Home Reptile search algorithm and kriging surrogate model for structural design optimization with natural frequency constraints
Article
Licensed
Unlicensed Requires Authentication

Reptile search algorithm and kriging surrogate model for structural design optimization with natural frequency constraints

  • Betül Sultan Yildiz , Sujin Bureerat , Natee Panagant

    Natee Panagant received a B.Eng. in Mechanical Engineering from Chulalongkorn University, Bangkok, Thailand, M.Eng. and Ph.D. in Mechanical Engineering from Khon Kaen University, Khon Kaen, Thailand. Currently, he is a lecturer at the Department of Mechanical Engineering, Khon Kaen University. His research interests include multidisciplinary design optimization, evolutionary computation, and finite element analysis.

         , Pranav Mehta

    Pranav Mehta is an Assistant Professor at the Department of Mechanical Engineering, Dharmsinh Desai University.

         and Ali Riza Yildiz EMAIL logo
Published/Copyright: October 7, 2022
Become an author with De Gruyter Brill
Submit Manuscript Author Information
Materials Testing
From the journal Materials Testing Volume 64 Issue 10

Abstract

This study explores the use of a recent metaheuristic algorithm called a reptile search algorithm (RSA) to handle engineering design optimization problems. It is the first application of the RSA to engineering design problems in literature. The RSA optimizer is first applied to the design of a bolted rim, which is constrained optimization. The developed algorithm is then used to solve the optimization problem of a vehicle suspension arm, which aims to solve the weight reduction under natural frequency constraints. As function evaluations are achieved by finite element analysis, the Kriging surrogate model is integrated into the RSA algorithm. It is revealed that the optimum result gives a 13% weight reduction compared to the original structure. This study shows that RSA is an efficient metaheuristic as other metaheuristics such as the mayfly optimization algorithm, battle royale optimization algorithm, multi-level cross-entropy optimizer, and red fox optimization algorithm.

Keywords: battle royale optimization algorithm; brake pedal; engineering structures; mayfly optimization algorithm; multi-level cross-entropy optimizer; optimization; red fox optimization algorithm; reptile search algorithm
Corresponding author: Ali Riza Yildiz, Department of Mechanical Engineering, Bursa Uludag University, Görükle, Bursa 16059, Turkey, E-mail:

About the authors

Natee Panagant

Natee Panagant received a B.Eng. in Mechanical Engineering from Chulalongkorn University, Bangkok, Thailand, M.Eng. and Ph.D. in Mechanical Engineering from Khon Kaen University, Khon Kaen, Thailand. Currently, he is a lecturer at the Department of Mechanical Engineering, Khon Kaen University. His research interests include multidisciplinary design optimization, evolutionary computation, and finite element analysis.

Pranav Mehta

Pranav Mehta is an Assistant Professor at the Department of Mechanical Engineering, Dharmsinh Desai University.

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

[1] L. Abualigah, M. AbdElaziz, P. Sumari, Z. WooGeem, and A. H. Gandomi, “Reptile search algorithm (RSA): a nature-inspired meta-heuristic optimizer,” Exp. Syst. Appl., vol. 191, no. 116158, 2022, https://doi.org/10.1016/j.eswa.2021.116158.Search in Google Scholar

[2] L. Abualigah, D. Yousri, M. Abd Elaziz, A. A. Ewees, M. A. A. Al-qaness, and A. H. Gandomi, “Aquila optimizer: a novel meta-heuristic optimization algorithm,” Comput. Indust. Eng., vol. 157, no. 107250, 2021, https://doi.org/10.1016/j.cie.2021.107250.Search in Google Scholar

[3] A. Kaveh, H. Akbari, and S. M. Hosseini, “Plasma generation optimization: a new physically-based metaheuristic algorithm for solving constrained optimization problems,” Eng. Comput., vol. 38, no. 4, pp. 1554–1606, 2021, https://doi.org/10.1108/EC-05-2020-0235.Search in Google Scholar

[4] A. Faramarzi, M. Heidarinejad, B. Stephens, and S. Mirjalili, “Equilibrium optimizer: a novel optimization algorithm,” Knowl. Based. Syst., vol. 191, no. 105190, 2020, https://doi.org/10.1016/j.knosys.2019.105190.Search in Google Scholar

[5] G. Dhiman, M. Garg, A. Nagar, V. Kumar, and M. Dehghani, “A novel algorithm for global optimization: rat swarm optimizer,” J. Ambient. Intell. Humaniz. Comput., vol. 12, no. 8, pp. 8457–8482, 2021, https://doi.org/10.1007/s12652-020-02580-0.Search in Google Scholar

