Keywords: truss structures, weight minimization, meta-heuristic optimization, harmony search, gradient information.

Truss weight minimization problems are taken as benchmark tests in structural optimization because of the relatively simple analytical form of the structural weight cost function. Meta-heuristic optimization algorithms explore large fractions of design space in order to increase the probability of capturing the global optimum. An extensive review of these algorithms is given in [1].

The harmony search (HS) method is a recently developed optimization algorithm that mimics the musical process of searching for a perfect state of harmony [2,3]. The harmony in music is analogous to the optimum design vector, and musician's improvisations are analogous to local and global search schemes in optimization techniques. The harmony memory stores the feasible designs currently included in the population. Each new trial design is generated by selecting the components of different vectors randomly in the harmony memory. The harmony memory is updated by replacing the trial design corresponding to the worst solution with each new trial design that improved the current optimal solution.

This paper presents an improved HS formulation in order to reduce the number of structural analyses and the amount of heuristics entailed by the optimization. Each new trial design lies on a descent direction and is compared not only with the worst design stored in the harmony memory but with all designs heavier than the trial itself. Approximate line search serves to update the harmony memory in a much faster way than in the classical HS implementation. The new HS formulation is tested in three examples of weight minimization of truss structures with respectively 10, 18 and 25 elements. Test problems either include local minima or have two distinct design spaces, the sizing and the layout variables.

Optimization results are compared with classical HS implementations and other state-of-the-art meta-heuristic optimization codes recently published [4,5,6]. The present algorithm always found feasible designs consistent with the literature. However, it was possible to reduce the number of iterations required to converge to optimum designs.

1

M.P. Saka, "Optimum Design of Steel Frames using Stochastic Search Techniques Based on Natural Phenomena: A Review", in B.H.V. Topping, (Editor), "Civil Engineering Computations: Tools and Techniques", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 6, 105-147, 2007. doi:10.4203/csets.16.6

2

K.S. Lee, Z.W. Geem, "A new structural optimization method based on the harmony search algorithm", Computers and Structures, 82, 781-798, 2004. doi:10.1016/j.compstruc.2004.01.002

3

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. doi:10.1016/j.cma.2004.09.007

4

L. Lamberti, "An efficient simulated annealing algorithm for design optimization of truss structures", Computers and Structures, 86, 1936-1953, 2008. doi:10.1016/j.compstruc.2008.02.004

5

J.L. Li, Z.B. Huang, F. Liu, Q.H. Wu, "A heuristic particle swarm optimizer for optimization of pin connected structures", Computers and Structures, 85, 340-349, 2007. doi:10.1016/j.compstruc.2006.11.020

6

A. Kaveh, S. Talatahari, "Particle swarm optimizer, ant colony strategy and search scheme hybridized for optimization of truss structures", Computers and Structures, 87, 267-283, 2009. doi:10.1016/j.compstruc.2009.01.003

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