Skip to main content
SpringerLink
Log in

Modified symbiotic organisms search for structural optimization

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

The structural dynamic response predominantly depends upon natural frequencies which fabricate these as a controlling parameter for dynamic response of the truss. However, truss optimization problems subjected to multiple fundamental frequency constraints with shape and size variables are more arduous due to its characteristics like non-convexity, non-linearity, and implicit with respect to design variables. In addition, mass minimization with frequency constraints are conflicting in nature which intricate optimization problem. Using meta-heuristic for such kind of problem requires harmony between exploration and exploitation to regulate the performance of the algorithm. This paper proposes a modification of a nature inspired Symbiotic Organisms Search (SOS) algorithm called a Modified SOS (MSOS) algorithm to enhance its efficacy of accuracy in search (exploitation) together with exploration by introducing an adaptive benefit factor and modified parasitism vector. These modifications improved search efficiency of the algorithm with a good balance between exploration and exploitation, which has been partially investigated so far. The feasibility and effectiveness of proposed algorithm is studied with six truss design problems. The results of benchmark planar/space trusses are compared with other meta-heuristics. Complementarily the feasibility and effectiveness of the proposed algorithms are investigated by three unimodal functions, thirteen multimodal functions, and six hybrid functions of the CEC2014 test suit. The experimental results show that MSOS is more reliable and efficient as compared to the basis SOS algorithm and other state-of-the-art algorithms. Moreover, the MSOS algorithm provides competitive results compared to the existing meta-heuristics in the literature.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Baykasoğlu A, Ozsoydan FB (2015) Adaptive firefly algorithm with chaos for mechanical design optimization problems. Appl Soft Comput 36:152–164. https://doi.org/10.1016/j.asoc.2015.06.056

    Article  Google Scholar 

  2. Bingul Z (2007) Adaptive genetic algorithms applied to dynamic multiobjective problems. Appl Soft Comput J 7:791–799. https://doi.org/10.1016/j.asoc.2006.03.001

    Article  Google Scholar 

  3. Cheng MY, Prayogo D (2014) Symbiotic Organisms Search: A new metaheuristic optimization algorithm. Comput Struct 139:98–112. https://doi.org/10.1016/j.compstruc.2014.03.007

    Article  Google Scholar 

  4. Cheng MY, Prayogo D, Wu YW (2018) Prediction of permanent deformation in asphalt pavements using a novel symbiotic organisms search – least squares support vector regression. Neural Comput Appl. https://doi.org/10.1007/s00521-018-3426-0

    Google Scholar 

  5. De Jong KA (1975) An Analysis of the Behavior of a Class of Genetic Adaptive Systems. Comput Commun Sci 56:266

    Google Scholar 

  6. Do DTT, Lee J (2017) A modified symbiotic organisms search (mSOS) algorithm for optimization of pin-jointed structures. Appl Soft Comput J 61:683–699. https://doi.org/10.1016/j.asoc.2017.08.002

    Article  Google Scholar 

  7. Dorigo M, Maniezzo V, Colorni A (1996) Ant System: Optimization by a Colony of Cooperating Agents. IEEE Trans Syst Man Cybern Part B 26:1–13. https://doi.org/10.1109/3477.484436

    Article  Google Scholar 

  8. Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. MHS’95 Proc Sixth Int Symp Micro Mach Hum Sci 39–43. https://doi.org/10.1109/MHS.1995.494215

  9. Erol OK, Eksin I (2006) A new optimization method: Big Bang-Big Crunch. Adv Eng Softw 37:106–111. https://doi.org/10.1016/j.advengsoft.2005.04.005

    Article  Google Scholar 

  10. Eskandar H, Sadollah A, Bahreininejad A, Hamdi M (2012) Water cycle algorithm—a novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput Struct 110–111:151–166. https://doi.org/10.1016/j.compstruc.2012.07.010

