# Application of Self-Adaptive Population Rao Algorithms to Optimization of Steel Grillage Structures

• Maksym Grzywiński Faculty of Civil Engineering, Czestochowa University of Technology, Czestochowa, Poland
• Tayfun Dede Department of Civil Engineering, Karadeniz Technical University, Trabzon, Turkey
• Barbaros Atmaca Department of Civil Engineering, Karadeniz Technical University, Trabzon, Turkey

### Abstract

The self-adaptive population Rao algorithms (SAP-Rao) are employed in this study to produce the optimal designs for steel grillage structures. The size variables in the optimization problem consist of the cross-sectional area of the discrete W-shapes of these beams. The LRFD-AISC design code was used to optimize the constrained size of this kind of structure. The solved problem’s primary goal is to determine the grillage structure’s minimum weight. As constraints, it is decided to use the maximum stress ratio and the maximum displacement at the inner point of the steel grillage structure. The finite element method (FEM) was employed to compute the moment and shear force of each member, as well as the joint displacement. A computer program for the study and design of grillage structures, as well as the optimization technique for SAP-Rao, was created in MATLAB. The outcomes of this study are compared to earlier efforts on grillage structures. The findings demonstrate that the optimal design of grillage structures can be successfully accomplished using the SAP-Rao method described in this paper.

### Keywords

Minimum weight, Grillage structures, Layout and size optimization, Discrete variables, SAP-Rao algorithms, MATLAB,

