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An improved differential evolution based on roulette wheel selection for shape and size optimization of truss structures with frequency constraints

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Abstract

Structural optimization with frequency constraints is well known as a highly nonlinear and complex optimization problem with many local optimum solutions. Therefore, to solve such problems effectively, designers need to use adequate optimization methods which can make a good balance between the computational cost and the quality of solutions. In this work, a novel differential evolution (DE) is proposed to solve the shape and size optimization problems for truss structures with frequency constraints. The proposed method, called ReDE, is a new version of the DE algorithm with two improvements. Firstly, the roulette wheel selection is employed to choose members for the mutation phase instead of random selection as in the conventional DE. Secondly, an elitist selection technique is applied to the selection phase instead of basic selection to improve the convergence speed of the method. The efficiency and reliability of the proposed method are demonstrated through five numerical examples. Numerical results reveal that the proposed algorithm outperforms many optimization methods in the literature.

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References

  1. Grandhi RV, Venkayya VB (1988) Structural optimization with frequency constraints. AIAA J 26:858–866. doi:10.2514/3.9979

    Article  MATH  Google Scholar 

  2. Lingyun W, Mei Z, Guangming W, Guang M (2005) Truss optimization on shape and sizing with frequency constraints based on genetic algorithm. Comput Mech 35:361–368. doi:10.1007/s00466-004-0623-8

    Article  MATH  Google Scholar 

  3. Kaveh A, Zolghadr A (2012) Truss optimization with natural frequency constraints using a hybridized CSS-BBBC algorithm with trap recognition capability. Comput Struct 102–103:14–27. doi:10.1016/j.compstruc.2012.03.016

    Article  Google Scholar 

  4. Gomes HM (2011) Truss optimization with dynamic constraints using a particle swarm algorithm. Expert Syst Appl 38:957–968. doi:10.1016/j.eswa.2010.07.086

    Article  Google Scholar 

  5. Miguel LFF, Fadel Miguel LF (2012) Shape and size optimization of truss structures considering dynamic constraints through modern metaheuristic algorithms. Expert Syst Appl 39:9458–9467. doi:10.1016/j.eswa.2012.02.113

    Article  Google Scholar 

  6. Zuo W, Bai J, Li B (2014) A hybrid OC–GA approach for fast and global truss optimization with frequency constraints. Appl Soft Comput 14(Part C):528–535. doi:10.1016/j.asoc.2013.09.002

    Article  Google Scholar 

  7. Kaveh A, Zolghadr A (2014) Democratic PSO for truss layout and size optimization with frequency constraints. Comput Struct 130:10–21. doi:10.1016/j.compstruc.2013.09.002

    Article  Google Scholar 

  8. Kaveh A, Ilchi Ghazaan M (2015) Hybridized optimization algorithms for design of trusses with multiple natural frequency constraints. Adv Eng Softw 79:137–147. doi:10.1016/j.advengsoft.2014.10.001

    Article  Google Scholar 

  9. Khatibinia M, Sadegh Naseralavi S (2014) Truss optimization on shape and sizing with frequency constraints based on orthogonal multi-gravitational search algorithm. J Sound Vib 333:6349–6369. doi:10.1016/j.jsv.2014.07.027

    Article  Google Scholar 

  10. Kaveh A, Zolghadr A (2011) Shape and size optimization of truss structures with frequency constraints using enhanced charged system search algorithm. Asian J Civ Eng 12:487–509

    Google Scholar 

  11. Kaveh A, Mahdavi VR (2013) Optimal design of structures with multiple natural frequency constraints using a hybridized BB-BC/Quasi-Newton algorithm. Period Polytech 1:27–38. doi:10.3311/PPci.2139

    Article  Google Scholar 

  12. Kaveh A, Zolghadr A (2014) A new PSRO algorithm for frequency constraint truss shape and size optimization. Struct Eng Mech 52:445–468. doi:10.12989/sem.2014.52.3.445

    Article  Google Scholar 

  13. Kaveh A, Zolghadr A (2014) Comparison of nine meta-heuristic algorithms for optimal design of truss structures with frequency constraints. Adv Eng Softw 76:9–30. doi:10.1016/j.advengsoft.2014.05.012

    Article  Google Scholar 

  14. Kaveh A, Ilchi Ghazaan M (2015) Layout and size optimization of trusses with natural frequency constraints using improved ray optimization algorithm. Iran J Sci Technol Trans Civ Eng 39:395–408

    Google Scholar 

  15. Kaveh A, Javadi SM (2014) 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. doi:10.1007/s00707-013-1006-z

    Article  MATH  Google Scholar 

  16. Kaveh A, Mahdavi V (2014) Colliding-bodies optimization for truss optimization with multiple frequency constraints. J Comput Civ Eng 29:4014078. doi:10.1061/(ASCE)CP.1943-5487.0000402

    Article  Google Scholar 

  17. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359. doi:10.1023/A:1008202821328

