A Hybrid Cuckoo Search Algorithm for Cost Optimization of Mechanically Stabilized Earth Walls

  • M. Altun
  • Y. Yalcin
  • O. PekcanEmail author
Part of the Springer Tracts in Nature-Inspired Computing book series (STNIC)


Having a wide range of applications in civil engineering practice, Mechanically Stabilized Earth Walls (MSEWs) are regarded as efficient and reliable alternatives to the conventional retaining structure types. As is often the case in engineering, the performance and cost-effectiveness of these structures rely on robust design strategies, which must be proficient to yield optimal solutions in multimodal spaces. While the inherent characteristics of engineering problems often render the design a challenging task, metaheuristic algorithms are suitable options provided that problem-specific considerations and modifications are implemented. In this regard, Cuckoo Search (CS) and its variants are successful in many engineering applications. In the present study, CS is adopted to optimize the reinforcement type, length, and layout of MSEWs and a hybrid CS (HCSDE) variant based on Differential Evolution formulation is developed to further enhance the search capability of the algorithm. The proposed algorithm is applied to various MSEW design benchmarks and comparatively evaluated with respect to well-established methods such as Genetic Algorithm and Particle Swarm Optimization. The results of the study indicate that CS is competent for the problem and the capability of the algorithm can be further enhanced through the proposed adaptations in HCSDE. The improved solutions of HCSDE compared to the other optimization methods highlight the proposed formulation as a promising algorithm for practical implementations.


Metaheuristics Cuckoo search Differential evolution Engineering optimization Mechanically stabilized earth walls 


