Discrete Optimum Design for Truss Structures by Subset Simulation Algorithm
Publication: Journal of Aerospace Engineering
Volume 28, Issue 4
Abstract
This article deals with the design optimization of truss structures with discrete design variables, which remains quite a challenging task in structural design. A new discrete search strategy based on the recently developed subset simulation optimization algorithm is proposed in detail for this type of structural optimization. The discrete design variables are transformed into standard normal variable space to implement the sampling procedure in subset simulation optimization, while the optimization is processed in the discrete design space in the mean time. The performance of the proposed method is illustrated by four representative benchmark optimization problems. Comparisons are made with other well known stochastic optimization algorithms. It is found that the proposed method can produce optimum designs as good as or better than those of other stochastic optimization algorithms.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors are grateful for the support of the Natural Science Foundation of China (Grant No. 11102084) and the Fundamental Research Funds for the Central Universities (Grant No. 3082012NS2012078).
References
Adeli, H., and Kumar, S. (1995). “Distributed genetic algorithm for structural optimization.” J. Aerosp. Eng., 156–163.
Au, S. K. (2005). “Reliability-based design sensitivity by efficient simulation.” Comput. Struct., 83(14), 1048–1061.
Au, S. K., and Beck, J. L. (2001). “Estimation of small failure probabilities in high dimensions by subset simulation.” Probab. Eng. Mech., 16(4), 263–277.
Au, S. K., Ching, J., and Beck, J. L. (2007). “Application of subset simulation methods to reliability benchmark problems.” Struct. Saf., 29(3), 183–193.
Bennage, W. A., and Dhingra, A. K. (1995). “Single and multiobjective structural optimization in discrete-continuous variables using simulated annealing.” Int. J. Numer. Methods Eng., 38(16), 2753–2773.
Camp, C. V., and Bichon, B. J. (2004). “Design of space trusses using ant colony optimization.” J. Struct. Eng., 741–751.
Coello, C. A. C. (2002). “Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: A survey of the state of the art.” Comput. Methods Appl. Mech. Eng., 191(11–12), 1245–1287.
Deb, K. (2000). “An efficient constraint handling method for genetic algorithms.” Comput. Methods Appl. Mech. Eng., 186(2–4), 311–338.
Degertekin, S. O., and Hayalioglu, M. S. (2013). “Sizing truss structures using teaching-learning-based optimization.” Comput. Struct., 119, 177–188.
Dong, Y., Tang, J., Xu, B., and Wang, D. (2005). “An application of swarm optimization to nonlinear programming.” Comput. Math. Appl., 49(11–12), 1655–1668.
Haftka, R., and Gurdal, Z. (1992). Elements of structural optimization, Kluwer Academic Publishers, Dordrecht, Netherlands.
Kameshki, E. S., and Saka, M. P. (2007). “Optimum geometry design of nonlinear braced domes using genetic algorithm.” Comput. Struct., 85(1–2), 71–79.
Kaveh, A., Farahmand Azar, B., Talatahari, S. (2008). “Ant colony optimization for design of space trusses.” Int. J. Space Struct., 23(3), 167–181.
Kaveh, A., and Shojaee, S. (2007). “ Optimal design of skeletal structures using ant colony optimisation.” Int. J. Numer. Methods Eng., 70(5), 563–581.
Kaveh, A., and Talatahari, S. (2009). “A particle swarm ant colony optimization for truss structures with discrete variables.” J. Constr. Steel Res., 65(8–9), 1558–1568.
Kaveh, A., and Talatahari, S. (2010). “Optimal design of skeletal structures via the charged system search algorithm.” Struct. Multidisc. Optim., 41(6), 893–911.
Lamberti, L. (2008). “An efficient simulated annealing algorithm for design optimization of truss structures.” Comput. Struct., 86(19–20), 1936–1953.
Lamberti, L., and Pappalettere, C. (2011). “Metaheuristic design optimization of skeletal structures: A review.” Comput. Technol. Rev., 4, 1–32.
Lee, K. S., and Geem, Z. W. (2004). “A new structural optimization method based on the harmony search algorithm.” Comput. Struct., 82(9–10), 781–798.
Lee, K. S., Geem, Z. W., Lee, S. H., and Bae, K. W. (2005). “The harmony search heuristic algorithm for discrete structural optimization.” Eng. Optim., 37(7), 663–684.
Leite, J. P. B., and Topping, B. H. V. (1999). “Parallel simulated annealing for structural optimization.” Comput. Struct., 73(1–5), 545–564.
Li, H. S. (2011). “Subset simulation for unconstrained global optimization.” Appl. Math. Model, 35(10), 5108–5120.
Li, H. S., and Au, S. K. (2010). “Design optimization using Subset Simulation algorithm.” Struct. Saf., 32(6), 384–392.
Li, L. J., Huang, Z. B., and Liu, F. (2009). “A heuristic particle swarm optimization method for truss structures with discrete variables.” Comput. Struct., 87(7–8), 435–443.
Li, L. J., Huang, Z. B., Liu, F., and Wu, Q. H. (2007). “A heuristic particle swarm optimizer for optimization of pin connected structures.” Comput. Struct., 85(7–8), 340–349.
Luh, G. C., and Lin, C. Y. (2011). “Optimal design of truss-structures using particle swarm optimization.” Comput. Struct., 89(23–24), 2221–2232.
Perez, R. E., and Behdinan, K. (2007). “Particle swarm approach for structural design optimization.” Comput. Struct., 85(19–20), 1579–1588.
Rajeev, S., and Krishnamoorthy, C. S. (1992). “Discrete optimization of structures using genetic algorithms.” J. Struct. Eng., 1233–1250.
Robert, C. P., and Casella, G. (2004). Monte Carlo statistical methods, Springer, New York.
Saka, M. (2007). “Optimum geometry design of geodesic domes using harmony search algorithm.” Adv. Struct. Eng., 10(6), 595–606.
Saka, M. P. (2003). “Optimum design of pitched roof steel frames with haunched rafters by genetic algorithm.” Comput. Struct., 81(18–19), 1967–1978.
Schueller, G. I. (2009). “Efficient Monte Carlo simulation procedures in structural uncertainty and reliability analysis—Recent advances.” Struct. Eng. Mech., 32(1), 1–20.
Sonmez, M. (2011). “Discrete optimum design of truss structures using artificial bee colony algorithm.” Struct. Multidiscip. Optim., 43(1), 85–97.
Togan, V. (2013). “Design of pin jointed structures using teaching-learning based optimization.” Struct. Eng. Mech., 47(2), 209–225.
Wu, S. J., and Chow, P. T. (1995). “Steady-state genetic algorithms for discrete optimization of trusses.” Comput. Struct., 56(6), 979–991.
Yuan, X., Lu, Z. Z., and Qiao, H. W. (2010). “Conditional probability Markov chain simulation based reliability analysis method for nonnormal variables.” Sci. China Technol. Sci., 53(5), 1434–1441.
Information & Authors
Information
Published In
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Aug 15, 2013
Accepted: Feb 5, 2014
Published online: Feb 7, 2014
Discussion open until: Dec 24, 2014
Published in print: Jul 1, 2015
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.