Skip to main content
SpringerLink
Log in

Probability Collectives for Discrete and Mixed Variable Problems

  • Chapter
  • First Online:
Probability Collectives

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 86))

  • 934 Accesses

Abstract

This chapter demonstrates the ability of PC for solving practically important discrete and mixed variable problems in structural and mechanical engineering domain. The truss structure problems such as 17-bar, 25-bar, 72-bar, 45-Bar, 10-Bar and 38-Bar, a helical compression spring design, a reinforced concrete beam design, stepped cantilever beam design and speed reducer were successfully solved.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Wu, S.J., Chow, P.T.: Steady-state genetic algorithms for discrete optimization of trusses. Comput. Struct. 56(6), 979–991 (1995)

    Article  MATH  Google Scholar 

  2. Adeli, H., Kumar, S.: Distributed genetic algorithm for structural optimization. J. Aerosp. Eng. ASCE 8(3), 156–163 (1995)

    Article  Google Scholar 

  3. Lee, K.S., Geem, Z.W.: A new structural optimization method based on the harmony search algorithm. Comput. Struct. 82, 781–798 (2004)

    Article  Google Scholar 

  4. Lee, K.S., Geem, Z.W., Lee, S.H., Bae, K.W.: The harmony search heuristic algorithm for discrete structural optimization. Eng. Optim. 37(7), 663–684 (2005)

    Article  MathSciNet  Google Scholar 

  5. Li, L.J., Huang, Z.B., Liu, F., Wu, Q.H.: A heuristic particle swarm optimization of pin connected structures. Comput. Struct. 85, 340–349 (2007)

    Article  Google Scholar 

  6. Li, L.J., Huang, Z.B., Liu, F.: A heuristic particle swarm optimization method for truss structures with discrete variables. Comput. Struct. 87(7–8), 435–443 (2009)

    Article  Google Scholar 

  7. Kaveh, A., Talatahari, S.: A particle swarm ant colony optimization for truss structures with discrete variables. J. Struct. Steel Res. 65, 1558–1568 (2009)

    Article  Google Scholar 

  8. Deb, K. Goyal, M.: Optimizing engineering designs using a combined genetic search. In: Proceedings Back IT, 7th International Conference of Genetic Algorithm, pp. 512–528 (1997)

    Google Scholar 

  9. Rajeev, S., Krishnamoorthy, C.S.: Discrete optimization of structures using genetic algorithm. J. Struct. Eng. ASCE 118(5), 1123–1250 (1992)

    Article  Google Scholar 

  10. Wu, S.J., Chow, P.E.: Genetic algorithms for nonlinear mixed discrete-integer optimization problems via metagenetic parameter optimizations. Eng. Optim. 24(2), 137–159 (1995)

    Article  MathSciNet  Google Scholar 

  11. Yun, Y.S.: Study on Adaptive Hybrid Genetic Algorithm and its Applications to Engineering Design Problems. M.Sc. thesis, Waseda University (2005)

    Google Scholar 

  12. Lemonge, A.C.C., Barbosa, H.J.C.: An adaptive penalty scheme for genetic algorithms in structural optimization. Int. J. Numer. Methods Eng. 59(5), 703–736 (2004)

    Article  MATH  Google Scholar 

  13. Erbatur, F., Hasancebi, O., Tutuncu, I., Kilic, H.: Optimal design of planar and space structures with genetic algorithms. Comput. Struct. 75(2), 209–224 (2000)

    Article  Google Scholar 

  14. Bernardino, H.S., Barbosa, H.J.C., Lemonge, A.C.C.: A hybrid genetic algorithm for constrained optimization problems in mechanical engineering. In: Proceedings IEEE Congress Evolution Computations, pp. 646–653 (2007)

    Google Scholar 

  15. Coello, C.A.C., Cortes, N.C.: Hybridizing a genetic algorithm with an artificial immune system for global optimization. Eng. Optim. 36(5), 607–634 (2004)

    Article  MathSciNet  Google Scholar 

  16. Azad, S.K., Azad, S.K., Kulkarni, A.J.: Structural optimization using a mutation-based genetic algorithm. Int. J. Optim. Civil Eng. 2(1), 80–100 (2012)