    Article  Google Scholar 

  11. Ezugwu AES, Adewumi AO, Frîncu ME (2017) Simulated annealing based symbiotic organisms search optimization algorithm for traveling salesman problem. Expert Syst Appl 77:189–210. https://doi.org/10.1016/j.eswa.2017.01.053

    Article  Google Scholar 

  12. Farshchin M, Camp CV, Maniat M (2016) Multi-class teaching-learning-based optimization for truss design with frequency constraints. Eng Struct 106:355–369. https://doi.org/10.1016/j.engstruct.2015.10.039

    Article  Google Scholar 

  13. Fogel DB (1988) An Evolutionary Approach to the Traveling Salesman Problem. Biol Cybern 60:139–144. https://doi.org/10.1007/BF00202901

    Article  MathSciNet  Google Scholar 

  14. Glover F (1975) Tabu search and adaptive memory programming—advances, applications and challenges. In: In Interfaces in computer science and operations research. pp 1–75

  15. Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3:95–99. https://doi.org/10.1023/A:1022602019183

    Article  Google Scholar 

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

    Article  Google Scholar 

  17. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471. https://doi.org/10.1007/s10898-007-9149-x

    Article  MathSciNet  MATH  Google Scholar 

  18. Kaveh A, Farhoudi N (2013) A new optimization method: Dolphin echolocation. Adv Eng Softw 59:53–70. https://doi.org/10.1016/j.advengsoft.2013.03.004

    Article  Google Scholar 

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

    Article  Google Scholar 

  20. Kaveh A, Ilchi Ghazaan M (2017) Vibrating particles system algorithm for truss optimization with multiple natural frequency constraints. Acta Mech 228:307–322. https://doi.org/10.1007/s00707-016-1725-z

    Article  MathSciNet  Google Scholar 

  21. Kaveh A, Jafari L, Farhoudi N (2015) Truss optimization with natural frequency constraints using a dolphin echolocation algorithm. Asian J Civ Eng 16:29–46

    Google Scholar 

  22. Kaveh A, Khayatazad M (2013) Ray optimization for size and shape optimization of truss structures. Comput Struct 117:82–94. https://doi.org/10.1016/j.compstruc.2012.12.010

    Article  Google Scholar 

  23. Kaveh A, Mahdavi VR (2014) Colliding bodies optimization: A novel meta-heuristic method. Comput Struct 139:18–27. https://doi.org/10.1016/j.compstruc.2014.04.005

    Article  Google Scholar 

  24. Kaveh A, Mahdavi VR (2015) Two-dimensional colliding bodies algorithm for optimal design of truss structures. Adv Eng Softw 83:70–79. https://doi.org/10.1016/j.advengsoft.2015.01.007

    Article  Google Scholar 

  25. Kaveh A, Talatahari S (2010) A novel heuristic optimization method: Charged system search. Acta Mech 213:267–289. https://doi.org/10.1007/s00707-009-0270-4

    Article  MATH  Google Scholar 

  26. 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 

  27. 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. https://doi.org/10.1016/j.compstruc.2012.03.016

    Article  Google Scholar 

  28. Kaveh A, Zolghadr A (2013) Topology optimization of trusses considering static and dynamic constraints using the CSS. Appl Soft Comput J 13:2727–2734. https://doi.org/10.1016/j.asoc.2012.11.014

    Article  Google Scholar 

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

    Article  Google Scholar 

  30. Kaveh A, Zolghadr A (2017) Truss shape and size optimization with frequency constraints using Tug of War Optimization. Asian J Civ Eng 18:311–313

    Google Scholar 

  31. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by Simulated Annealing. Science 220:671–680. https://doi.org/10.1126/science.220.4598.671

    Article  MathSciNet  MATH  Google Scholar 

  32. Koza JR (1994) Genetic programming as a means for programming computers by natural selection. Stat Comput 4:87–112. https://doi.org/10.1007/BF00175355

    Article  Google Scholar 

  33. Lee KS, Geem ZW (2004) A new structural optimization method based on the harmony search algorithm. Comput Struct 82:781–798. https://doi.org/10.1016/j.compstruc.2004.01.002

