Abstract
The evaporation rate-based water cycle algorithm (WCA-ER) is one of the famous nature-inspired metaheuristic optimization methods asserted to simulate principal idea behind observation of water cycle process with evaporation rate where how rivers and streams flow to the sea. In WCA-ER, an evaporation rate notion was identified formatively to standard WCA for achieving a better balance between the exploration and exploitation phases. This enables making better choice decision. Furthermore, in this study the WCA-ER is equipped with a greedy selection scheme bringing about much efficient search technique for obtaining the optimal designs by maintaining solution diversity and enhancing the exploitation phase. So, the main objective of this paper is to attain optimal sizing designs of both planar and space steel frame structures using WCA-ER with greedy selection. In this context, the WCA-ER with greedy selection choses the W steel sections to assign the member groups treated as design variables. Not only the strength and stability constraints imposing from LRFD-AISC code of practice design, but also the deflection, drift, and geometric constraints are taken into account in design optimization. The optimally frame designs obtained by WCA-ER with greedy selection are tabulated and they are compared with previously reported optimum solutions via other metaheuristic algorithms. The achieved best feasible steel frame structures for design examples illustrate the robustness and efficiency of the algorithmic performance of the WCA-ER with greedy selection.
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References
AISC. (1999). Load and resistance factor design specification for structural steel buildings.
Aydodu, I., & Saka, M. P. (2012). Ant colony optimization of irregular steel frames including elemental warping effect. Advances in Engineering Software, 44, 150–169. https://doi.org/10.1016/J.ADVENGSOFT.2011.05.029
Aydogdu, I. (2010). Optimum design of 3-d irregular steel frames using ant colony optimization and harmony search algorithms. Middle East Technical University.
Aydogdu, I., Carbas, S., & Akin, A. (2017). Effect of Levy Flight on the discrete optimum design of steel skeletal structures using metaheuristics. Steel and Composite Structures, 24, 93–112. https://doi.org/10.12989/scs.2017.24.1.093
Azad, S. K. (2021). Design optimization of real-size steel frames using monitored convergence curve. Structural and Multidisciplinary Optimization, 63, 267–288. https://doi.org/10.1007/S00158-020-02692-3/FIGURES/23
Babaei, M., & Mollayi, M. (2019). An improved constrained differential evolution for optimal design of steel frames with discrete variables. Mechanics Based Design of Structures and Machines, 48, 697–723. https://doi.org/10.1080/15397734.2019.1657890
Baradaran, M. R., & Madhkhan, M. (2019). Application of an improved genetic algorithm for optimal design of planar steel frames. Periodica Polytechnica Civil Engineering, 63, 141–151. https://doi.org/10.3311/PPCI.13039
Bybordiani, M., & Kazemzadeh Azad, S. (2019). Optimum design of steel braced frames considering dynamic soil-structure interaction. Structural and Multidisciplinary Optimization, 60, 1123–1137. https://doi.org/10.1007/s00158-019-02260-4
Carbas, S., Aydogdu, I. (2018). Optimal design of 2-D steel frames utilizing symbiotic organisms search algorithm. In: Akgul, M., Yilmaz, I., Ipek, A. (eds.) Proceedings of The international conference on mathematical studies and applications. Karaman, Turkey, pp 215–220.
Carbas, S., & Aydogdu, I. (2021). Cuckoo search for optimum design of real-sized high-level steel frames (pp. 123–145). Springer.
Carbas, S., Toktas, A., & Ustun, D. (Eds.). (2021). Nature-inspired metaheuristic algorithms for engineering optimization applications. Springer.
Cui, L., Li, G., Zhu, Z., Lin, Q., Wong, K.-C., Chen, J., Lu, N., & Lu, J. (2018). Adaptive multiple-elites-guided composite differential evolution algorithm with a shift mechanism. Information Sciences (ny), 422, 122–143. https://doi.org/10.1016/j.ins.2017.09.002
Daloglu, A. T., Artar, M., Özgan, K., & Karakas, A. (2016). Optimum design of steel space frames including soil-structure interaction. Structural and Multidisciplinary Optimization, 54, 117–131. https://doi.org/10.1007/S00158-016-1401-X
Dogan, E., & Ozyuksel Ciftcioglu, A. (2019). Weight optimization of steel frames with cellular beams through improved hunting search algorithm. Advances in Structural Engineering, 23, 1024–1037. https://doi.org/10.1177/1369433219884456
Dogan, E., & Saka, M. P. (2012). Optimum design of unbraced steel frames to LRFD–AISC using particle swarm optimization. Advances in Engineering Software, 46, 27–34. https://doi.org/10.1016/J.ADVENGSOFT.2011.05.008
Dorigo, M., & Stützle, T. (2004). Ant colony optimization. MIT Press.