    Article  MathSciNet  MATH  Google Scholar 

  18. Wang ZWZ, Tang HTH, Li PLP (2009) Optimum design of truss structures based on differential evolution strategy. In: 2009 international conference on information engineering and computer science, pp 0–4. doi:10.1109/ICIECS.2009.5365996

  19. Wu C-Y, Tseng K-Y (2010) Truss structure optimization using adaptive multi-population differential evolution. Struct Multidiscip Optim 42:575–590. doi:10.1007/s00158-010-0507-9

    Article  Google Scholar 

  20. Le-Anh L, Nguyen-Thoi T, Ho-Huu V et al (2015) Static and frequency optimization of folded laminated composite plates using an adjusted differential evolution algorithm and a smoothed triangular plate element. Compos Struct 127:382–394. doi:10.1016/j.compstruct.2015.02.069

    Article  Google Scholar 

  21. Ho-Huu V, Nguyen-Thoi T, Nguyen-Thoi MH, Le-Anh L (2015) An improved constrained differential evolution using discrete variables (D-ICDE) for layout optimization of truss structures. Expert Syst Appl 42:7057–7069. doi:10.1016/j.eswa.2015.04.072

    Article  Google Scholar 

  22. Fan HY, Lampinen J (2003) A trigonometric mutation operation to differential evolution. J Glob Optim 27:105–129. doi:10.1023/A:1024653025686

    Article  MathSciNet  MATH  Google Scholar 

  23. Noman N, Iba H (2008) Accelerating differential evolution using an adaptive local search. IEEE Trans Evol Comput 12:107–125. doi:10.1109/TEVC.2007.895272

    Article  Google Scholar 

  24. Civicioglu P, Besdok E (2013) A conceptual comparison of the Cuckoo-search, particle swarm optimization, differential evolution and artificial bee colony algorithms. Artif Intell Rev. doi:10.1007/s10462-011-9276-0

    Google Scholar 

  25. Wang Y, Cai Z, Zhang Q (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15:55–66. doi:10.1109/TEVC.2010.2087271

    Article  Google Scholar 

  26. Lipowski A, Lipowska D (2012) Roulette-wheel selection via stochastic acceptance. Phys A 391:2193–2196. doi:10.1016/j.physa.2011.12.004

    Article  Google Scholar 

  27. Padhye N, Bhardawaj P, Deb K (2013) Improving differential evolution through a unified approach. J Glob Optim 55:771–799. doi:10.1007/s10898-012-9897-0

    Article  MathSciNet  MATH  Google Scholar 

  28. Ho-Huu V, Nguyen-Thoi T, Vo-Duy T, Nguyen-Trang T (2016) An adaptive elitist differential evolution for truss optimization with discrete variables. Comput Struct 165:59–75. doi:10.1016/j.compstruc.2015.11.014

    Article  Google Scholar 

  29. Sedaghati R (2005) Benchmark case studies in structural design optimization using the force method. Int J Solids Struct 42:5848–5871. doi:10.1016/j.ijsolstr.2005.03.030

    Article  MATH  Google Scholar 

  30. Nanthakumar SS, Valizadeh N, Park HS, Rabczuk T (2015) Surface effects on shape and topology optimization of nanostructures. Comput Mech 56:97–112. doi:10.1007/s00466-015-1159-9

    Article  MathSciNet  MATH  Google Scholar 

  31. Ghasemi H, Brighenti R, Zhuang X et al (2015) Optimal fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach. Struct Multidiscip Optim 51:99–112. doi:10.1007/s00158-014-1114-y

    Article  MathSciNet  Google Scholar 

  32. Ghasemi H, Kerfriden P, Bordas SPA et al (2015) Probabilistic multiconstraints optimization of cooling channels in ceramic matrix composites. Compos Part B Eng 81:107–119. doi:10.1016/j.compositesb.2015.06.023

    Article  Google Scholar 

  33. Ghasemi H, Rafiee R, Zhuang X et al (2014) Uncertainties propagation in metamodel-based probabilistic optimization of CNT/polymer composite structure using stochastic multi-scale modeling. Comput Mater Sci 85:295–305. doi:10.1016/j.commatsci.2014.01.020

    Article  Google Scholar 

Download references

Acknowledgments

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 107.99-2014.11.

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Authors and Affiliations

  1. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    V. Ho-Huu, T. Nguyen-Thoi, T. Truong-Khac, L. Le-Anh & T. Vo-Duy

  2. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    V. Ho-Huu, T. Nguyen-Thoi, T. Truong-Khac, L. Le-Anh & T. Vo-Duy

  3. Faculty of Information Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam

    T. Truong-Khac

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  1. V. Ho-Huu
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  4. L. Le-Anh
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Correspondence to T. Nguyen-Thoi.

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Ho-Huu, V., Nguyen-Thoi, T., Truong-Khac, T. et al. An improved differential evolution based on roulette wheel selection for shape and size optimization of truss structures with frequency constraints. Neural Comput & Applic 29, 167–185 (2018). https://doi.org/10.1007/s00521-016-2426-1

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