  1. 1.
    Dhadwal M, Jung S, Kim C (2014) Advanced particle swarm assisted genetic algorithm for constrained optimization problems. Comput Optim Appl 58:781–806MathSciNetzbMATHGoogle Scholar
  2. 2.
    Gogna A, Tayal A (2013) Metaheuristics: review and application. J Exp Theor Artif Intell 25:503–526Google Scholar
  3. 3.
    Boussaïd I, Lepagnot J, Siarry P (2013) A survey on optimization metaheuristics. Inf Sci (Ny) 237:82–117MathSciNetzbMATHGoogle Scholar
  4. 4.
    Altun M, Pekcan O (2017) A modified approach to cross entropy method: Elitist stepped distribution algorithm. Appl Soft Comput J 58:756–769Google Scholar
  5. 5.
    Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley Longman Publishing Co., Inc., BostonzbMATHGoogle Scholar
  6. 6.
    Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359MathSciNetzbMATHGoogle Scholar
  7. 7.
    Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE international conference on neural networks. Proceedings, pp 1942–1948Google Scholar
  8. 8.
    Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680Google Scholar
  9. 9.
    Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci (Ny) 179:2232–2248zbMATHGoogle Scholar
  10. 10.
    Rao RV, Savsani VJ, Vakharia DP (2011) Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Des 43:303–315Google Scholar
  11. 11.
    Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82Google Scholar
  12. 12.
    Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471MathSciNetzbMATHGoogle Scholar
  13. 13.
    Yang X, Deb S, Behaviour ACB (2009) Cuckoo search via Levy flights. In: 2009 world congress on nature & biologically inspired computing (NaBIC). Coimbatore, India, pp 210–214Google Scholar
  14. 14.
    Hasançebi O, Teke T, Pekcan O (2013) A bat-inspired algorithm for structural optimization. Comput Struct 128:77–90Google Scholar
  15. 15.
    Lei H, Chuanxin Z, Changzhi W et al (2017) Discrete firefly algorithm for scaffolding construction scheduling. J Comput Civ Eng 31:4016064Google Scholar
  16. 16.
    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 110–111:151–166Google Scholar
  17. 17.
    Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61Google Scholar
  18. 18.
    Gandomi AH (2014) Interior search algorithm (ISA): a novel approach for global optimization. ISA Trans 53:1168–1183Google Scholar
  19. 19.
    Cheng M-Y, Prayogo D (2014) Symbiotic organisms search: a new metaheuristic optimization algorithm. Comput Struct 139:98–112Google Scholar
  20. 20.
    Hasançebi O, Azad SK (2015) Adaptive dimensional search: a new metaheuristic algorithm for discrete truss sizing optimization. Comput Struct 154:1–16Google Scholar
  21. 21.
    Askarzadeh A (2016) A novel metaheuristic method for solving constrained engineering optimization problems: crow search algorithm. Comput Struct 169:1–12Google Scholar
  22. 22.
    Yalcin Y, Pekcan O (2018) Nuclear fission–nuclear fusion algorithm for global optimization: a modified big bang–big crunch algorithm. Neural Comput ApplGoogle Scholar
  23. 23.
    Jain M, Singh V, Rani A (2019) A novel nature-inspired algorithm for optimization: squirrel search algorithm. Swarm Evol Comput 44:148–175Google Scholar
  24. 24.
    Pakzad-Moghaddam SH, Mina H, Mostafazadeh P (2019) A novel optimization booster algorithm. Comput Ind Eng 136:591–613Google Scholar
  25. 25.
    Greiner D, Periaux J, Quagliarella D et al (2018) Evolutionary algorithms and metaheuristics: applications in engineering design and optimization. Math Probl Eng 2018:2793762Google Scholar
  26. 26.
    Yalcin Y, Orhon M, Pekcan O (2019) An automated approach for the design of mechanically stabilized earth walls incorporating metaheuristic optimization algorithms. Appl Soft Comput J 74:547–566Google Scholar
  27. 27.
    Shehab M, Khader AT, Al-Betar MA (2017) A survey on applications and variants of the cuckoo search algorithm. Appl Soft Comput J 61:1041–1059Google Scholar
  28. 28.
    Fister I, Fister D, Fistar I (2013) A comprehensive review of cuckoo search: variants and hybrids. Int J Math Model Numer Optim 4:387–409zbMATHGoogle Scholar
  29. 29.
    Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29:17–35Google Scholar
  30. 30.
    Abdel-Basset M, Hessin AN, Abdel-Fatah L (2018) A comprehensive study of cuckoo-inspired algorithms. Neural Comput Appl 29:345–361Google Scholar
  31. 31.
    Ouaarab A, Ahiod B, Yang XS (2014) Discrete cuckoo search algorithm for the travelling salesman problem. Neural Comput Appl 24:1659–1669Google Scholar
  32. 32.
    Rodrigues D, Pereira LAM, Almeida TNS et al (2013) BCS: a binary cuckoo search algorithm for feature selection. In: Proceedings of IEEE international symposium on circuits and systems, Beijing, China, pp 465–468Google Scholar
  33. 33.
    Li Z, Dey N, Ashour AS, Tang Q (2018) Discrete cuckoo search algorithms for two-sided robotic assembly line balancing problem. Neural Comput Appl 30:2685–2696Google Scholar
  34. 34.
    Walton S, Hassan O, Morgan K, Brown MR (2011) Modified cuckoo search: a new gradient free optimisation algorithm. Chaos Solitons Fractals 44:710–718Google Scholar
  35. 35.
    Zhang Y, Wang L, Wu Q (2012) Modified adaptive cuckoo search (MACS) algorithm and formal description for global optimisation. Int J Comput Appl Technol 44:73–79Google Scholar
  36. 36.
    Binh HTT, Hanh NT, Van Quan L, Dey N (2018) Improved cuckoo search and chaotic flower pollination optimization algorithm for maximizing area coverage in wireless sensor networks. Neural Comput Appl 30:2305–2317Google Scholar
  37. 37.
    Wang GG, Deb S, Gandomi AH et al (2014) A novel cuckoo search with chaos theory and elitism scheme. In: Proceedings of 2014 international conference on soft computing and machine intelligence, ISCMI 2014, New Delhi, India, pp 64–69Google Scholar
  38. 38.
    Valian E, Mohanna S, Tavakoli S (2011) Improved cuckoo search algorithm for global optimization. Int J Commun Inf Technol 1:31–44zbMATHGoogle Scholar
  39. 39.
    Raju R, Babukarthik RG, Dhavachelvan P (2013) Hybrid ant colony optimization and cuckoo search algorithm for job scheduling. In: Meghanathan N, Nagamalai D, Chaki N (eds) Advances in computing and information technology. Springer, Berlin, Heidelberg, pp 491–501Google Scholar
  40. 40.
    Singla S, Jarial P, Mittal G (2015) Hybridization of cuckoo search & artificial bee colony optimization for satellite image classification. Int J Adv Res Comput Commun Eng 4:326–331Google Scholar
  41. 41.
    Kanagaraj G, Ponnambalam SG, Jawahar N (2013) A hybrid cuckoo search and genetic algorithm for reliability-redundancy allocation problems. Comput Ind Eng 66:1115–1124Google Scholar
  42. 42.
    Liu X, Fu M (2015) Cuckoo search algorithm based on frog leaping local search and chaos theory. Appl Math Comput 266:1083–1092MathSciNetzbMATHGoogle Scholar
  43. 43.
    Zhang Y, Yu C, Fu X et al (2015) Spectrum parameter estimation in Brillouin scattering distributed temperature sensor based on cuckoo search algorithm combined with the improved differential evolution algorithm. Opt Commun 357:15–20Google Scholar
  44. 44.
    Huang J, Gao L, Li X (2015) An effective teaching-learning-based cuckoo search algorithm for parameter optimization problems in structure designing and machining processes. Appl Soft Comput J 36:349–356Google Scholar
  45. 45.
    Sheikholeslami R, Zecchin AC, Zheng F, Talatahari S (2015) A hybrid cuckoo–harmony search algorithm for optimal design of water distribution systems. J Hydroinformatics 18:544–563Google Scholar
  46. 46.
    Elias V, Christopher BR, Berg RR (2001) Mechanically stabilized earth walls and reinforced soil slopes design & construction guidelines. Federal Highway Administration (FHWA), Washington, DCGoogle Scholar
  47. 47.
    Berg RR, Christopher BR, Samtani NC (2009) Design and construction of mechanically stabilized earth walls and reinforced soil slopes. Federal Highway Administration (FHWA), Washington, DCGoogle Scholar
  48. 48.
    Basudhar PK, Vashistha A, Deb K, Dey A (2008) Cost optimization of reinforced earth walls. Geotech Geol Eng 26:1–12Google Scholar
  49. 49.
    Javidy B, Hatamlou A, Mirjalili S (2015) Ions motion algorithm for solving optimization problems. Appl Soft Comput 32:72–79Google Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021

Authors and Affiliations

  1. 1.Civil Engineering DepartmentMiddle East Technical UniversityAnkaraTurkey

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