    Google Scholar 

  17. Ringertz, U.T.: On methods for discrete structural constraints. Eng. Optim. 13(1), 47–64 (1988)

    Article  Google Scholar 

  18. Guo, C.X., Hu, J.S., Ye, B., Cao, Y.J.: Swarm intelligence for mixed-variable design optimization. J. Zhejiang Univ. Sci. 5(7), 851–860 (2004)

    Article  MATH  Google Scholar 

  19. Sadollah, A., Bahreininejad, A., Eskandar, H., Hamdi, M.: Mine blast algorithm for optimization of truss structures with discrete variables. Comput. Struct. 49(63), 102–103 (2012)

    Google Scholar 

  20. Gandomi, A.H., Xin-She Yang., Alavi, A.H.: Mixed variable structural optimization using Firefly algorithm. Comput. Struct. 89(23–24), pp. 2325–2336 (2011)

    Google Scholar 

  21. Shih, C.J., Yang, Y.C.: Generalized Hopfield network based structural optimization using sequential unconstrained minimization technique with additional penalty strategy, Adv. Eng. Softw. 33 (7–10), pp. 721–729 (2002)

    Google Scholar 

  22. Sandgren, E.: Nonlinear integer and discrete programming in mechanical design optimization. J. Mech. Des. 112(2), 223–229 (1990)

    Article  Google Scholar 

  23. Amir, H.M., Hasegawa, T.: Nonlinear mixed-discrete structural optimization. J. Struct. Eng. 115(3), 626–645 (1989)

    Article  Google Scholar 

  24. Efren, M., Coello, C.A.C., Ricardo, L.: Engineering optimization using a simple evolutionary algorithm. In: Proceedings 15th International Conference on Tools with Artificial Intelligence (ICTAI), pp. 149–156 (2003)

    Google Scholar 

  25. Pant, M., Thangaraj, R., Singh, V.P.: Optimization of mechanical engineering design problems using improved differential evolutionary algorithm. Int. J. Resent Trend Eng. 1(5), 21–25 (2009)

    Google Scholar 

  26. Chen, T.Y., Chen, H.C.: Mixed-discrete structural optimization using a rank-niche evolution strategy. Eng. Optim. 41(1), 39–58 (2009)

    Article  Google Scholar 

  27. Montes, E.M., Ocana, B.H.: Modified bacterial foraging optimization for engineering design. In: C.H. Dagli, et al., of the Artificial Neural Networks in Engineering Conference (ANNIE), ASME Press series, Intelligent Engineering Systems through Artificial Neural Networks, 19, pp. 357–364 (2009)

    Google Scholar 

  28. Thanedar, P.B., Vanderplaats, G.N.: Survey of discrete variable optimization for structural design. J. Struct. Eng. 121(2), 301–306 (1995)

    Article  Google Scholar 

  29. Arnout, S.: International Student Competition in Structural Optimization, Aug. 26–27 (2011)

    Google Scholar 

  30. Rudolph, S., Schmidt, J.: International Student Competition in Structural Optimization, Aug. 26–27 (2012)

    Google Scholar 

  31. Kulkarni, A.J., Kale, I.R., Tai, K.: Probability collectives for solving discrete and mixed variable problems. In: International Journal of Computer Aided Engineering and Technology (2014) (In Press)

    Google Scholar 

  32. Kulkarni, A.J., Kale, I.R., Tai, K., Azad, S.K.: Discrete optimization of truss structure using probability collectives. In: Proceedings IEEE 12th International Conference of Hybrid Intelligence System, pp. 225–230 (2002)

    Google Scholar 

  33. Kulkarni, A.J., Kale, I.R., Tai, K.: Probability collectives for solving truss structure problems. In: 10th World Congress on Structural and Multidisciplinary Optimization, paper no. 5395 (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, Singapore

    Anand Jayant Kulkarni & Kang Tai

  2. Scientific Network for Innovation and Research Excellence, Machine Intelligence Research Labs (MIR Labs), Auburn, WA, USA

    Ajith Abraham

Authors
  1. Anand Jayant Kulkarni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kang Tai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ajith Abraham
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anand Jayant Kulkarni .

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Kulkarni, A.J., Tai, K., Abraham, A. (2015). Probability Collectives for Discrete and Mixed Variable Problems. In: Probability Collectives. Intelligent Systems Reference Library, vol 86. Springer, Cham. https://doi.org/10.1007/978-3-319-16000-9_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-16000-9_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15999-7

  • Online ISBN: 978-3-319-16000-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation