Skip to main content
Log in

Bonobo optimizer (BO): an intelligent heuristic with self-adjusting parameters over continuous spaces and its applications to engineering problems

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

In this paper, an intelligent optimization technique, namely Bonobo Optimizer (BO), is proposed. It mimics several interesting reproductive strategies and social behaviour of Bonobos. Bonobos live in a fission-fusion type of social organization, where they form several groups (fission) of different sizes and compositions within the society and move throughout the territory. Afterward, they merge (fusion) again with their society members for conducting specific activities. Bonobos adopt four different reproductive strategies, like restrictive mating, promiscuous mating, extra-group mating, and consortship mating to maintain a proper harmony in the society. These natural strategies are mathematically modeled in the proposed BO to solve an optimization problem. The searching mechanism with self-adjusting controlling parameters of the BO is designed in such a way that it can cope with various situations efficiently, while solving a variety of problems. Moreover, fission-fusion strategy is followed to select the mating partner, which is a unique approach in the literature of meta-heuristics. The performance of BO has been tested on CEC’13 and CEC’14 test functions and compared to that of other efficient and popular optimization algorithms of recent times. The comparisons show some comparable results and statistically superior performances of the proposed BO. Besides these, five complex real-life optimization problems are solved using BO and the results are compared with those reported in the literature. Here also, the performance of BO is found to be either better or comparable than that of others. These results establish the applicability of proposed BO to solve optimization problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

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

Similar content being viewed by others

References

  1. Fernández JR, López-Campos JA, Segade A, Vilán JA (2018) A genetic algorithm for the characterization of hyperelastic materials. Appl Math Comput 329:239–250. https://doi.org/10.1016/j.amc.2018.02.008

    Article  MathSciNet  MATH  Google Scholar 

  2. Gao H, Pun C-M, Kwong S (2016) An efficient image segmentation method based on a hybrid particle swarm algorithm with learning strategy. Inf Sci 369:500–521. https://doi.org/10.1016/j.ins.2016.07.017

    Article  MathSciNet  Google Scholar 

  3. Meng T, Pan Q-K, Li J-Q, Sang H-Y (2018) An improved migrating birds optimization for an integrated lot-streaming flow shop scheduling problem. Swarm Evol Comput 38:64–78. https://doi.org/10.1016/j.swevo.2017.06.003

    Article  Google Scholar 

  4. Gong X, Plets D, Tanghe E, De Pessemier T, Martens L, Joseph W (2018) An efficient genetic algorithm for large-scale planning of dense and robust industrial wireless networks. Expert Syst Appl 96:311–329

    Article  Google Scholar 

  5. Deep K, Thakur M (2007) A new crossover operator for real coded genetic algorithms. Appl Math Comput 188(1):895–911. https://doi.org/10.1016/j.amc.2006.10.047

    Article  MathSciNet  MATH  Google Scholar 

  6. Das AK, Pratihar DK (2019) A new search space reduction technique for genetic algorithms. In: Mandal J, Sinha D, Bandopadhyay J (eds) Contemporary advances in innovative and applicable information technology. Advances in Intelligent Systems and Computing, vol 812. Springer, Singapore, pp 111–119. https://doi.org/10.1007/978-981-13-1540-4_12

  7. Das AK, Pratihar DK (2018) A novel restart strategy for solving complex multi-modal optimization problems using real-coded genetic algorithm. In: Abraham A, Muhuri P, Muda A, Gandhi N (eds) Intelligent systems design and applications (ISDA 2017). Advances in Intelligent Systems and Computing, vol 736. Springer, Cham, pp 1–10. https://doi.org/10.1007/978-3-319-76348-4_4

  8. Das AK, Pratihar DK (2019) Performance improvement of a genetic algorithm using a novel restart strategy with elitism principle. Int J Hybrid Intell Syst 15(1):1–15. https://doi.org/10.3233/HIS-180257

    Article  Google Scholar 

  9. AkpıNar S, Bayhan GM, Baykasoglu A (2013) Hybridizing ant colony optimization via genetic algorithm for mixed-model assembly line balancing problem with sequence dependent setup times between tasks. Appl Soft Comput 13(1):574–589

    Article  Google Scholar 

  10. Mahmoodabadi MJ, Safaie AA, Bagheri A, Nariman-Zadeh N (2013) A novel combination of particle swarm optimization and genetic algorithm for Pareto optimal design of a five-degree of freedom vehicle vibration model. Appl Soft Comput 13(5):2577–2591

    Article  Google Scholar 

  11. Abualigah L, Diabat A, Mirjalili S, Abd Elaziz M, Gandomi AH (2021) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609. https://doi.org/10.1016/j.cma.2020.113609

    Article  MathSciNet  MATH  Google Scholar 

  12. Khishe M, Mosavi MR (2020) Chimp optimization algorithm. Expert Syst Appl 149:113338. https://doi.org/10.1016/j.eswa.2020.113338

    Article  Google Scholar 

  13. Holland JH, Reitman JS (1978) Cognitive systems based on adaptive algorithms. In: Waterman DA, Fredrick HR (eds) Pattern-directed inference systems. Academic press, pp 313–329. https://doi.org/10.1016/B978-0-12-737550-2.50020-8

  14. Fahimnia B, Luong L, Marian R (2008) Optimization/simulation modeling of the integrated production-distribution plan: an innovative survey. WSEAS Trans Bus Econ 3:52–65

    Google Scholar 

  15. Pratihar DK (2016) Realizing the need for intelligent optimization tool. In: Mandal J, Sinha D, Mukhopadhyay S, Pal T (eds) Handbook of research on natural computing for optimization problems. IGI Global, pp. 1–9. https://doi.org/10.4018/978-1-5225-0058-2.ch001

  16. Rechenberg I (1978) Simulationsmethoden in der Medizin und Biologie. Springer Verlag, Berlin

    Google Scholar 

  17. Reynolds RG (1994) An introduction to cultural algorithms. In: Proceedings of the third annual conference on evolutionary programming, vol. 24. World Scientific Publishing, River Edge, NJ, pp 131–139

  18. Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    Article  MathSciNet  Google Scholar 

  19. Hansen N (2006) The CMA evolution strategy: a comparing review. In: Lozano JA, Larrañaga P, Inza I, Bengoetxea E (eds) Towards a new evolutionary computation: advances in the estimation of distribution algorithms. Springer, Berlin, Heidelberg, pp 75–102. https://doi.org/10.1007/3-540-32494-1_4

    Chapter  Google Scholar 

  20. Eberhart R, Kennedy J A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science (MHS'95), 1995. IEEE, pp 39-43. https://doi.org/10.1109/MHS.1995.494215.

  21. Yuce B, Packianather MS, Mastrocinque E, Pham DT, Lambiase A (2013) Honey bees inspired optimization method: the bees algorithm. Insects 4(4):646–662

    Article  Google Scholar 

  22. Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE computational intelligence magazine, vol. 1, no. 4, pp. 28–39. https://doi.org/10.1109/MCI.2006.329691

  23. 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 

  24. Kirkpatrick S (1984) Optimization by simulated annealing: quantitative studies. J Stat Phys 34(5–6):975–986

    Article  MathSciNet  Google Scholar 

  25. Yang XS (2012) Flower pollination algorithm for global optimization. In: Durand-Lose J, Jonoska N (eds) Unconventional computation and natural computation. UCNC 2012. Lecture Notes in Computer Science, vol 7445. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32894-7_27

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

    Article  Google Scholar 

  27. Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2013) Mine blast algorithm: a new population based algorithm for solving constrained engineering optimization problems. Appl Soft Comput 13(5):2592–2612

    Article  Google Scholar 

  28. Rao RV, Savsani VJ, Vakharia D (2011) Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des 43(3):303–315

    Article  Google Scholar 

  29. Mortazavi A, Toğan V, Nuhoğlu A (2018) Interactive search algorithm: a new hybrid metaheuristic optimization algorithm. Eng Appl Artif Intell 71:275–292. https://doi.org/10.1016/j.engappai.2018.03.003

    Article  Google Scholar 

  30. Elsisi M (2019) Future search algorithm for optimization. Evol Intel 12(1):21–31. https://doi.org/10.1007/s12065-018-0172-2

    Article  Google Scholar 

  31. Dhiman G, Kumar V (2019) Seagull optimization algorithm: theory and its applications for large-scale industrial engineering problems. Knowl-Based Syst 165:169–196. https://doi.org/10.1016/j.knosys.2018.11.024

    Article  Google Scholar 

  32. Zervoudakis K, Tsafarakis S (2020) A mayfly optimization algorithm. Comput Ind Eng 145:106559. https://doi.org/10.1016/j.cie.2020.106559

    Article  Google Scholar 

  33. dos Santos CL, Ayala HVH, Mariani VC (2014) A self-adaptive chaotic differential evolution algorithm using gamma distribution for unconstrained global optimization. Appl Math Comput 234:452–459