[6] A. Hassan and M. Abomoharam, “Modeling and design optimization of a robot gripper mechanism,” Robot. Comput. Integ. Manufact., vol. 46, pp. 94–103, 2017, https://doi.org/10.1016/j.rcim.2016.12.012.Search in Google Scholar

[7] S. Kumar, G. G. Tejani, N. Pholdee, S. Bureerat, and P. Mehta, “Hybrid heat transfer search and passing vehicle search optimizer for multi-objective structural optimization,” Knowl. Based. Syst., vol. 212, no. 106556, 2021, https://doi.org/10.1016/j.knosys.2020.106556.Search in Google Scholar

[8] G. Dhiman “SSC: a hybrid nature-inspired meta-heuristic optimization algorithm for engineering applications,” Knowl. Based. Syst., vol. 222, no. 106926, 2021, https://doi.org/10.1016/j.knosys.2021.106926.Search in Google Scholar

[9] M. Premkumar, P. Jangir, and R. Sowmya, “MOGBO: a new Multiobjective Gradient-Based Optimizer for real-world structural optimization problems,” Knowl. Based Syst., vol. 218, no. 106856, 2021, https://doi.org/10.1016/j.knosys.2021.106856.Search in Google Scholar

[10] E. J. Park, L. F. da Luz, and A. Suleman, “Multidisciplinary design optimization of an automotive magnetorheological brake design,” Comput. Struct., vol. 86, nos. 3–5, pp. 207–216, 2008, https://doi.org/10.1016/j.compstruc.2007.01.035.Search in Google Scholar

[11] S. Mirjalili, Genetic Algorithm Evolutionary Algorithms and Neural Networks, Cham, Springer International Publishing, 2019, vol. 780, pp. 43–55.10.1007/978-3-319-93025-1_4Search in Google Scholar

[12] S. Mirjalili, “The ant lion optimizer,” Adv. Eng. Softw., vol. 83, pp. 80–98, 2015, https://doi.org/10.1016/j.advengsoft.2015.01.010.Search in Google Scholar

[13] S. Mirjalili, A. H. Gandomi, S. Z. Mirjalili, S. Saremi, H. Faris, and S. M. Mirjalili, “Salp Swarm Algorithm: a bio-inspired optimizer for engineering design problems,” Adv. Eng. Softw., vol. 114, pp. 163–191, 2017, https://doi.org/10.1016/j.advengsoft.2017.07.002.Search in Google Scholar

[14] S. Mirjalili and A. Lewis, “The whale optimization algorithm,” Adv. Eng. Softw., vol. 95, pp. 51–67, 2016, https://doi.org/10.1016/j.advengsoft.2016.01.008.Search in Google Scholar

[15] B. Abdollahzadeh, F. S. Gharehchopogh, and S. Mirjalili, “Artificial gorilla troops optimizer: a new nature-inspired metaheuristic algorithm for global optimization problems,” Int. J. Intellig. Syst., vol. 36, no. 10, pp. 5887–5958, 2021, https://doi.org/10.1002/int.22535.Search in Google Scholar

[16] A. Srivastava and D. K. Das, “A New Kho-Kho optimization algorithm: An application to solve combined emission economic dispatch and combined heat and power economic dispatch problem,” Eng Appl. Artifi. Intell., vol. 94, no. 103763, 2020, https://doi.org/10.1016/j.engappai.2020.103763.Search in Google Scholar

[17] I. Ahmadianfar, O. Bozorg-Haddad, and X. Chu, “Gradient-based optimizer: A new metaheuristic optimization algorithm,” Inform. Sci., vol. 540, pp. 131–159, 2020, https://doi.org/10.1016/j.ins.2020.06.037.Search in Google Scholar

[18] V. Hayyolalam and A. A. P. Kazem, “Black widow optimization algorithm: a novel meta-heuristic approach for solving engineering optimization problems,” Eng. Appl. Artif. Intell., vol. 87, no. 103249, 2020, https://doi.org/10.1016/j.engappai.2019.103249.Search in Google Scholar

[19] M. Jain, V. Singh, and A. Rani, “A novel nature-inspired algorithm for optimization: squirrel search algorithm,” Swarm Evol. Comput., vol. 44, pp. 148–175, 2019, https://doi.org/10.1016/j.swevo.2018.02.013.Search in Google Scholar

