Skip to main content
SpringerLink
Log in

Stochastic paint optimizer: theory and application in civil engineering

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

Abstract

This paper presents an art-inspired optimization algorithm, which is called Stochastic Paint Optimizer (SPO). The SPO is a population-based optimizer inspired by the art of painting and the beauty of colors plays the main role in this algorithm. The SPO, as an optimization algorithm, simulates the search space as a painting canvas and applies a different color combination for finding the best color. Four simple color combination rules without the need for any internal parameter provide a good exploration and exploitation for the SPO. The performance of the algorithm is evaluated by twenty-three mathematical well-known benchmark functions, and the results are verified by a comparative study with recent well-studied algorithms. In addition, a set of IEEE Congress of Evolutionary Computation benchmark test functions (CEC-C06 2019) are utilized. On the other hand, the Wilcoxon test, as a non-parametric statistical test, is used to determine the significance of the results. Finally, to prove the practicability of the SPO, this algorithm is applied to four different structural design problems, known as challenging problems in civil engineering. The results of all these problems indicate that the SPO algorithm is able to provide very competitive results compared to the other algorithms.

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
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

Similar content being viewed by others

References

  1. Kaveh A (2017) Advances in metaheuristic algorithms for optimal design of structures, 2nd edn. Springer, Switzerland

    Book  Google Scholar 

  2. Talbi E-G (2009) Metaheuristics: from design to implementation, vol 74. Wiley, Hoboken

    Book  Google Scholar 

  3. De Jong KA (1975) Analysis of the behavior of a class of genetic adaptive systems, Technical Report

  4. Fogel LJ, Owens AJ, Walsh MJ (1966) Artificial intelligence through simulated evolution

  5. Holland JH (1992) Adaptation in natural and artificial systems: an introduSPOry analysis with applications to biology, control, and artificial intelligence, MIT press.

  6. Goldberg DE (2006) Genetic algorithms, Pearson Education India.

  7. Yang X-S et al. (2013) Swarm intelligence and bio-inspired computation: theory and applications, Newnes.

  8. Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39. https://doi.org/10.1109/MCI.2006.329691

    Article  Google Scholar 

  9. Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science. IEEE. https://doi.org/10.1109/MHS.1995.494215

  10. Karaboga D (2010) Artificial bee colony algorithm. Scholarpedia 5(3):6915

    Article  Google Scholar 

  11. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  12. Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213(3):267–289. https://doi.org/10.1007/s00707-009-0270-4

    Article  MATH  Google Scholar 

  13. Erol OK, Eksin I (2006) A new optimization method: big bang–big crunch. Adv Eng Softw 37(2):106–111. https://doi.org/10.1016/j.advengsoft.2005.04.005

    Article  Google Scholar 

  14. 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 

  15. Rashedi E, Nezamabadi-Pour H, Saryazdi SJIS (2009) GSA: a gravitational search algorithm 179(13): 2232–2248. https://doi.org/10.1016/j.ins.2009.03.004

  16. Van Laarhoven PJ, Aarts EH (1987) Simulated annealing. Simulated annealing: theory and applications. Springer, Berlin, pp 7–15

    Chapter  Google Scholar 

  17. Li S et al (2020) Slime mould algorithm: a new method for stochastic optimization. Future Generation Comput Syst. https://doi.org/10.1016/j.future.2020.03.055

    Article  Google Scholar 

  18. Kaveh A, Dadras Eslamlou A (2020.) Water strider algorithm: A new metaheuristic and applications. Structures, Elsevier, https://doi.org/10.1016/j.istruc.2020.03.033

  19. Kahraman HT, Aras S, Gedikli E (2020) Fitness-distance balance (FDB): a new selection method for meta-heuristic search algorithms. Knowl-Based Syst 190:105169. https://doi.org/10.1016/j.knosys.2019.105169

    Article  Google Scholar 

  20. Kaveh A, Talatahari S, Khodadadi N (2019) Hybrid invasive weed optimization-shuffled frog-leaping algorithm for optimal design of truss structures. Iran J Sci Technol Trans Civ Eng 2019:1–16. https://doi.org/10.3311/PPci.14576

    Article  Google Scholar 

  21. Pijarski P, Kacejko P (2019) A new metaheuristic optimization method: the algorithm of the innovative gunner (AIG). Eng Opt 51(12):2049–2068. https://doi.org/10.1080/0305215X.2019.1565282

    Article  MathSciNet  Google Scholar 

  22. Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Tavakkoli-Moghaddam (2020) Red deer algorithm (RDA): a new nature-inspired meta-heuristic. Soft Computing, 2020: 1–29. https://doi.org/10.1007/s00500-020-04812-z