### References

1. AISC Manual of Steel Construction: Load and Resistance Factor Design, Vols. 1 & 2, AISC, Chicago, 1999.
2. B. Atmaca, T. Dede, M. Grzywinski, Optimization of cables size and prestressing force for a single pylon cable-stayed bridge with Jaya algorithm, Steel & Composite Structures, 34(6): 853–862, 2020, doi: 10.12989/scs.2020.34.6.853.
3. Z. Aydin, JayaX algorithm for simultaneous layout and size optimization of grillages, Arabian Journal for Science and Engineering, 48: 4991–5004, 2023, doi: 10.1007/s13369-022-07195-5.
4. S. Behera, S. Sahoob, B.B. Pati, A review on optimization algorithms and application to wind energy integration to grid, Renewable and Sustainable Energy Reviews, 48: 214–227, 2015, doi: 10.1016/j.rser.2015.03.066.
5. K. Bołbotowski, L. He, M. Gilbert, Design of optimum grillages using layout optimization, Structural and Multidisciplinary Optimization, 58: 851–868, 2018, doi: 10.1007/s00158-018-1930-6.
6. T. Dede, Optimum design of grillage structures to LRFD-AISC with teaching-learning based optimization, Structural and Multidisciplinary Optimization, 48(5): 955–964, 2013, doi: 10.1007/s00158-013-0936-3.
7. T. Dede, Jaya algorithm to solve single objective size optimization problem for steel grillage structures, Steel & Composite Structures, 26(2): 163–170, 2018, doi: 10.12989/scs.2018.26.2.163.
8. T. Dede, M. Grzywinski, R.V. Rao, B. Atmaca, The size optimization of steel braced barrel vault structure by using Rao-1 algorithm, Sigma Journal of Engineering and Natural Sciences, 38(3): 1415–1425, 2020.
9. T. Dede, B. Atmaca, M. Grzywinski, R.V. Rao, Optimal design of dome structures with recently developed algorithm: Rao series, Structures, 42: 65–79, 2022, doi: 10.1016/j.istruc.2022.06.010.
10. F. Erdal, M.P. Saka, Effect of beam spacing in the harmony search based optimum design of grillages, Asian Journal of Civil Engineering, 9(3): 215–228, 2008.
11. F. Erdal, E. Dogan, M.P. Saka, An improved particle swam optimizer for steel grillage systems, Structural Engineering and Mechanics, 47(4): 513–530, 2013, doi: 10.12989/sem.2013.47.4.513.
12. Z.W. Geem, J.H. Kim, G.V. Loganathan, A new heuristic optimization algorithm: harmony search, Simulation, 76(2): 60–68, 2001, doi: 10.1177/003754970107600201.
13. Z.W. Geem, Optimal cost design of water distribution networks using harmony search, Dissertation, Korea University, South Korea, 2000.
14. M. Grzywinski, T. Dede, Y.I. Ozdemir, Optimization of the braced dome structures by using Jaya algorithm with frequency constraints, Steel & Composite Structures, 30(1): 47–55, 2019, doi: 10.12989/scs.2019.30.1.047.
15. M. Grzywinski, T. Dede, B. Atmaca, Optimum design of barrel vaults structures using Rao algorithm, [in:] J. Szafran, M. Kaminski [Eds.], Lightweight Structures in Civil Engineering, Lodz University of Technology, pp. 37–46, 2022, doi: 10.34658/9788366741591.
16. M. Grzywinski, Size and shape design optimization of truss structures using the Jaya algorithm, Computer Assisted Methods in Engineering and Science, 27(2–3): 177–184, 2020, doi: 10.24423/cames.282.
17. M. Grzywinski, Optimization of spatial truss towers based on Rao algorithms, Structural Engineering and Mechanics, 81(3): 367–378, 2022, doi: 10.12989/sem.2022.81.3.367.
18. J.H. Holland, Adaptation in Natural and Artificial System, MIT Press, 1992, doi: 10.7551/mitpress/1090.001.0001.
19. D. Karaboga, Artificial bee colony algorithm, Scholarpedia, 5(3): 6915, 2010, doi: 10.4249/scholarpedia.6915.
20. A. Kaveh, S. Talatahari, Charged system search for optimum grillage design using the LRFD-AISC code, Journal of Constructional Steel Research, 66: 767–771, 2010, doi: 10.1016/j.jcsr.2010.01.007.
21. A. Kaveh, P. Asadi, V.R. Mahdavi, Enhaced two-dimensional CBO algorithm for design of grillage systems, Iranian Journal of Science and Technology, Transactions of Civil Engineering, 41: 263–273, 2017, doi: 10.1007/s40996-017-0059-y.
22. T. Lewinski, J.J. Telega, Michell-like grillages and structures with locking, Archives of Mechanics, 53(4–5): 457–485, 2001.
23. B. Pokusinski, M. Kaminski, Lattice domes reliability by the perturbation-based approaches vs. semi-analytical method, Computers and Structures, 221: 179–192, 2019, doi: 10.1016/j.compstruc.2019.05.012.
24. R.V. Rao, V.J. Savsani, D.P. Vakharia, Teaching-learning based optimization: A novel method for constrained mechanical design optimization problems, Computer-Aided Design, 43(3): 303–315, 2011, doi: 10.1016/j.cad.2010.12.015.
25. R.V. Rao, Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems, International Journal of Industrial Engineering Computations, 7: 19–34, 2016, doi: 10.5267/j.ijiec.2015.8.004.
26. R.V. Rao, Teaching-learning-based optimization algorithm, [in:] Teaching Learning Based Optimization Algorithm: And Its Engineering Applications, Springer International Publishing Switzerland, pp. 9–39, 2016, doi: 10.1007/978-3-319-22732-0.
27. R.V. Rao, Rao algorithms: Three metaphor-less simple algorithms for solving optimization problems, International Journal of Industrial Engineering Computations, 11: 107–130, 2020, doi: 10.5267/j.ijiec.2019.6.002.
28. R.V. Rao, H.S. Keesari, A self-adaptive population Rao algorithm for optimization of selected bio-energy systems, Journal of Computational Design and Engineering, 8(1): 69–96, 2021, doi: 10.1093/jcde/qwaa063.
29. M.P. Saka, Optimum design of grillage systems using genetic algorithms, Computer-Aided Civil and Infrastructure Engineering, 13(4): 297–302, 1998, doi: 10.1111/0885-9507.00108.
30. M.P. Saka, A. Daloglu, F. Malhas, Optimum spacing design of grillage systems using a genetic algorithm, Advances in Engineering Software, 31: 863–873, 2000, doi: 10.1016/S0965-9978(00)00048-X.
31. M.P. Saka, F. Erdal, Harmony search based algorithm for the optimum design of grillage systems to LRFD-AISC, Structural and Multidisciplinary Optimization, 38: 25–41, 2009, doi: 10.1007/s00158-008-0263-2.
32. Rao algorithms and R-method, https://sites.google.com/view/raoalgorithms/.
Published
Nov 7, 2023
How to Cite
GRZYWIŃSKI, Maksym; DEDE, Tayfun; ATMACA, Barbaros. Application of Self-Adaptive Population Rao Algorithms to Optimization of Steel Grillage Structures. Computer Assisted Methods in Engineering and Science, [S.l.], v. 30, n. 4, p. 505–520, nov. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/1000>. Date accessed: 23 june 2024. doi: http://dx.doi.org/10.24423/cames.1000.
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CMM-SolMech 2022