    Article  Google Scholar 

  34. Li X, Yin M (2015) Modified cuckoo search algorithm with self adaptive parameter method. Inf Sci (Ny) 298:80–97. https://doi.org/10.1016/j.ins.2014.11.042

    Article  Google Scholar 

  35. Liao TW, Kuo RJ (2018) Five discrete symbiotic organisms search algorithms for simultaneous optimization of feature subset and neighborhood size of KNN classification models. Appl Soft Comput J 64:581–595. https://doi.org/10.1016/j.asoc.2017.12.039

    Article  Google Scholar 

  36. 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. https://doi.org/10.1016/j.eswa.2012.02.113

    Article  Google Scholar 

  37. Mortazavi A, Toğan V (2017) Sizing and layout design of truss structures under dynamic and static constraints with an integrated particle swarm optimization algorithm. Appl Soft Comput J 51:239–252. https://doi.org/10.1016/j.asoc.2016.11.032

    Article  Google Scholar 

  38. Noilublao N, Bureerat S (2011) Simultaneous topology, shape and sizing optimisation of a three-dimensional slender truss tower using multiobjective evolutionary algorithms. Comput Struct 89:2531–2538. https://doi.org/10.1016/j.compstruc.2011.08.010

    Article  Google Scholar 

  39. Osman IH, Laporte G (1996) Metaheuristics: A bibliography. Ann Oper Res 63:511–623. https://doi.org/10.1007/BF02125421

    Article  MATH  Google Scholar 

  40. Patel V, Savsani V (2014) Optimization of a plate-fin heat exchanger design through an improved multi-objective teaching-learning based optimization (MO-ITLBO) algorithm. Chem Eng Res Des 92:2371–2382. https://doi.org/10.1016/j.cherd.2014.02.005

    Article  Google Scholar 

  41. Piotrowski AP (2013) Adaptive memetic differential evolution with global and local neighborhood-based mutation operators. Inf Sci (Ny) 241:164–194. https://doi.org/10.1016/j.ins.2013.03.060

    Article  Google Scholar 

  42. Savsani VJ, Tejani GG, Patel VK (2016) Truss topology optimization with static and dynamic constraints using modified subpopulation teaching–learning-based optimization. Eng Optim 48:1990–2006. https://doi.org/10.1080/0305215X.2016.1150468

    Article  MathSciNet  Google Scholar 

  43. Savsani VJ, Tejani GG, Patel VK, Savsani P (2017) Modified meta-heuristics using random mutation for truss topology optimization with static and dynamic constraints. J Comput Des Eng 4:106–130. https://doi.org/10.1016/j.jcde.2016.10.002

    Google Scholar 

  44. Shan H, Yasuda T, Ohkura K (2015) A self adaptive hybrid enhanced artificial bee colony algorithm for continuous optimization problems. BioSystems 132–133:43–53. https://doi.org/10.1016/j.biosystems.2015.05.002

    Article  Google Scholar 

  45. Tejani GG, Savsani VJ, Bureerat S, Patel VK (2018) Topology and Size Optimization of Trusses with Static and Dynamic Bounds by Modified Symbiotic Organisms Search. J Comput Civ Eng 32:1–11. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000741

    Article  Google Scholar 

  46. Tejani GG, Savsani VJ, Patel VK (2016) Adaptive symbiotic organisms search (SOS) algorithm for structural design optimization. J Comput Des Eng 3:226–249. https://doi.org/10.1016/j.jcde.2016.02.003

    Google Scholar 

  47. Tejani GG, Savsani VJ, Patel VK (2016) Modified sub-population teaching-learning-based optimization for design of truss structures with natural frequency constraints. Mech Based Des Struct Mach 44:495–513. https://doi.org/10.1080/15397734.2015.1124023

