Keywords: skeletal structures, design optimization, meta-heuristic algorithms.

Design optimization of skeletal structures is an important field of engineering under continuous development. In sizing optimization problems, structures must be designed with respect to the size of members (i.e. cross-sectional area values, length and thickness of cross-section segments, etc.). In layout optimization problems, spatial coordinates of nodes are included as design variables. In topology optimization problems, the number of elements can change in the optimization process based on the local distribution of stiffness/compliance required by structures.

Random generation of trial designs in principle allows exploration of a larger fraction of the search space than in the case of gradient-based optimization. However, purely random search may entail a large number of structural analyses yielding marginal improvement in weight or even violation of optimization constraints. In order to rationalize the search process and approach the region hosting the global optimum by performing only a limited number of structural analyses, a variety of meta-heuristic optimization methods inspired by biology, evolution theory, social sciences, music, physics and astronomy were developed [1-3]: for example, genetic algorithms (GA), simulated annealing (SA), particle swarm optimization (PSO), ant colony optimization (ACO), harmony search (HS), big bang-big crunch (BB-BC), hunting search (HuS), firefly algorithm (FA), charged system search (CSS), etc. Basically, meta-heuristic optimization algorithms generate new trial designs by following a random strategy which is however “guided” by the inspiring criterion. Therefore, the optimization search is termed “meta-heuristic” to differentiate this class of algorithms from the fully heuristic optimization search.

GA [4] and SA [5,6] were the first meta-heuristic optimization methods to be applied in structural design problems and are still widely utilized. The second generation of meta-heuristic algorithms includes PSO [7-9], ACO [10], HS [11,12] and BB-BC [13]. In addition, HuS [14], FA [15] and CSS [16] are the meta-heuristic algorithms most recently applied to design optimization of skeletal structures.

This paper reviews the meta-heuristic algorithms that are currently most used in weight optimization problems of skeletal structures. Alternative formulations recently developed in literature to improve convergence behaviour of meta-heuristic algorithms in design optimization of skeletal structures are presented. The suitability of each optimization algorithm for problems including discrete variables as well as its ability to find the global optimum for large-scale problems also is discussed.

[1]

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O. Hasancebi, S. Carbas, E. Dogan, F. Erdal, M.P. Saka, "Performance evaluation of metaheuristic search techniques in the optimum design of real size pin jointed structures", Computers and Structures, 87, 284-302, 2009.

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O. Hasancebi, S. Carbas, E. Dogan, F. Erdal, M.P. Saka, "Comparison of non-deterministic search techniques in the optimum design of real size steel frames", Comput. Struct., 88, 1033-1048, 2010.

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P.J.M. Van Laarhoven, E.H.L. Aarts, "Simulated Annealing: Theory and Applications", Kluwer Academic Publishers, Dordrecht, The Netherlands, 1987.

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A.P. Engelbrecht, "Fundamentals of Computational Swarm Intelligence", John Wiley & Sons, Chichester, UK, 2005.

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M. Clerc, "Particle Swarm Optimization", ISTE Publishing Comp., London, UK, 2006.

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M. Dorigo, T. Stutzle, "Ant Colony Optimization", MIT Press, Cambridge (MA), USA, 2004.

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K.S. Lee, Z.W. Geem, "A new structural optimization method based on the harmony search algorithm", Computers and Structures, 82, 781-798, 2004.

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K.S. Lee, Z.W. Geem, "A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice", Computer Methods in Applied Mechanics and Engineering, 194, 3902-3933, 2005.

[13]

O.K. Erol, I. Eksin, "New optimization method: Big Bang–Big Crunch", Advances in Engineering Software, 37, 106-111, 2006.

[14]

R. Oftadeh, M.J. Mahjoob, M. Shariatpanahi, "A novel meta-heuristic optimization algorithm inspired by group hunting of animals: Hunting Search", Computers and Mathematics with Applications, 60, 2087-2098, 2010.

[15]

X.S. Yang, "Firefly algorithm, Levy flights and global optimization", in M. Bramer et al., (Editors), "Research and Development in Intelligent Systems", XXVI, 209-218, 2010.

[16]

A. Kaveh, S. Talatahari, "Optimal design of skeletal structures via the charged system search algorithm", Structural and Multidisciplinary Optimization, 41, 893-911, 2010.

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