  23. Mafarja M et al. Dragonfly algorithm: theory, literature review, and application in feature selection, in Nature-Inspired Optimizers. 2020, Springer, Berlin, pp 47–67. https://doi.org/10.1007/978-3-030-12127-3_4

  24. Kaveh A, Dadras Eslamlou A (2020) Metaheuristic optimization algorithms in civil engineering: new applications. Springer, Berlin

    Book  Google Scholar 

  25. Kaveh A, Ilchi Ghazaan M (2018) Meta-heuristic algorithms for optimal design of real-size structures. Springer, Berlin

    Book  Google Scholar 

  26. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68. https://doi.org/10.1177%2F003754970107600201

  27. Zaeimi M, Ghoddosian A (2020) Color harmony algorithm: an art-inspired metaheuristic for mathematical function optimization. Soft Comput 2020: 1–40. https://doi.org/10.1007/s00500-019-04646-4

  28. Matsuda YJAS (1995) Color design 2(4):10

    Google Scholar 

  29. Tokumaru M, Muranaka N, Imanishi S (2002) Color design support system considering color harmony. In: 2002 IEEE world congress on computational intelligence. 2002 IEEE international conference on fuzzy systems. FUZZ-IEEE'02. Proceedings (Cat. No. 02CH37291). 2002. IEEE. https://doi.org/10.1109/FUZZ.2002.1005020

  30. Cheng S, Shi Y (2011) Diversity control in particle swarm optimization. In: 2011 IEEE symposium on swarm intelligence. IEEE. https://doi.org/10.1109/SIS.2011.5952581

  31. Wolpert DH, W.G.J.I.t.o.e.c. (1997) Macready, No free lunch theorems for optimization. 1(1): p. 67–82. https://doi.org/10.1109/4235.585893

  32. Wool LE et al (2015) Salience of unique hues and implications for color theory. J Vis 15(2):10–10. https://doi.org/10.1167/15.2.10

    Article  Google Scholar 

  33. Parkhurst C, Feller RL (1982) Who invented the color wheel? Color Res Appl 7(3):217–230. https://doi.org/10.1002/col.5080070302

    Article  Google Scholar 

  34. Feisner EA (2006) Colour: how to use colour in art and design. Laurence King Publishing.

  35. Westland S et al (2007) Colour harmony. Colour: Design Creativity 1(1):1–15

    Google Scholar 

  36. Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3(2):82–102. https://doi.org/10.1109/4235.771163

    Article  Google Scholar 

  37. Digalakis JG, Margaritis KG (2001) On benchmarking functions for genetic algorithms. Int J Comput Math 77(4):481–506

    Article  MathSciNet  Google Scholar 

  38. Molga M, Smutnicki C (2005) Test functions for optimization needs. Test functions for optimization needs, 101.

  39. Yang X-S Test problems in optimization. arXiv preprint arXiv:1008.0549, 2010.

  40. Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248. https://doi.org/10.1016/j.ins.2009.03.004

    Article  MATH  Google Scholar 

  41. Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133. https://doi.org/10.1016/j.knosys.2015.12.022

    Article  Google Scholar 

  42. Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249. https://doi.org/10.1016/j.knosys.2015.07.006

    Article  Google Scholar 

  43. Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27(2):495–513. https://doi.org/10.1007/s00521-015-1870-7

    Article  Google Scholar 

  44. Price K et al (2018) The 100-digit challenge: Problem definitions and evaluation criteria for the 100-digit challenge special session and competition on single objective numerical optimization. Nanyang Technological University, Singapore

    Google Scholar 

  45. Rahman CM, Rashid TA (2019) Dragonfly algorithm and its applications in applied science survey. Comput Intell Neurosci. https://doi.org/10.1155/2019/9293617

    Article  Google Scholar 

  46. Mohammed HM, Umar SU, Rashid TA (2019) A systematic and meta-analysis survey of whale optimization algorithm. Comput Intell Neurosci. https://doi.org/10.1155/2019/8718571

    Article  Google Scholar 

  47. Arora S, Singh S (2019) Butterfly optimization algorithm: a novel approach for global optimization. Soft Comput 23(3):715–734. https://doi.org/10.1007/s00500-018-3102-4

    Article  Google Scholar 

  48. Ahmed AM, Rashid TA, Saeed SAM (2020) Cat swarm optimization algorithm: a survey and performance evaluation. Comput Intell Neurosci. https://doi.org/10.1155/2020/4854895

    Article  Google Scholar 

  49. Mirjalili S et al (2017) Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems 114:163–191. https://doi.org/10.1016/j.advengsoft.2017.07.002