El-Hameed, M. A., & El-Fergany, A. A. (2016). Water cycle algorithm-based load frequency controller for interconnected power systems comprising non-linearity. IET Generation, Transmission and Distribution, 10, 3950–3961. https://doi.org/10.1049/iet-gtd.2016.0699
Ellingwood, B. (1986). Structural serviceability: A critical appraisal and research needs. Journal of the Structural Engineering. American Society of Civil Engineers, 112, 2646–2664. https://doi.org/10.1061/(asce)0733-9445(1986)112:12(2646)
Erol, O. K., & Eksin, I. (2006). A new optimization method: Big bang-big crunch. Advances in Engineering Software, 37, 106–111. https://doi.org/10.1016/J.ADVENGSOFT.2005.04.005
Eskandar, H., Sadollah, A., & Bahreininejad, A. (2013). Weight optimization of truss structures using water cycle algorithm. International Journal of Optimization in Civil Engineering, 3, 115–129.
Eskandar, H., Sadollah, A., Bahreininejad, A., & Hamdi, M. (2012). Water cycle algorithm: A novel metaheuristic optimization method for solving constrained engineering optimization problems. International Journal of Optimization in Civil Engineering, 110–111, 151–166. https://doi.org/10.1016/j.compstruc.2012.07.010
Farrokh Ghatte, H. (2021). A hybrid of firefly and biogeography-based optimization algorithms for optimal design of steel frames. Arabian Journal for Science and Engineering, 46, 4703–4717. https://doi.org/10.1007/S13369-020-05118-W/FIGURES/13
Farshchin, M., Maniat, M., Camp, C. V., & Pezeshk, S. (2018). School based optimization algorithm for design of steel frames. Engineering Structures, 171, 326–335. https://doi.org/10.1016/J.ENGSTRUCT.2018.05.085
Fathali, M. A., & Hoseini Vaez, S. R. (2020). Optimum performance-based design of eccentrically braced frames. Engineering Structures, 202, 109857. https://doi.org/10.1016/J.ENGSTRUCT.2019.109857
Gao, K., Zhang, Y., Sadollah, A., Lentzakis, A., & Rong, S. (2017). Jaya, harmony search and water cycle algorithms for solving large-scale real-life urban traffic light scheduling problem. Swarm and Evolutionary Computation, 37, 58–72. https://doi.org/10.1016/j.swevo.2017.05.002
Geem, Z. W., Kim, J. H., & Loganathan, G. V. (2001). A new heuristic optimization algorithm: Harmony search. SIMULATION, 76, 60–68. https://doi.org/10.1177/003754970107600201
Gholizadeh, S., Danesh, M., & Gheyratmand, C. (2020). A new Newton metaheuristic algorithm for discrete performance-based design optimization of steel moment frames. Computers & Structures, 234, 106250. https://doi.org/10.1016/J.COMPSTRUC.2020.106250
Gholizadeh, S., & Ebadijalal, M. (2018). Performance based discrete topology optimization of steel braced frames by a new metaheuristic. Advances in Engineering Software, 123, 77–92. https://doi.org/10.1016/J.ADVENGSOFT.2018.06.002
Gholizadeh, S., & Milany, A. (2018). An improved fireworks algorithm for discrete sizing optimization of steel skeletal structures. Engineering Optimization, 50, 1829–1849. https://doi.org/10.1080/0305215X.2017.1417402
Glover, F. (1989). Tabu search: Part I. ORSA Journal on Computing, 1, 190–206. https://doi.org/10.1287/IJOC.1.3.190
Goldberg, D. E., & Holland, J. H. (1988). Genetic algorithms and machine learning. Machine Learning, 3, 95–99.
Haddad, O. B., Moravej, M., & Loáiciga, H. A. (2015). Application of the water cycle algorithm to the optimal operation of reservoir systems. Journal of Irrigation and Drainage Engineering, 141, 04014064. https://doi.org/10.1061/(asce)ir.1943-4774.0000832
Hasançebi, O., & Azad, S. K. (2019). Discrete sizing of steel frames using adaptive dimensional search algorithm. Periodica Polytechnica Civil Engineering, 63, 1062–1079. https://doi.org/10.3311/PPCI.14746
Hasançebi, O., & Carbas, S. (2014). Bat inspired algorithm for discrete size optimization of steel frames. Advances in Engineering Software. https://doi.org/10.1016/j.advengsoft.2013.10.003
Jafar, R. M. S., Geng, S., Ahmad, W., Hussain, S., & Wang, H. (2018). A comprehensive evaluation: Water cycle algorithm and its applications. In J. Qiao, X. Zhao, L. Pan, X. Zuo, X. Zhang, Q. Zhang, & S. Huang (Eds.), Bio-inspired computing: Theories and applications: 13th international conference, BIC-TA 2018, Beijing, China, November 2–4, 2018, proceedings, Part II (pp. 360–376). Springer. https://doi.org/10.1007/978-981-13-2829-9_33
Karaboga D (2005) an idea based on honey bee swarm for numerical optimization.