    Article  Google Scholar 

  48. Tejani GG, Savsani VJ, Patel VK, Bureerat S (2017) Topology, shape, and size optimization of truss structures using modified teaching-learning based optimization. Adv Comput Des 2:313–331. https://doi.org/10.12989/acd.2017.2.4.313

    Google Scholar 

  49. Tollo G di, Lardeux F, Maturana J, Saubion F (2015) An experimental study of adaptive control for evolutionary algorithms. Appl Soft Comput 35:359–372. https://doi.org/10.1016/j.asoc.2015.06.016

    Article  Google Scholar 

  50. Tran DH, Cheng MY, Prayogo D (2016) A novel Multiple Objective Symbiotic Organisms Search (MOSOS) for time-cost-labor utilization tradeoff problem. Knowledge-Based Syst 94:132–145. https://doi.org/10.1016/j.knosys.2015.11.016

    Article  Google Scholar 

  51. Tran DH, Luong-Duc L, Duong MT et al (2018) Opposition multiple objective symbiotic organisms search (OMOSOS) for time, cost, quality and work continuity tradeoff in repetitive projects. J Comput Des Eng 5:160–172. https://doi.org/10.1016/j.jcde.2017.11.008

    Google Scholar 

  52. Tejani GG, Pholdee N, Bureerat S, Prayogo D (2018) Multiobjective adaptive symbiotic organisms search for truss optimization problems. Knowl-Based Syst. https://doi.org/10.1016/j.knosys.2018.08.005

    Google Scholar 

  53. Wang D, Zhang WH, Jiang JS (2004) Truss optimization on shape and sizing with frequency constraints. AIAA J 42:622–630. https://doi.org/10.2514/1.1711

    Article  Google Scholar 

  54. Wei L, Tang T, Xie X, Shen W (2011) Truss optimization on shape and sizing with frequency constraints based on parallel genetic algorithm. Struct Multidiscip Optim 43:665–682

    Article  Google Scholar 

  55. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82. https://doi.org/10.1109/4235.585893

    Article  Google Scholar 

  56. Yang XS (2009) Firefly Algorithms for Multimodal Optimization. In: In International symposium on stochastic algorithms. pp 169–178

  57. Yang XS, Deb S (2009) Cuckoo search via Levy flights. In: 2009 World Congress on Nature and Biologically Inspired Computing, NABIC 2009 - Proceedings. pp 210–214

  58. Yu VF, Redi AANP, Yang CL et al (2017) Symbiotic organisms search and two solution representations for solving the capacitated vehicle routing problem. Appl Soft Comput J 52:657–672. https://doi.org/10.1016/j.asoc.2016.10.006

    Article  Google Scholar 

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

    Article  Google Scholar 

  60. Cheng M-Y, Prayogo D, Tran D-H (2016) Optimizing Multiple-Resources Leveling in Multiple Projects Using Discrete Symbiotic Organisms Search. J Comput Civ Eng 30:04015036. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000512

    Article  Google Scholar 

  61. Duman S (2017) Symbiotic organisms search algorithm for optimal power flow problem based on valve-point effect and prohibited zones. Neural Comput Appl 28:3571–3585. https://doi.org/10.1007/s00521-016-2265-0

    Article  Google Scholar 

  62. Prasad D, Mukherjee V (2016) A novel symbiotic organisms search algorithm for optimal power flow of power system with FACTS devices. Eng Sci Technol Int J 19:79–89. https://doi.org/10.1016/j.jestch.2015.06.005

    Article  Google Scholar 

  63. Abdullahi M, Ngadi MA, Abdulhamid SM (2016) Symbiotic Organism Search optimization based task scheduling in cloud computing environment. Futur Gener Comput Syst 56:640–650. https://doi.org/10.1016/j.future.2015.08.006

    Article  Google Scholar 

  64. Panda A, Pani S (2016) A Symbiotic Organisms Search algorithm with adaptive penalty function to solve multi-objective constrained optimization problems. Appl Soft Comput J 46:344–360. https://doi.org/10.1016/j.asoc.2016.04.030