    Article  Google Scholar 

  50. Van den Bergh F, Engelbrecht AP (2006) A study of particle swarm optimization particle trajeSPOries. Inf Sci 176(8):937–971. https://doi.org/10.1016/j.ins.2005.02.003

    Article  MATH  Google Scholar 

  51. Wu S-J, Chow P-T (1995) Steady-state genetic algorithms for discrete optimization of trusses. Comput Struct 56(6):979–991. https://doi.org/10.1016/0045-7949(94)00551-D

    Article  MATH  Google Scholar 

  52. Lee KS et al (2005) The harmony search heuristic algorithm for discrete structural optimization. Eng Opt 37(7):663–684. https://doi.org/10.1080/03052150500211895

    Article  MathSciNet  Google Scholar 

  53. Kalatjari VR, Talebpour MH (2017) An improved ant colony algorithm for the optimization of skeletal structures by the proposed sampling search space method. Periodica Polytechnica Civ Eng 61(2):232–243. https://doi.org/10.3311/PPci.9153

    Article  Google Scholar 

  54. Sadollah A et al (2012) Mine blast algorithm for optimization of truss structures with discrete variables. Comput Struct 102:49–63. https://doi.org/10.1016/j.compstruc.2012.03.013

    Article  Google Scholar 

  55. Cheng M-Y, 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 

  56. Soh CK, Yang J (1996) Fuzzy controlled genetic algorithm search for shape optimization. J Comput Civ Eng 10(2):143–150. https://doi.org/10.1061/(ASCE)0887-3801(1996)10:2(143)

    Article  Google Scholar 

  57. American Institute of Steel Construction (AISC) Manual of steel construction: allowable stress design. 1989.

  58. Kaveh A, Talatahari S (2010) Optimal design of skeletal structures via the charged system search algorithm 41(6):893–911. https://doi.org/10.1007/s00158-009-0462-5

    Article  Google Scholar 

  59. Kaveh A, Khayatazad M (2012) A new meta-heuristic method: ray optimization. Comput Struct 112:283–294

    Article  Google Scholar 

  60. Kaveh A, Mahdavi VR (2015) Colliding bodies optimization: extensions and applications. Springer, Berlin

    Book  Google Scholar 

  61. Jalili S, Hosseinzadeh Y (2015) A cultural algorithm for optimal design of truss structures. Latin Am J Solids Struct 12(9):1721–1747. https://doi.org/10.1590/1679-78251547

    Article  Google Scholar 

  62. Kaveh A, Talatahari S (2010) Optimum design of skeletal structures using imperialist competitive algorithm. 88(21–22): 1220–1229. https://doi.org/10.1016/j.compstruc.2010.06.011

  63. Kaveh A, Talatahari S (2012) Charged system search for optimal design of frame structures. 12(1): 382-393. https://doi.org/10.1016/j.asoc.2011.08.034

  64. Kaveh A, Farhoudi N (2013) A new optimization method. Dolphin Echolocation 59:53–70. https://doi.org/10.1016/j.advengsoft.2013.03.004

    Article  Google Scholar 

  65. Kaveh A, Bakhshpoori T (2016) An accelerated water evaporation optimization formulation for discrete optimization of skeletal structures. Comput Struct 177:218–228. https://doi.org/10.1016/j.compstruc.2016.08.006

    Article  Google Scholar 

  66. Camp CV, Bichon BJ, Stovall SP (2005) Design of steel frames using ant colony optimization. J Struct Eng 131(3):369–379. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:3(369)

    Article  Google Scholar 

  67. Degertekin SO (2008) Optimum design of steel frames using harmony search algorithm. Struct Multidisciplinary Opt 36(4):393–401. https://doi.org/10.1007/s00158-007-0177-4

    Article  Google Scholar 

  68. Gholizadeh S, Davoudi H, Fattahi F (2017) Design of steel frames by an enhanced moth-flame optimization algorithm. Steel Compos Struct 24(1):129–140. https://doi.org/10.12989/scs.2017.24.1.129

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran

    Ali Kaveh & Nima Khodadadi

  2. Department of Civil Engineering, University of Tabriz, Tabriz, Iran

    Siamak Talatahari

Authors
  1. Ali Kaveh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Siamak Talatahari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nima Khodadadi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ali Kaveh.

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

Kaveh, A., Talatahari, S. & Khodadadi, N. Stochastic paint optimizer: theory and application in civil engineering. Engineering with Computers 38, 1921–1952 (2022). https://doi.org/10.1007/s00366-020-01179-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-020-01179-5

Keywords

Search

Navigation