[20] A. A. Heidari, S. Mirjalili, H. Faris, I. Aljarah, M. Mafarja, and H. Chen, “Harris hawks optimization: algorithm and applications,” Future Gener. Comput. Syst., vol. 97, pp. 849–872, 2019, https://doi.org/10.1016/j.future.2019.02.028.Search in Google Scholar

[21] A. Kaveh, M. Khanzadi, and M. Rastegar Moghaddam, “Billiards-inspired optimization algorithm; a new meta-heuristic method,” Structures, vol. 27, pp. 1722–1739, 2020, https://doi.org/10.1016/j.istruc.2020.07.058.Search in Google Scholar

[22] K. Zervoudakis and S. Tsafarakis, “A mayfly optimization algorithm,” Comput. Indust. Eng., vol. 145, no. 106559, 2020, https://doi.org/10.1016/j.cie.2020.106559.Search in Google Scholar

[23] S. Talatahari and M. Azizi, “Chaos Game Optimization: a novel metaheuristic algorithm,” Artifi. Intell. Rev., vol. 54, no. 2, pp. 917–1004, 2021, https://doi.org/10.1007/s10462-020-09867-w.Search in Google Scholar

[24] G. Dhiman, K. K. Singh, A. Slowik, and V. Chang, “EMoSOA: a new evolutionary multi-objective seagull optimization algorithm for global optimization,” Int. J. Mach. Learn. Cybe., vol. 12, no. 2, pp. 571–596, 2021, https://doi.org/10.1007/s13042-020-01189-1.Search in Google Scholar

[25] T. R. Farshi, “Battle royale optimization algorithm,” Neural Comput. Appl., vol. 33, no. 4, pp. 1139–1157, 2021, https://doi.org/10.1007/s00521-020-05004-4.Search in Google Scholar

[26] B. S. Yildiz, “Slime mould algorithm and kriging surrogate model-based approach for enhanced crashworthiness of electric vehicles,” International Journal of Vehicle Design, vol. 83, no. 1, pp. 54–65, 2020. https://doi.org/10.1504/IJVD.2020.114786.Search in Google Scholar

[27] B. S. Yildiz, N. Pholdee, N. Panagant, S. Bureerat, A. R. Yildiz, and S. M. Sait, “A novel chaotic Henry gas solubility optimization algorithm for solving real-world engineering problems,” Engineering with Computers, vol. 38, pp. 871–883, 2022. https://doi.org/10.1007/s00366-020-01268-5.Search in Google Scholar

[28] B. S. Yildiz, N. Pholdee, S. Bureerat, A. R. Yildiz, and S. M. Sait, “Robust design of a robot gripper mechanism using new hybrid grasshopper optimization algorithm,” Exp. Syst., vol. 38, no. 3, 2021, Art no. e12666, https://doi.org/10.1111/exsy.12666.Search in Google Scholar

[29] E. Demirci and A. R. Yildiz, “An experimental and numerical investigation of the effects of geometry and spot welds on the crashworthiness of vehicle thin-walled structure,” Mater. Test., vol. 60, no. 6, pp. 553–561, 2018, https://doi.org/10.3139/120.111187.Search in Google Scholar

[30] B. S. Yildiz, V. Patel, N. Pholdee, S. M. Sait, S. Bureerat, and A. R. Yildiz, “Conceptual comparison of the ecogeography-based algorithm, equilibrium algorithm, marine predators algorithm and slime mold algorithm for optimal product design,” Mater. Test., vol. 63, no. 4, pp. 336–340, 2021, https://doi.org/10.1515/mt-2020-0049.Search in Google Scholar

[31] B. S. Yildiz, “Marine predators algorithm and multi-verse optimisation algorithm for optimal battery case design of electric vehicles,” International Journal of Vehicle Design, vol. 88, no. 1, pp. 1–11, 2022. https://doi.org/10.1504/IJVD.2022.124866.Search in Google Scholar

[32] E. Demirci and A. R. Yıldız, “A new hybrid approach for reliability-based design optimization of structural components,” Mater. Test., vol. 61, pp. 111–119, 2019, https://doi.org/10.3139/120.111291.Search in Google Scholar

[33] A. R. Yildiz and M. U. Erdaş, “A new Hybrid Taguchi salp swarm optimization algorithm for the robust design of real-world engineering problems,” Mater. Test., vol. 63, pp. 157–162, 2021, https://doi.org/10.1515/mt-2020-0022.Search in Google Scholar

[34] A. R. Yildiz, N. Kaya, and F. Öztürk, “Optimal design of vehicle components using topology design and optimisation,” International Journal of Vehicle Design, vol. 34, no. 4, pp. 387–398, 2004. https://doi.org/10.1504/IJVD.2004.004064.Search in Google Scholar