    Article  Google Scholar 

  65. Panda A, Pani S (2017) An orthogonal parallel symbiotic organism search algorithm embodied with augmented Lagrange multiplier for solving constrained optimization problems. Soft Comput doi. https://doi.org/10.1007/s00500-017-2693-5

    MATH  Google Scholar 

  66. Prayogo D (2018) Optimization model for construction project resource leveling using a novel modified symbiotic organisms search. Asian J Civ Eng 3456789:. https://doi.org/10.1007/s42107-018-0048-x

  67. Subhabrata Banerjee SC (2017) Power Optimization of Three Dimensional Turbo Code Using a Novel Modified Symbiotic Organism Search. Wirel Pers Commun doi. https://doi.org/10.1007/s11277-016-3586-0

    Google Scholar 

  68. Guha D, Kumar P, Banerjee S (2018) Symbiotic organism search algorithm applied to load frequency control of multi-area power system. Energy Syst. https://doi.org/10.1007/s12667-017-0232-1

    Google Scholar 

  69. Dosoglu MK, Guvenc U, Duman S, Sonmez Y (2018) Symbiotic organisms search optimization algorithm for economic / emission dispatch problem in power systems. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2481-7

    Google Scholar 

  70. Saha S, Mukherjee V (2016) Optimal placement and sizing of DGs in RDS using chaos embedded SOS algorithm. 3671–3680. https://doi.org/10.1049/iet-gtd.2016.0151

  71. Zhou Y, Wu H, Luo Q, Abdel-baset M (2018) Automatic data clustering using nature-inspired symbiotic organism search algorithm. Knowledge-Based Syst. https://doi.org/10.1016/j.knosys.2018.09.013

    Google Scholar 

  72. Prayogo D, Cheng MY, Prayogo H (2017) A Novel implementation of nature-inspired optimization for civil engineering: a comparative study of symbiotic organisms search. 19:36–43. https://doi.org/10.9744/CED.19.1.36-43

  73. Jaffel Z, Farah M (2018, March) A symbiotic organisms search algorithm for feature selection in satellite image classification. In: Advanced Technologies for Signal and Image Processing (ATSIP), 2018 4th International Conference on(pp. 1–5). IEEE

  74. Sulaiman M, Ahmad A, Khan A, Muhammad S (2018) Hybridized symbiotic organism search algorithm for the optimal operation of directional overcurrent relays. Hindawi Complex 2018:11. https://doi.org/10.1155/2018/4605769

    MATH  Google Scholar 

  75. Tejani GG, Savsani VJ, Patel VK, Mirjalili S (2018) Knowledge-Based Systems Truss optimization with natural frequency bounds using improved symbiotic organisms search. Knowledge-Based Syst 5:1–17. https://doi.org/10.1016/j.knosys.2017.12.012

    Google Scholar 

  76. Zheng Y (2015) Computers & Operations Research Water wave optimization: A new nature-inspired metaheuristic. Comput Oper Res 55:1–11. https://doi.org/10.1016/j.cor.2014.10.008

    Article  MathSciNet  MATH  Google Scholar 

  77. Črepinšek M, Liu S-H, Mernik M (2013) Exploration and Exploitation in Evolutionary Algorithms: A Survey. ACM Comput 45:1–33. https://doi.org/10.1145/2480741.2480752

    MATH  Google Scholar 

  78. Geem Z, Kim J, Loganathan GV (2001) A New Heuristic Optimization Algorithm: Harmony Search. Simulation 76:60–68. https://doi.org/10.1177/003754970107600201

    Article  Google Scholar 

  79. Al-sharhan S (2016) An enhanced symbiosis organisms search algorithm: an empirical study. Neural Comput Appl doi. https://doi.org/10.1007/s00521-016-2624-x

    Google Scholar 

  80. Liang JJ, Qu BY, Suganthan PN (2014) Problem Definitions and Evaluation Criteria for the CEC 2014 Special Session and Competition on Single Objective Real-Parameter Numerical Optimization

