Combining Migration and Differential Evolution Strategies for Optimum Design of Truss Structures with Dynamic Constraints

  • Shahin JaliliEmail author
  • Yousef Hosseinzadeh
Research paper


The structural optimization problem with frequency constraints is one of the most challenging problems in the field of structural optimization as it typically involves a high degree of nonlinearity which makes the challenge of finding optimum solutions hard. In this study, a combined migration and differential evolution strategies (MS–DE) algorithm is presented for optimum design of truss structures with multiple frequency constraints. In the proposed method, the migration strategy (MS) is helpful to provide an accurate exploitation in the search space by sharing information between the individuals, while the differential evolution (DE) strategy is beneficial for increasing diversity of the population and performing efficient search within the global range. Numerical results and comparisons to some existing optimization techniques based on six benchmark truss design examples with multiple frequency constraints demonstrate the effectiveness of the proposed MS–DE method.


Truss structures Frequency constraints Migration strategy Differential evolution 


  1. Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, MHS’95. IEEE, pp 39–43Google Scholar
  2. Erol OK, Eksin I (2006) A new optimization method: big bang–big crunch. Adv Eng Softw 37:106–111CrossRefGoogle Scholar
  3. Goldberg D (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, ReadingzbMATHGoogle Scholar
  4. Gomes HM (2011) Truss optimization with dynamic constraints using a particle swarm algorithm. Expert Syst Appl 38:957–968CrossRefGoogle Scholar
  5. Gong W, Cai Z, Ling CX (2010) DE/BBO: a hybrid differential evolution with biogeography-based optimization for global numerical optimization. Soft Comput 15:645–665CrossRefGoogle Scholar
  6. Grandhi R (1993) Structural optimization with frequency constraints—a review. AIAA J 31:2296–2303CrossRefGoogle Scholar
  7. Grandhi R, Venkayya V (1988) Structural optimization with frequency constraints. AIAA J 26:858–866CrossRefGoogle Scholar
  8. Hartmann D, König M (2012) A distributed agent-based approach for simulation-based optimization. Adv Eng Inform 26:814–832CrossRefGoogle Scholar
  9. Hasançebi O, Çarbaş S, Doğan E, Erdal F, Saka M (2009) Performance evaluation of metaheuristic search techniques in the optimum design of real size pin jointed structures. Comput Struct 87:284–302CrossRefGoogle Scholar
  10. Hosseinzadeh Y, Taghizadieh N, Jalili S (2016) Hybridizing electromagnetism-like mechanism algorithm with migration strategy for layout and size optimization of truss structures with frequency constraints. Neural Comput Appl 27:953–971CrossRefGoogle Scholar
  11. Jalili S, Hosseinzadeh Y (2015) A cultural algorithm for optimal design of truss structures. Lat Am J Solids Struct 12:1721–1747CrossRefGoogle Scholar
  12. Jalili S, Hosseinzadeh Y (2017) Design of pin jointed structures under stress and deflection constraints using hybrid electromagnetism-like mechanism and migration strategy algorithm. Periodica Polytechnica Civ Eng 61:780Google Scholar
  13. Jalili S, Hosseinzadeh Y (2018) Design optimization of truss structures with continuous and discrete variables by hybrid of biogeography-based optimization and differential evolution methods. Struct Des Tall Special Build. CrossRefGoogle Scholar
  14. Jalili S, Husseinzadeh Kashan A (2018) Optimum discrete design of steel tower structures using optics inspired optimization method. Struct Des Tall Spec Build 27(9):e1466CrossRefGoogle Scholar
  15. Jalili S, Talatahari S (2017) Optimum design of truss structures under frequency constraints using hybrid CSS-MBLS algorithm. KSCE J Civil Eng 22(5):1840–1853CrossRefGoogle Scholar
  16. Jalili S, Hosseinzadeh Y, Kaveh A (2014) Chaotic biogeography algorithm for size and shape optimization of truss structures with frequency constraints. Periodica Polytechnica Civ Eng 58:397CrossRefGoogle Scholar
  17. Jalili S, Hosseinzadeh Y, Taghizadieh N (2016a) A biogeography-based optimization for optimum discrete design of skeletal structures. Eng Optim 48:1491–1514CrossRefGoogle Scholar
  18. Jalili S, Kashan AH, Hosseinzadeh Y (2016b) League championship algorithms for optimum design of pin-jointed structures. J Comput Civil Eng 31:04016048CrossRefGoogle Scholar
  19. Kashan AH (2014) League Championship algorithm (LCA): an algorithm for global optimization inspired by sport championships. Appl Soft Comput 16:171–200CrossRefGoogle Scholar
  20. Kashan AH (2015) A new metaheuristic for optimization: optics inspired optimization (OIO). Comput Oper Res 55:99–125MathSciNetCrossRefGoogle Scholar
  21. Kaveh A, Ghazaan MI (2015) Hybridized optimization algorithms for design of trusses with multiple natural frequency constraints. Adv Eng Softw 79:137–147CrossRefGoogle Scholar
  22. Kaveh A, Ilchi Ghazaan M (2015) Layout and size optimization of trusses with natural frequency constraints using improved ray optimization algorithm Iranian. J Sci Technol Trans Civil Eng 39:395–408Google Scholar