[35] F. MiarNaeimi, G. Azizyan, and M. Rashki, “Multi-level cross entropy optimizer (MCEO): an evolutionary optimization algorithm for engineering problems,” Eng. Comput., vol. 34, no. 4, pp. 719–739, 2018, https://doi.org/10.1007/s00366-017-0569-z.Search in Google Scholar

[36] B. S. Yıldız, N. Pholdee, S. Bureerat, M. U. Erdaş, A. R. Yıldız, and S. M. Sait, “Comparision of the political optimization algorithm, the archimedes optimization algorithm and the Levy flight algorithm for design optimization in industry,” Mater. Test., vol. 63, no. 4, pp. 356–359, 2021, https://doi.org/10.1515/mt-2020-0053.Search in Google Scholar

[37] B. S. Yildiz, “Robust design of electric vehicle components using a new hybrid salp swarm algorithm and radial basis function-based approach,” International Journal of Vehicle Design, vol. 83, no. 1, pp. 38–53, 2020. https://doi.org/10.1504/IJVD.2020.114779.Search in Google Scholar

[38] F. MiarNaeimi, G. Azizyan, and M. Rashki, “Horse herd optimization algorithm: a nature-inspired algorithm for high-dimensional optimization problems,” Knowl. Based. Syst., vol. 213, no. 106711, 2021, https://doi.org/10.1016/j.knosys.2020.106711.Search in Google Scholar

[39] T. Guler, A. Demirci, A. R. Yildiz, and U. Yavuz, “Lightweight design of an automobile hinge component using glass fiber polyamide composites,” Materials Testing, vol. 60, no. 3, pp. 306–310, 2018. https://doi.org/10.3139/120.111152.Search in Google Scholar

[40] B. S. Yıldız, N. Pholdee, S. Bureerat, A. R. Yıldız, and S. M. Sait, “Sine-cosine optimization algorithm for the conceptual design of automobile components,” Mater. Test., vol. 62, no. 7, pp. 744–748, 2020, https://doi.org/10.3139/120.111541.Search in Google Scholar

[41] E. Demirci and A. R. Yildiz, “An investigation of the crash performance of magnesium, aluminum and advanced high strength steels and different cross-sections for vehicle thin-walled energy absorber,” Mater. Test., vol. 60, nos. 7–8, pp. 661–668, 2018, https://doi.org/10.3139/120.111201.Search in Google Scholar

[42] B. S. Yıldız, S. Kumar, N. Pholdee, S. Bureerat, S. M. Sait, and A. R. Yildiz, “A new chaotic Lévy flight distribution optimization algorithm for solving constrained engineering problems,” Exp. Syst., no. E12992, 2022, https://doi.org/10.1111/exsy.12992.Search in Google Scholar

[43] D. Połap and W. Marcin, “Red fox optimization algorithm,” Exp. Syst. Appl., vol. 166, no. 114107, 2021, https://doi.org/10.1016/j.eswa.2020.114107.Search in Google Scholar

[44] A. R. Yildiz and F. Öztürk, “Hybrid Taguchi-Harmony search approach for shape optimization,” Recent Advances in Harmony Search Algorithm, Studies in Computational Intelligence, vol. 270, pp. 89–93, 2010. https://doi.org/10.1007/978-3-642-04317-8_8.Search in Google Scholar

[45] P. Mehta, B. S. Yildiz, S. M. Sait, and A. R. Yildiz, “Hunger games search algorithm for global optimization of engineering design problems,” Mater. Test., vol. 64, no. 4, pp. 524–532, 2022, https://doi.org/10.1515/mt-2022-0013.Search in Google Scholar

[46] A. R. Yildiz and P. Mehta, “Manta ray foraging optimization algorithm and hybrid Taguchi salp swarm-Nelder–Mead algorithm for the structural design of engineering components,” Mater. Test., vol. 64, no. 5, pp. 706–713, 2022, https://doi.org/10.1515/mt-2022-0012.Search in Google Scholar

[47] P. Mehta, B. S. Yildiz, S. M. Sait, and A. R. Yildiz, “Gradient-based optimizer for economic optimization of engineering problems,” Mater. Test., vol. 64, no. 5, pp. 690–696, 2022, https://doi.org/10.1515/mt-2022-0055.Search in Google Scholar

