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Keywords: firefly algorithm, truss structures, geometry optimization, topology optimization, metaheuristics, mixed integer-continuous variables.

Summary

Methods for the optimization of truss topology, where the member areas are taken as design variables, are well established and there is a rich literature on this subject. However, the problem of truss geometry optimization, where the nodes positions are taken as design variables, was not studied as extensively as the topology one, and consequently references on this subject are not so vast.

In the design of real structures, some of the design variables are usually taken from discrete values because of manufacturing constraints. The problem becomes a mixed variable optimization problem, i.e. it deals simultaneously with integer and continuous design variables. Moreover, the simultaneous optimization of the size, shape and topology of trusses is known to be non-convex and multimodal [1,2].

Metaheuristic optimization algorithms are well-suited to solve this kind of optimization problem. Known advantages of the use of them include the following: (i) they do not require gradient information and can be applied to problems where the gradient is hard to obtain or simply does not exist; (ii) if correctly tuned, they do not get stuck in local minima; (iii) they can be applied to nonsmooth or discontinuous functions; and (iv) they furnish a set of optimal solutions instead of a single one, thus giving the designer a set of options.

In this study, a recently developed metaheuristic optimization algorithm, the firefly algorithm (FA) [3], is used for solving this mixed continuous-discrete truss size, shape and topology optimization problem. The FA mimics the social behaviour of fireflies based on their flashing characteristics. The flashing light can be formulated in such a way that it is associated with the objective function to be optimised.

The main contribution of this paper is the demonstration of the efficiency of the FA to solve the simultaneous size, shape and topology optimization of trusses. The effectiveness of the proposed approach was demonstrated through a benchmark problem and the results obtained were better than those reported in the literature, with lower computational cost, emphasising the capacity of the proposed methodology.

References

1: W. Achtziger, "On simultaneous optimization of truss geometry and topology", Structural and Multidisciplinary Optimization, 33, 285-305, 2007. doi:10.1007/s00158-006-0092-0
2: A.J. Torii, R.H. Lopez, F. Biondini, "An approach to reliability-based shape and topology optimization of truss structures", Engineering Optimization, 44, 37-53, 2012. doi:10.1080/0305215X.2011.558578
3: X.-S. Yang, "Firefly algorithms for multimodal optimization", in O. Watanabe, T. Zeugmann, (Editors), "Stochastic algorithms: foundations and applications", SAGA 2009, Lecture notes in computer science, 5792, 169-178, Springer-Verlag, Berlin, 2009. doi:10.1007/978-3-642-04944-6_14

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 99 PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping Paper 214 Firefly Metaheuristics for the Size, Shape and Topology Optimization of Truss Structures L.F. Fadel Miguel¹, R.H. Lopez¹, A. El-Hami² and L.F.F. Miguel³ ¹Civil Engineering Department, Federal University of Santa Catarina, Florianopolis, Brazil ²Mechanical Engineering Department, National Institute of Applied Sciences (INSA), Rouen, France ³Mechanical Engineering Department, Federal University of Rio Grande do Sul, Porto Alegre, Brazil doi:10.4203/ccp.99.214 purchase the full-text of this paper Full Bibliographic Reference for this paper L.F. Fadel Miguel, R.H. Lopez, A. El-Hami, L.F.F. Miguel, "Firefly Metaheuristics for the Size, Shape and Topology Optimization of Truss Structures", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 214, 2012. doi:10.4203/ccp.99.214 Keywords: firefly algorithm, truss structures, geometry optimization, topology optimization, metaheuristics, mixed integer-continuous variables. Summary Methods for the optimization of truss topology, where the member areas are taken as design variables, are well established and there is a rich literature on this subject. However, the problem of truss geometry optimization, where the nodes positions are taken as design variables, was not studied as extensively as the topology one, and consequently references on this subject are not so vast. In the design of real structures, some of the design variables are usually taken from discrete values because of manufacturing constraints. The problem becomes a mixed variable optimization problem, i.e. it deals simultaneously with integer and continuous design variables. Moreover, the simultaneous optimization of the size, shape and topology of trusses is known to be non-convex and multimodal [1,2]. Metaheuristic optimization algorithms are well-suited to solve this kind of optimization problem. Known advantages of the use of them include the following: (i) they do not require gradient information and can be applied to problems where the gradient is hard to obtain or simply does not exist; (ii) if correctly tuned, they do not get stuck in local minima; (iii) they can be applied to nonsmooth or discontinuous functions; and (iv) they furnish a set of optimal solutions instead of a single one, thus giving the designer a set of options. In this study, a recently developed metaheuristic optimization algorithm, the firefly algorithm (FA) [3], is used for solving this mixed continuous-discrete truss size, shape and topology optimization problem. The FA mimics the social behaviour of fireflies based on their flashing characteristics. The flashing light can be formulated in such a way that it is associated with the objective function to be optimised. The main contribution of this paper is the demonstration of the efficiency of the FA to solve the simultaneous size, shape and topology optimization of trusses. The effectiveness of the proposed approach was demonstrated through a benchmark problem and the results obtained were better than those reported in the literature, with lower computational cost, emphasising the capacity of the proposed methodology. References 1 W. Achtziger, "On simultaneous optimization of truss geometry and topology", Structural and Multidisciplinary Optimization, 33, 285-305, 2007. doi:10.1007/s00158-006-0092-0 2 A.J. Torii, R.H. Lopez, F. Biondini, "An approach to reliability-based shape and topology optimization of truss structures", Engineering Optimization, 44, 37-53, 2012. doi:10.1080/0305215X.2011.558578 3 X.-S. Yang, "Firefly algorithms for multimodal optimization", in O. Watanabe, T. Zeugmann, (Editors), "Stochastic algorithms: foundations and applications", SAGA 2009, Lecture notes in computer science, 5792, 169-178, Springer-Verlag, Berlin, 2009. doi:10.1007/978-3-642-04944-6_14 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £65 +P&P)
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