Kaveh, A., & Abbasgholiha, H. (2011). Optimum design of steel sway frames using big bang-big crunch algorithm. Asian Journal of Civil Engineering (building Housing), 12, 293–317.
Kaveh, A., Biabani Hamedani, K., Milad Hosseini, S., & Bakhshpoori, T. (2020). Optimal design of planar steel frame structures utilizing meta-heuristic optimization algorithms. Structures, 25, 335–346. https://doi.org/10.1016/j.istruc.2020.03.032
Kaveh, A., & Dadras Eslamlou, A. (2020). Metaheuristic optimization algorithms in civil engineering: New applications. Springer.
Kaveh, A., & Ghazaan, M. I. (2018a). Optimum seismic design of 3D irregular steel frames using recently developed metaheuristic algorithms. Journal of Computing in Civil Engineering, 32, 04018015. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000760
Kaveh, A., & Ghazaan, M. I. (2018b). Meta-heuristic algorithms for optimal design of real-size structures. Springer.
Kaveh, A., Kamalinejad, M., & Biabani Hamedani, K. (2021). Enhanced versions of the shuffled shepherd optimization algorithm for the optimal design of skeletal structures. Structures, 29, 1463–1495. https://doi.org/10.1016/j.istruc.2020.12.032
Kaveh, A., Khodadadi, N., Azar, B. F., & Talatahari, S. (2021). Optimal design of large-scale frames with an advanced charged system search algorithm using box-shaped sections. Engineering Computations, 37, 2521–2541. https://doi.org/10.1007/S00366-020-00955-7/FIGURES/14
Kaveh, A., Rohollah-Hoseini-Vaez, S., & Hosseini, P. (2018). Simplified dolphin echolocation algorithm for optimum design of frame. Smart Structures and System, 21, 321–333. https://doi.org/10.12989/sss.2018.21.3.321
Kennedy, J., Eberhart, R. (1995). Particle swarm optimization. In Proceedings of ICNN’95: International Conference on Neural Networks. IEEE, pp 1942–1948.
Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220, 671–680. https://doi.org/10.1126/SCIENCE.220.4598.671
Korashy, A., Kamel, S., Youssef, A.R., Jurado, F. (2019). Evaporation rate water cycle algorithm for optimal coordination of direction overcurrent relays. In 2018 20th International Middle East Power Systems Conference, MEPCON 2018: Proceedings. Institute of Electrical and Electronics Engineers Inc., pp 643–648.
Liu, Y., Lv, M., & Zuo, W. (2012). A new multimodal particle swarm optimization algorithm based on greedy algorithm. International Journal of Computational Intelligence and Applications. https://doi.org/10.1142/S1469026812500204
Maheri, M. R., & Talezadeh, M. (2018). An enhanced imperialist competitive algorithm for optimum design of skeletal structures. Swarm and Evolutionary Computation, 40, 24–36. https://doi.org/10.1016/j.swevo.2017.12.001
Mouatadid L (2016) Greedy Algorithms: Interval Scheduling. In: Algorithm Des. Anal. Complex. (Lecture Notes). . Retrieved 5 Jul 2021 from http://www.cs.toronto.edu/~lalla/373s16/notes/ISP.pdf.
Pahnehkolaei, S. M. A., Alfi, A., Sadollah, A., & Kim, J. H. (2017). Gradient-based Water cycle algorithm with evaporation rate applied to chaos suppression. Applied Soft Computing, 53, 420–440. https://doi.org/10.1016/j.asoc.2016.12.030
Rechenberg, I. (1965). Cybernetic solution path of an experimental problem, Technical Report Library Translation No. 1122. Farnborough.
Rezk, H., Fathy, A., Zaki Diab, A. A., & Al-Dhaifallah, M. (2019). The application of water cycle optimization algorithm for optimal placement of wind turbines in wind farms. Energies, 12, 4335. https://doi.org/10.3390/en12224335
Sadollah, A., Kim, J. H., Eskandar, H., & Yoo, D. G. (2013). Sizing optimization of sandwich panels having prismatic core using water cycle algorithm. In Proceedings 2013 4th global congress on intelligent systems, GCIS 2013. IEEE Computer Society, pp 325–328.