  23. Kaveh A, Javadi S (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 225:1595–1605CrossRefGoogle Scholar
  24. Kaveh A, Mahdavi VR (2013) Optimal design of structures with multiple natural frequency constraints using a hybridized BB-BC/Quasi-Newton algorithm. Periodica Polytechnica Civ Eng 57:27CrossRefGoogle Scholar
  25. Kaveh A, Mahdavi V (2014) Colliding-bodies optimization for truss optimization with multiple frequency constraints. J Comput Civil Eng 29:04014078CrossRefGoogle Scholar
  26. Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213:267–289CrossRefGoogle Scholar
  27. 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(4):487–509Google Scholar
  28. Kaveh A, Zolghadr A (2012) Truss optimization with natural frequency constraints using a hybridized CSS-BBBC algorithm with trap recognition capability. Comput Struct 102:14–27CrossRefGoogle Scholar
  29. Kaveh A, Zolghadr A (2014a) Comparison of nine meta-heuristic algorithms for optimal design of truss structures with frequency constraints. Adv Eng Softw 76:9–30CrossRefGoogle Scholar
  30. Kaveh A, Zolghadr A (2014b) Democratic PSO for truss layout and size optimization with frequency constraints. Comput Struct 130:10–21CrossRefGoogle Scholar
  31. Kaveh A, Zolghadr A (2014c) A new PSRO algorithm for frequency constraint truss shape and size optimization. Struct Eng Mech 52:445–468CrossRefGoogle Scholar
  32. Kaveh A, Jafari L, Farhoudi N (2015) Truss optimization with natural frequency constraints using a dolphin echolocation algorithm. Asian J Civ Eng 16(1):29–46Google Scholar
  33. Khatibinia M, Naseralavi SS (2014) Truss optimization on shape and sizing with frequency constraints based on orthogonal multi-gravitational search algorithm. J Sound Vib 333:6349–6369CrossRefGoogle Scholar
  34. Lin J, Che W, Yu Y (1982) Structural optimization on geometrical configuration and element sizing with statical and dynamical constraints. Comput Struct 15:507–515CrossRefGoogle Scholar
  35. Lingyun W, Mei Z, Guangming W, Guang M (2005) Truss optimization on shape and sizing with frequency constraints based on genetic algorithm. Comput Mech 35:361–368CrossRefGoogle Scholar
  36. Lohokare M, Pattnaik SS, Panigrahi BK, Das S (2013) Accelerated biogeography-based optimization with neighborhood search for optimization. Appl Soft Comput 13:2318–2342CrossRefGoogle Scholar
  37. Ma H (2010) An analysis of the equilibrium of migration models for biogeography-based optimization. Inf Sci 180:3444–3464CrossRefGoogle Scholar
  38. Ma Z-D, Kikuchi N, Hagiwara I (1993) Structural topology and shape optimization for a frequency response problem. Comput Mech 13:157–174MathSciNetCrossRefGoogle Scholar
  39. Ma Z-D, Cheng H-C, Kikuchi N (1994) Structural design for obtaining desired eigenfrequencies by using the topology and shape optimization method. Comput Syst Eng 5:77–89CrossRefGoogle Scholar
  40. MacArthur R, Wilson E (1967) The theory of biogeography. Princeton University Press, PrincetonGoogle Scholar
  41. Mezura-Montes E, Velázquez-Reyes J, Coello Coello CA (2006) A comparative study of differential evolution variants for global optimization. In: Proceedings of the 8th annual conference on genetic and evolutionary computation. ACM, pp 485–492Google Scholar
  42. Noman N, Iba H (2008) Accelerating differential evolution using an adaptive local search. IEEE Trans Evol Comput 12:107–125CrossRefGoogle Scholar
  43. Price K, Storn RM, Lampinen JA (2006) Differential evolution: a practical approach to global optimization. Springer, New YorkzbMATHGoogle Scholar
  44. Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13:398–417CrossRefGoogle Scholar
  45. Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179:2232–2248CrossRefGoogle Scholar
  46. Reynolds RG (1994) An introduction to cultural algorithms. In: Proceedings of the third annual conference on evolutionary programming. World Scientific, pp 131–139Google Scholar
  47. Sedaghati R, Suleman A, Tabarrok B (2002) Structural optimization with frequency constraints using the finite element force method. AIAA J 40:382–388CrossRefGoogle Scholar
  48. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12:702–713CrossRefGoogle Scholar
  49. Storn R (1999) System design by constraint adaptation and differential evolution. IEEE Trans Evol Comput 3:22–34CrossRefGoogle Scholar
  50. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359MathSciNetCrossRefGoogle Scholar
  51. Taheri SHS, Jalili S (2016) Enhanced biogeography-based optimization: a new method for size and shape optimization of truss structures with natural frequency constraints. Lat Am J Solids Struct 13:1406–1430CrossRefGoogle Scholar
  52. Wang D, Zhang W, Jiang J (2004) Truss optimization on shape and sizing with frequency constraints. AIAA J 42:622–630CrossRefGoogle Scholar
  53. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82CrossRefGoogle Scholar
  54. Zhang Y, Lü C, Zhou N, Su C (2010) Frequency reliability sensitivity for dynamic structural systems#. Mech Des Struct Mach 38:74–85CrossRefGoogle Scholar

Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Faculty of Civil EngineeringUniversity of TabrizTabrizIran

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