[48] N. Panagant, N. Pholdee, S. Bureerat, K. Kaen, A. R. Yıldız, and S. M. Sait, “Seagull optimization algorithm for solving real-world design optimization problems,” Mater. Test., vol. 62, no. 6, pp. 640–644, 2020, https://doi.org/10.3139/120.111529.Search in Google Scholar

[49] D. Gürses, S. Bureerat, S. M. Sait, and A. R. Yıldız, “Comparison of the arithmetic optimization algorithm, the slime mold optimization algorithm, the marine predators algorithm, the salp swarm algorithm for real-world engineering applications,” Mater. Test., vol. 63, no. 5, pp. 448–452, 2021, https://doi.org/10.1515/mt-2020-0076.Search in Google Scholar

[50] B. S. Yildiz, N. Pholdee, S. Bureerat, A. R. Yildiz, and S. M. Sait, “Enhanced grasshopper optimization algorithm using elite opposition-based learning for solving real-world engineering problems,” Eng. Comput., 2021, https://doi.org/10.1007/s00366-021-01368-w.Search in Google Scholar

[51] A. R. Yildiz, N. Kaya, N. Öztürk, and F. Öztürk, “Hybrid approach for genetic algorithm and Taguchi’s method based design optimization in the automotive industry,” Int. J. Production Research, vol. 44, pp. 4897–4914, 2006, https://doi.org/10.1080/00207540600619932.Search in Google Scholar
Received: 2022-06-04
Accepted: 2022-07-30
Published Online: 2022-10-07
Published in Print: 2022-10-26

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. In situ corrosion fatigue life of 2198-T8 Al–Li alloy based on tests and DIC technique
  3. Characterisation of a wire arc additive manufactured 308L stainless steel cylindrical component
  4. Mechanical properties of a 7075-T6 aluminum alloy at elevated temperatures
  5. Low-velocity single and repeated impact behavior of 3D printed honeycomb cellular panels
  6. Fracture mechanical evaluation of the material HCT590X
  7. Effects of forging on the mechanical properties of B4Cp/Al composite with flaked Al and Al2O3 particles
  8. Homogenization effect on precipitation kinetics and mechanical properties of an extruded AA7050 alloy
  9. Low velocity impact response of sandwich composites with hybrid glass/natural fiber face-sheet and PET foam core
  10. Earing prediction of 2090-T3 aluminum-cups using a complete homogenous fourth-order polynomial yield function
  11. Imitation of human muscle by using an electromechanical system
  12. Reptile search algorithm and kriging surrogate model for structural design optimization with natural frequency constraints
  13. Online magnetic flux leakage detection of inclusions and inhomogeneities in cold rolled steel plate
  14. Characterization of hydrogen assisted corrosion cracking of a high strength aluminum alloy
  15. Influence of illuminance on indication detectability during visual testing
  16. Quality optimization of FDM-printed (fused deposition modeling) components based on differential scanning calorimetry
https://doi.org/10.1515/mt-2022-0048
Keywords for this article
battle royale optimization algorithm; brake pedal; engineering structures; mayfly optimization algorithm; multi-level cross-entropy optimizer; optimization; red fox optimization algorithm; reptile search algorithm

Articles in the same Issue

  1. Frontmatter
  2. In situ corrosion fatigue life of 2198-T8 Al–Li alloy based on tests and DIC technique
  3. Characterisation of a wire arc additive manufactured 308L stainless steel cylindrical component
  4. Mechanical properties of a 7075-T6 aluminum alloy at elevated temperatures
  5. Low-velocity single and repeated impact behavior of 3D printed honeycomb cellular panels
  6. Fracture mechanical evaluation of the material HCT590X
  7. Effects of forging on the mechanical properties of B4Cp/Al composite with flaked Al and Al2O3 particles
  8. Homogenization effect on precipitation kinetics and mechanical properties of an extruded AA7050 alloy
  9. Low velocity impact response of sandwich composites with hybrid glass/natural fiber face-sheet and PET foam core
  10. Earing prediction of 2090-T3 aluminum-cups using a complete homogenous fourth-order polynomial yield function
  11. Imitation of human muscle by using an electromechanical system
  12. Reptile search algorithm and kriging surrogate model for structural design optimization with natural frequency constraints
  13. Online magnetic flux leakage detection of inclusions and inhomogeneities in cold rolled steel plate
  14. Characterization of hydrogen assisted corrosion cracking of a high strength aluminum alloy
  15. Influence of illuminance on indication detectability during visual testing
  16. Quality optimization of FDM-printed (fused deposition modeling) components based on differential scanning calorimetry
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 27.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/mt-2022-0048/html
Scroll to top button