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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 99
Edited by: B.H.V. Topping
Paper 67

Particle Swarm Optimization for Non-Convex Problems of Size and Shape Optimization of Trusses

Y.J. Xu1, M. Domaszewski2,3, D. Chamoret2, W.H. Zhang1 and J.G. Korvink3,4

1The Key Laboratory of Contemporary Design and Manufacturing Technology, Northwestern Polytechnical University, Xi'an Shaanxi, China
2M3M Laboratory, University of Technology of Belfort-Montbéliard, Belfort, France
3Department of Microsystems Engineering (IMTEK), 4Freiburg Institute for Advanced Studies (FRIAS),
University of Freiburg, Germany

Full Bibliographic Reference for this paper
Y.J. Xu, M. Domaszewski, D. Chamoret, W.H. Zhang, J.G. Korvink, "Particle Swarm Optimization for Non-Convex Problems of Size and Shape Optimization of Trusses", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 67, 2012. doi:10.4203/ccp.99.67
Keywords: particle swarm optimization, truss structural optimization, constraint handling, size and shape optimization.

Recently, a variety of metaheuristic optimization methods inspired by biology, evolution theory, social sciences, music have been developed in purpose to rationalizing the search process. These methods constitute an alternative approach with respect to the gradient based techniques to solve the difficult optimization problems. A survey of metaheuristic techniques in structural optimization has been presented in [1].

This paper presents the simultaneous size and shape optimization of truss structures using modified particle swarm optimization (PSO) algorithm. In the considered optimization problems, structural weight is minimized subject to the constraints on nodal displacements and stresses in the bars. The optimization variables are the nodal coordinates and the cross-sectional areas. The lower and upper bounds are imposed on these two types of design variables. The constraints are strongly nonlinear and can result in non-convex optimization problems. The classical PSO algorithm [2] is modified to satisfy that all the particles fly inside the variable boundaries. A method derived from the harmony search algorithm [3] is used to deal with the particles which fly outside the variables boundaries. The multi-stage penalty function method is adopted within PSO to satisfy the constraints of the optimization problem and obtain the feasible optimal solutions.

Three numerical examples are presented: 1) simultaneous size and shape optimization of 15-bar planar truss, 2) simultaneous size and shape optimization of 18-bar planar truss, 3) simple and simultaneous size and shape optimization of 25-bar space truss. The obtained results are compared with the known results from the literature.

M. Domaszewski, D. Strohmeier, J.G. Korvink, "A Survey of Metaheuristic Techniques in Structural Optimization", in Y. Tsompanakis, B.H.V. Topping, (Editor), "Soft Computing Methods for Civil and Structural Engineering", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 3, 41-58, 2011. doi:10.4203/csets.29.3
J. Kennedy, R.C. Eberhart, "Particle swarm optimization", Proceedings of the IEEE international conference on neural networks, 4, 1942-1948, 1995. doi:10.1109/ICNN.1995.488968
K. Lee, Z. 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

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