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Mathematical Problems in Engineering
Volume 2017, Article ID 1457297, 12 pages
https://doi.org/10.1155/2017/1457297
Research Article

Size and Topology Optimization for Trusses with Discrete Design Variables by Improved Firefly Algorithm

1Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China
2Faculty of Architecture and Built Environment, Delft University of Technology, Julianalaan 134, 2628 BL Delft, Netherlands
3Hangzhou Xiaoshan Urban Planning Institute, Hangzhou 311200, China
4Hangzhou Xiaoshan District Housing & Construction Bureau, Hangzhou 311200, China

Correspondence should be addressed to Qingpeng Li; moc.liamg@pqlcrsstih

Received 2 January 2017; Revised 14 March 2017; Accepted 23 April 2017; Published 4 June 2017

Academic Editor: Nantiwat Pholdee

Copyright © 2017 Yue Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. Rozvany and N. Olhoff, Topology Optimization of Structures and Composite Continua, vol. 7, Springer Science and Business Media, 2001.
  2. A. G. M. Michell, “The limits of economy of material in frame structures,” Philosophical Magazine Ser, vol. 8, pp. 589–597, 1904. View at Google Scholar
  3. J. C. Maxwell, “On reciprocal figures, frames and diagrams of forces,” Edinb Roy Soc Proc, vol. 7, pp. 160–208, 1970. View at Google Scholar
  4. W. S. Dorn, “Automatic design of optimal structures,” Journal de Mecanique, vol. 3, 1964. View at Google Scholar
  5. M. W. Dobbs and L. P. Felton, “Optimization of truss geometry,” ASCE Journal of Structural Division, vol. 95, pp. 2105–2118, 1969. View at Google Scholar
  6. U. Kirsch and B. H. V. Topping, “Minimum weight design of structural topologies,” Journal of Structural Engineering, vol. 118, no. 7, pp. 1770–1785, 1992. View at Publisher · View at Google Scholar · View at Scopus
  7. S. L. Lipson and L. B. Gwin, “Discrete sizing of trusses for optimal geometry,” Journal of the Structural Division, vol. 103, no. 5, pp. 1031–1046, 1977. View at Google Scholar · View at Scopus
  8. H. C. Sun, S. Chai, Y. Wang, and L. S. Shi, Discrete Optimum Design of Structures, Dalian University of Technology, 1995.
  9. B. Jarraya and A. Bouri, “Metaheuristic optimization backgrounds: a literature review,” International Journal of Contemporary Business Studies, vol. 3, p. 12, 2012. View at Google Scholar
  10. S. Y. Wang and K. Tai, “Structural topology design optimization using genetic algorithms with a bit-array representation,” Computer Methods in Applied Mechanics and Engineering, vol. 194, no. 36–38, pp. 3749–3770, 2005. View at Publisher · View at Google Scholar · View at Scopus
  11. H. Zhou, “Topology optimization of compliant mechanisms using hybrid discretization model,” Journal of Mechanical Design, vol. 132, no. 11, Article ID 111003, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. R. Balamurugan, C. V. Ramakrishnan, and N. Singh, “Performance evaluation of a two stage adaptive genetic algorithm (TSAGA) in structural topology optimization,” Applied Soft Computing Journal, vol. 8, no. 4, pp. 1607–1624, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. R. Balamurugan, C. V. Ramakrishnan, and N. Swaminathan, “A two phase approach based on skeleton convergence and geometric variables for topology optimization using genetic algorithm,” Structural and Multidisciplinary Optimization, vol. 43, no. 3, pp. 381–404, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. C. Jain and A. Saxena, “An improved material-mask overlay strategy for topology optimization of structures and compliant mechanisms,” Journal of Mechanical Design, vol. 132, no. 6, pp. 0610061–06100610, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. J. F. A. Madeira, H. L. Pina, and H. C. Rodrigues, “GA topology optimization using random keys for tree encoding of structures,” Structural and Multidisciplinary Optimization, vol. 40, no. 1-6, pp. 227–240, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. G.-C. Luh and C.-H. Chueh, “Multi-modal topological optimization of structure using immune algorithm,” Computer Methods in Applied Mechanics and Engineering, vol. 193, no. 36-38, pp. 4035–4055, 2004. View at Publisher · View at Google Scholar · View at Scopus
  17. W. A. Bennage and A. K. Dhingra, “Optimization of truss topology using tabu search,” International Journal for Numerical Methods in Engineering, vol. 38, no. 23, pp. 4035–4052, 2005. View at Publisher · View at Google Scholar · View at Scopus
