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Shape and size optimization of trusses with multiple frequency constraints using harmony search and ray optimizer for enhancing the particle swarm optimization algorithm

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Abstract

In this paper, size and shape optimization of truss structures is performed using an efficient hybrid method. This algorithm uses a particle swarm strategy and ray optimizer, and utilizes additional harmony search for a better exploitation. Here, multiple frequency constraints are considered making the optimization a highly nonlinear problem. Some basic benchmark problems are solved by this hybrid method, and the numerical results demonstrate the efficiency and robustness of this method compared to other mathematical and heuristic algorithms.

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References

  1. Canfield, R.: An approximation function for frequency constrained structural optimization. Technical Report N89-25196, Flight Dynamics Laboratory Air Force Wright Aeronautical Laboratories, Wright-Patterson AFB, Ohio, pp. 937–953 (1989)

  2. Bellagamba L., Yang T.: Minimum-mass truss structures with constraints on fundamental natural frequency. AIAA J. 19, 1452–1458 (1981)

    Article  Google Scholar 

  3. Lingyun W., Mei Z., Guangming W., Guang M.: Truss optimization on shape and sizing with frequency constraints based on genetic algorithm. Comput. Mech. 35(5), 361–368 (2005)

    Article  MATH  Google Scholar 

  4. Kaveh A., Talatahari S.: A novel heuristic optimization method: charged system search. Acta Mech. 213(3), 267–289 (2010)

    Article  MATH  Google Scholar 

  5. Khot N.: Optimization of structures with multiple frequency constraints. Comput. Struct. 20(5), 869–876 (1985)

    Article  MATH  Google Scholar 

  6. Wang D., Zhang W., Jiang J.: Truss optimization on shape and sizing with frequency constraints. AIAA J. 42(3), 622–630 (2004)

    Article  Google Scholar 

  7. Sedaghati R.: Benchmark case studies in structural design optimization using the force method. Int. J. Solids Struct. 42(21), 5848–5871 (2005)

    Article  MATH  Google Scholar 

  8. Gomes H.M.: Truss optimization with dynamic constraints using a particle swarm algorithm. Expert Syst. Appl. 38(1), 957–968 (2011)

    Article  Google Scholar 

  9. Kaveh, A., Zolghadr, A.: Truss optimization with natural frequency constraints using a hybridized CSS-BBBC algorithm with trap recognition capability. Comput. Struct. 102–103, 14–27 (2012)

    Google Scholar 

  10. Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. MHS’95. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science (1995)

  11. Yang X.S.: Engineering Optimization: An Introduction with Metaheuristic Applications. Wiley, London (2010)

    Book  Google Scholar 

  12. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings, IEEE International Conference on Neural Networks (1995)

  13. Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: Proceedings, IEEE World Congress on Evolutionary Computation, The 1998 IEEE International Conference on Computational Intelligence (1998)

  14. Lee K.S., Geem Z.W.: A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput. Methods Appl. Mech. Eng. 194(36), 3902–3933 (2005)

    Article  MATH  Google Scholar 

  15. Lee K.S., Geem Z.W.: A new structural optimization method based on the harmony search algorithm. Comput. Struct. 82(9), 781–798 (2004)

    Article  Google Scholar 

  16. Kaveh A., Khayatazad M.: A new meta-heuristic method: ray optimization. Comput. Struct. 112, 283–294 (2012)

    Article  Google Scholar 

  17. Kaveh A., Khayatazad M.: Ray optimization for size and shape optimization of truss structures. Comput. Struct. 117, 82–94 (2013)

    Article  Google Scholar 

  18. He S., Wu Q., Wen J., Saunders J., Paton R.: A particle swarm optimizer with passive congregation. Biosystems 78(1), 135–147 (2004)

    Article  Google Scholar 

  19. Grandhi, R.V., Venkayya, V.B.: Structural optimization with frequency and constraints. AIAA J. 26(7), 858–866 (1988)

    Google Scholar 

  20. Konzelman, C.J.: Dual methods and approximation concepts for structural optimization. MA.Sc. thesis, Department of Mechanical Engineering, U.o.T. (1986)

  21. Lin, J.H., Chen, W.Y., Yu, Y.S.: Structural optimization on geometrical, c.a.e.s.w.s.a.d. constraints. Comput. Struct. 15(5), 507–515 (1982)

    Google Scholar 

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Kaveh, A., Javadi, S.M. Shape and size optimization of trusses with multiple frequency constraints using harmony search and ray optimizer for enhancing the particle swarm optimization algorithm. Acta Mech 225, 1595–1605 (2014). https://doi.org/10.1007/s00707-013-1006-z

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  • DOI: https://doi.org/10.1007/s00707-013-1006-z

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