  81. Grandhi R (1993) Structural Optimization with Frequency Constraints — A Review. AIAA J 31:2296–2303. https://doi.org/10.2514/3.11928

    Article  MATH  Google Scholar 

  82. Kaveh A, Ilchi M, Taha G (2013) An improved ray optimization algorithm for design of truss structures. Period Polytech 2:97–112. https://doi.org/10.3311/PPci.7166

    Article  Google Scholar 

  83. Kaveh A, Ghazaan MI (2014) Enhanced colliding bodies algorithm for truss optimization with frequency constraints. J Comput Civ Eng 29:1–11. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000445

    Google Scholar 

  84. Miao F, Zhou Y, Luo Q (2018) A modified symbiotic organisms search algorithm for unmanned combat aerial vehicle route planning problem. J Oper Res Soc 5682:1–32. https://doi.org/10.1080/01605682.2017.1418151

    Google Scholar 

  85. Bureerat S, Ph D, Pholdee N, Ph D (2015) Optimal Truss Sizing Using an Adaptive Differential Evolution Algorithm. J Comput Civ Eng. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000487

    Google Scholar 

  86. Ou-yang C, Hanyata TB, Samadhi TMAA (2015) Hybrid self-adaptive-velocity particle swarm optimisation-Cooper heuristic for the facility location allocation problem in Jakarta. https://doi.org/10.1080/23302674.2015.1029565

  87. Pham HA (2016) Advances in Engineering Software Truss optimization with frequency constraints using enhanced differential evolution based on adaptive directional mutation and nearest neighbor comparison. Adv Eng Softw 102:142–154. https://doi.org/10.1016/j.advengsoft.2016.10.004

    Article  Google Scholar 

  88. Lieu QX, Do DTT, Lee J (2018) An adaptive hybrid evolutionary firefly algorithm for shape and size optimization of truss structures with frequency constraints. Comput Struct 195:99–112. https://doi.org/10.1016/j.compstruc.2017.06.016

    Article  Google Scholar 

  89. Ho-Huu V, Nguyen-Thoi T, Truong-Khac T, Le-Anh L, Vo-Duy T (2016) An improved differential evolution based on roulette wheel selection for shape and size optimization of truss structures with frequency constraints. Neural Comput Appl 29:167–185. https://doi.org/10.1007/s00521-016-2426-1

    Article  Google Scholar 

  90. Kaveh A, Javadi SM (2013) Shape and size optimization of trusses with multiple frequency constraints using harmony search and ray optimizer for enhancing the particle swarm optimization algorithm. 1605:1595–1605. https://doi.org/10.1007/s00707-013-1006-z

  91. Kaveh A, Zolghadr A (2017) Cyclical parthenogenesis algorithm for layout optimization of truss structures with frequency constraints. Eng Optim 0:1–18. https://doi.org/10.1080/0305215X.2016.1245730

    Google Scholar 

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

    Article  Google Scholar 

  93. Jalili S, Talatahari S (2017) Optimum Design of Truss Structures Under Frequency Constraints using Hybrid CSS-MBLS Algorithm. 00:1–14. https://doi.org/10.1007/s12205-017-1407-y

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, GPERI, Gujarat Technological University, Ahmedabad, Gujarat, India

    Sumit Kumar

  2. Department of Mechanical Engineering, School of Technology, GSFC University, Vadodara, Gujarat, India

    Ghanshyam G. Tejani

  3. School of Information and Communication Technology, Griffith University, Nathan Campus, Brisbane, QLD, 4111, Australia

    Seyedali Mirjalili

Authors
  1. Sumit Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ghanshyam G. Tejani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Seyedali Mirjalili
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ghanshyam G. Tejani.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kumar, S., Tejani, G.G. & Mirjalili, S. Modified symbiotic organisms search for structural optimization. Engineering with Computers 35, 1269–1296 (2019). https://doi.org/10.1007/s00366-018-0662-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-018-0662-y

Keywords

Search

Navigation