Sadollah, A., Eskandar, H., Bahreininejad, A., & Kim, J. H. (2015a). Water cycle algorithm with evaporation rate for solving constrained and unconstrained optimization problems. Applied Soft Computing, 30, 58–71. https://doi.org/10.1016/j.asoc.2015.01.050
Sadollah, A., Eskandar, H., Bahreininejad, A., & Kim, J. H. (2015b). Water cycle, mine blast and improved mine blast algorithms for discrete sizing optimization of truss structures. Computers & Structures, 149, 1–16. https://doi.org/10.1016/j.compstruc.2014.12.003
Sadollah, A., Yoo, D. G., Yazdi, J., & Kim, J. H. (2014). Application of water cycle algorithm for optimal cost design of water distribution systems. The 11th International Conference on Hydroinformatics (pp. 516–523). Curran Associates Inc.
Saedi Daryan, A., Salari, M., Farhoudi, N., & Palizi, S. (2021). Seismic design optimization of steel frames with steel shear wall system using modified dolphin algorithm. Int J Steel Struct, 21, 771–786. https://doi.org/10.1007/S13296-021-00472-3/FIGURES/16
Saka MP, Dogan E (2012) Design optimization of moment resisting steel frames using a cuckoo search algorithm. In: Topping BHV (ed) Proceedings of the Eleventh International Conference on Computational Structures Technology. Civil-Comp Press.
Saka, M. P. (2007). Optimum design of steel frames using stochastic search techniques based on natural phenomena: A review. In B. H. V. Topping (Ed.), Civil engineering computations: Tools and techniques (pp. 105–147). Saxe-Coburg Publications.
Saka, M. P., & Aydogdu, I. (2021). Performance evaluation of artificial bee colony algorithm and its variants in the optimum design of steel skeletal structures. Asian J Civ Eng, 22, 73–91. https://doi.org/10.1007/s42107-020-00299-z
Shi, Y. (2011). Brain storm optimization algorithm. In: Ying, T., Yuhui, Shi, Yi, C., Guoyin, W. (eds) International conference in swarm intelligence (ICSI 2011: Advances in Swarm Intelligence). Springer, Berlin, Heidelberg, pp 303–309.
Simon, D. (2008). Biogeography-based optimization. IEEE Transactions on Evolutionary Computation, 12, 702–713. https://doi.org/10.1109/TEVC.2008.919004
Talatahari, S., & Azizi, M. (2020a). Optimum design of building structures using tribe-interior search algorithm. Structures, 28, 1616–1633. https://doi.org/10.1016/j.istruc.2020.09.075
Talatahari, S., & Azizi, M. (2020b). Optimal design of real-size building structures using quantum-behaved developed swarm optimizer. The Structural Design of Tall and Special Buildings, 29, e1747. https://doi.org/10.1002/TAL.1747
Talatahari, S., Jalili, S., & Azizi, M. (2021). Optimum design of steel building structures using migration-based vibrating particles system. Structures, 33, 1394–1413. https://doi.org/10.1016/j.istruc.2021.05.028
Tunca, O., Aydogdu, I., Carbas, S. (2018). Structural design optimization through water cycle algorithm with evaporation rate. In International conference on applied mathematics in engineering. Balıkesir, Turkey, p 169.
Tunca, O., & Carbas, S. (2016). Biogeography-based optimization algorithm for designing of planar steel frames. International Journal of Intelligent Systems and Applications in Engineering, 4, 53–57. https://doi.org/10.18201/IJISAE.266128
Xiang, X. (2015). An improved firefly algorithm for numerical optimisation. International Journal of Computing Science and Mathematics, 6, 201–210. https://doi.org/10.1504/IJCSM.2015.069466
Xin, J., Zhong, J., Li, S., Sheng, J., & Cui, Y. (2019). Greedy mechanism based particle swarm optimization for path planning problem of an unmanned surface vehicle. Sensors (switzerland). https://doi.org/10.3390/s19214620
Yang, X.S., Deb, S. (2009). Cuckoo search via Lévy flights. In 2009 World congress on nature and biologically inspired computing, NABIC 2009: Proceedings. pp 210–214.
Yang, X. S., et al. (2010). A new metaheuristic bat-inspired algorithm. In J. R. González, D. A. Pelta, & C. Cruz (Eds.), Studies in computational intelligence; nature inspired cooperative strategies for optimization (NICSO 2010) (pp. 65–74). Springer.
Zakian, P. (2019). Meta-heuristic design optimization of steel moment resisting frames subjected to natural frequency constraints. Advances in Engineering Software, 135, 102686. https://doi.org/10.1016/J.ADVENGSOFT.2019.102686
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Carbas, S. Optimum Sizing Design of Steel Frame Structures Using Evaporation Rate-Based Water Cycle Algorithm with Greedy Selection. Int J Steel Struct 22, 958–981 (2022). https://doi.org/10.1007/s13296-022-00616-z
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DOI: https://doi.org/10.1007/s13296-022-00616-z