  18. A. Kaveh, B. Hassani, S. Shojaee, and S. M. Tavakkoli, “Structural topology optimization using ant colony methodology,” Engineering Structures, vol. 30, no. 9, pp. 2559–2565, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. G.-C. Luh and C.-Y. Lin, “Structural topology optimization using ant colony optimization algorithm,” Applied Soft Computing Journal, vol. 9, no. 4, pp. 1343–1353, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. G.-C. Luh, C.-Y. Lin, and Y.-S. Lin, “A binary particle swarm optimization for continuum structural topology optimization,” Applied Soft Computing Journal, vol. 11, no. 2, pp. 2833–2844, 2011. View at Publisher · View at Google Scholar · View at Scopus
  21. P. Y. Shim and S. Manoochehri, “Generating optimal configurations in structural design using simulated annealing,” International Journal for Numerical Methods in Engineering, vol. 40, no. 6, pp. 1053–1069, 1997. View at Publisher · View at Google Scholar · View at Scopus
  22. K. S. Lee and Z. W. Geem, “A new structural optimization method based on the harmony search algorithm,” Computers and Structures, vol. 82, no. 9-10, pp. 781–798, 2004. View at Publisher · View at Google Scholar · View at Scopus
  23. C. Wu and K. Tseng, “Topology optimization of structures using modified binary differential evolution,” Structural and Multidisciplinary Optimization, vol. 42, no. 6, pp. 939–953, 2010. View at Publisher · View at Google Scholar · View at Scopus
  24. O. Sigmund, “On the usefulness of non-gradient approaches in topology optimization,” Structural and Multidisciplinary Optimization, vol. 43, no. 5, pp. 589–596, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. X. S. Yang, “Firefly algorithms for multimodal optimization,” in Lecture Notes in Computer Science, pp. 169–178, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  26. I. Fister, I. Fister Jr., X.-S. Yang, and J. Brest, “A comprehensive review of firefly algorithms,” Swarm and Evolutionary Computation, vol. 13, no. 1, pp. 34–46, 2013. View at Publisher · View at Google Scholar · View at Scopus
  27. L. F. F. Miguel, R. H. Lopez, and L. F. F. Miguel, “Multimodal size, shape, and topology optimisation of truss structures using the firefly algorithm,” Advances in Engineering Software, vol. 56, no. 2, pp. 23–37, 2013. View at Publisher · View at Google Scholar · View at Scopus
  28. S. Chai, L. S. Shi, and H. C. Sun, “Topology optimization of truss structures with discrete variables including two kinds of variables,” Acta Mechanica Sinica, vol. 31, pp. 574–584, 1999 (Chinese). View at Google Scholar
  29. H. L. Luo, Research on genetic-tabu algorithms for topology optimization of structures with discrete variables Beijing, Beijing University of Technology, 2006, (Chinese).
  30. D. Datta and J. R. Figueira, “A real-integer-discrete-coded particle swarm optimization for design problems,” Applied Soft Computing Journal, vol. 11, no. 4, pp. 3625–3633, 2011. View at Publisher · View at Google Scholar · View at Scopus
  31. D. Datta and J. R. Figueira, “A real-integer-discrete-coded differential evolution,” Applied Soft Computing Journal, vol. 13, no. 9, pp. 3884–3893, 2013. View at Publisher · View at Google Scholar · View at Scopus
  32. V. Ho-Huu, T. Nguyen-Thoi, M. H. Nguyen-Thoi, and L. Le-Anh, “An improved constrained differential evolution using discrete variables (D-ICDE) for layout optimization of truss structures,” Expert Systems with Applications, vol. 42, no. 20, pp. 7057–7069, 2015. View at Publisher · View at Google Scholar · View at Scopus
  33. T. Y. Chen and H. C. Chen, “Mixed-discrete structural optimization using a rank-niche evolution strategy,” Engineering Optimization, vol. 41, no. 1, pp. 39–58, 2009. View at Publisher · View at Google Scholar · View at Scopus
  34. V. Ho-Huu, T. Nguyen-Thoi, T. Vo-Duy, and T. Nguyen-Trang, “An adaptive elitist differential evolution for optimization of truss structures with discrete design variables,” Computers and Structures, vol. 165, pp. 59–75, 2016. View at Publisher · View at Google Scholar · View at Scopus
  35. V. Ho-Huu, T. Nguyen-Thoi, T. Truong-Khac, L. Le-Anh, and T. Vo-Duy, “An improved differential evolution based on roulette wheel selection for shape and size optimization of truss structures with frequency constraints,” Neural Computing and Applications, pp. 1–19, 2016. View at Publisher · View at Google Scholar · View at Scopus