described. This algorithm belongs to a class of algorithms referred to as swarm intelligence which are inspired by the collective behaviour of species such as ants, birds, fishes, bees and termites. Swarm intelligence originated from the social behaviour of those species that compete for foods. In the PSO algorithm, only three parameters should be chosen. They are problem dependent and some recommendations on how to choose them are discussed in [4]. The PSO has not been used in the field of structural optimization until very recently. The first application of the PSO to size and shape structural optimization [5] was presented in 2002. Another eight papers concerning the various applications of PSO to sizing, shape and topology structural optimization are reviewed. An interesting paper [6] proposing a hybrid PSO-SQP algorithm has been published recently in 2011.

Section four concentrates on the ant colony optimization (ACO) and their applications to structural optimization. The main idea in ant colony optimization (ACO) is to imitate the cooperative behaviour of real ants to solve optimization problems. The ACO metaheuristics have been developed in [7,8]. They are inspired by the behaviour of colonies of ants when they try to find food. The eight papers on the applications of the ACO techniques to sizing, shape and topology optimization are reviewed.

The last section gives some critical points about the applications of the metaheuristic techniques to structural optimization. The literature concerning the application of metaheuristics to structural optimization is vast. Here, only a limited number of papers are reviewed. It should be mentioned that a number of papers are seriously questioning the validity of metaheuristic methods [9]. The hybridization strategies combining the metaheuristics with gradient-based methods (not reported in this paper) could essentially improve the domain of structural optimization.

[1]

E.-G. Talbi, "Metaheuristics: From Design to Implementation", Wiley, 2009.

[2]

J. Holland, "Adaptation in natural and artificial Systems", University of Michigan Press, Ann Arbor, Michigan, 1975.

[3]

J. Kennedy, R.C. Eberhart, "Particle swarm optimization", Proceedings of the IEEE International Conference on Neural Networks, 4, 1942-1948, 1995.

[4]

I.C. Trelea, "The particle swarm optimization algorithm: convergence analysis and parameter selection", Information Processing Letters, 85, 317-325, 2003.

[5]

P. Fourie, A. Groenwold, "The particle swarm optimization algorithm in size and shape optimization", Structural and Multidisciplinary Optimization, 23, 259-267, 2002.

[6]

V. Plevris, M. Papadrakakis, "A hybrid particle swarm-gradient algorithm for global structural optimization", Computer-Aided Civil and Infrastructure Engineering, 26, 48-68, 2011.

[7]

M. Dorigo, "Optimization, learning and natural algorithms", PhD Thesis, Politecnico di Milano, Italy, 1992.

[8]

M. Dorigo, C. Blum, "Ant Colony Optimization: A survey", Theoretical Computer Science, 344, 243-278, 2005.

[9]

O. Sigmund, "On the usefulness of non-gradient approaches in topology optimization", Struct. Multidisc. Optim., 43, 589-596, 2011.

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