    MathSciNet  MATH  Google Scholar 

  34. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82

    Article  Google Scholar 

  35. Tao F, Laili Y, Zhang L (2015) Brief history and overview of intelligent optimization algorithms. In: Tao F, Zhang L, Laili Y (eds) Configurable intelligent optimization algorithm: design and practice in manufacturing. Springer International Publishing, Cham, pp 3–33. https://doi.org/10.1007/978-3-319-08840-2_1

    Chapter  MATH  Google Scholar 

  36. Das AK, Pratihar DK A (2019) New Bonobo optimizer (BO) for Real-Parameter optimization. In: IEEE Region 10 Symposium (TENSYMP). pp 108–113. https://doi.org/10.1109/TENSYMP46218.2019.8971108

  37. Kanō T (1992) The last ape: pygmy chimpanzee behavior and ecology. Stanford University Press, Stanford, CA

    Google Scholar 

  38. De Waal FB (1995) Bonobo sex and society. Sci Am 272(3):82–88

    Article  Google Scholar 

  39. Wrangham RW, Peterson D (1996) Demonic males: apes and the evolution of human aggression. Hough-ton Mifflin, New York

    Google Scholar 

  40. Kano T (1996) Male rank order and copulation rate in a unit-group of bonobos at Wamba, Zaïre. In: Goodall J, Itani J, Foundation W (Authors) & McGrew W, Marchant L, Nishida T (eds) Great ape societies. Cambridge University Press, Cambridge, pp. 135–145. https://doi.org/10.1017/CBO9780511752414.012

  41. Gagneux P, Boesch C, Woodruff DS (1999) Female reproductive strategies, paternity and community structure in wild west African chimpanzees. Anim Behav 57(1):19–32

    Article  Google Scholar 

  42. Symington MM (1990) Fission-fusion social organization inAteles andPan. Int J Primatol 11(1):47–61. https://doi.org/10.1007/BF02193695

    Article  Google Scholar 

  43. Goodall J (1986) The chimpanzees of Gombe: patterns of behavior. The Belknap Press of Harvard University Press, Cambridge, MA

    Google Scholar 

  44. Liang J, Qu B, Suganthan P, Hernández-Díaz AG (2013) Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization. Comput Intell Lab Zhengzhou Univ Zhengzhou, China Nanyang Technol Univ Singapore Tech Rep 201212(34):281–295

    Google Scholar 

  45. Liang JJ, Qu BY, Suganthan PN (2013) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization. Comput Intell Lab Zhengzhou Univ Zhengzhou China Tech Rep Nanyang Technol Univ Singapore 635:490

    Google Scholar 

  46. Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18

    Article  Google Scholar 

  47. García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J Heuristics 15(6):617–644

    Article  Google Scholar 

  48. García S, Fernández A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power. Inf Sci 180(10):2044–2064

    Article  Google Scholar 

  49. Derrac J, García S, Hui S, Suganthan PN, Herrera F (2014) Analyzing convergence performance of evolutionary algorithms: a statistical approach. Inf Sci 289:41–58. https://doi.org/10.1016/j.ins.2014.06.009

    Article  Google Scholar 

  50. Belegundu AD, Arora JS (1985) A study of mathematical programming methods for structural optimization. Part I: Theory. International Journal for Numerical Methods in Engineering 21(9):1583–1599. https://doi.org/10.1002/nme.1620210904

  51. Belegundu AD, Arora JS (1985) A study of mathematical programming methods for structural optimization. Part I: theory. Int J Numer Methods Eng 21(9):1583–1599

    Article  Google Scholar 

  52. Coello CAC (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41(2):113–127

    Article  Google Scholar 

  53. He Q, Wang L (2007) An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng Appl Artif Intell 20(1):89–99. https://doi.org/10.1016/j.engappai.2006.03.003

    Article  Google Scholar 

  54. F-z H, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186(1):340–356

    MathSciNet  MATH  Google Scholar 

  55. Mezura-Montes E, Coello CAC (2008) An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. Int J Gen Syst 37(4):443–473

    Article  MathSciNet  Google Scholar 

  56. Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579

    MathSciNet  MATH  Google Scholar 

  57. Coello CAC, Montes EM (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inform 16(3):193–203

    Article  Google Scholar 

  58. Deb K (1997) GeneAS: a robust optimal design technique for mechanical component design. In: Dasgupta D, Michalewicz Z (eds) Evolutionary algorithms in engineering applications. Springer, Berlin, Heidelberg, pp 497–514. https://doi.org/10.1007/978-3-662-03423-1_27

  59. Kaveh A, Talatahari S (2010) An improved ant colony optimization for constrained engineering design problems. Eng Comput 27(1):155–182

    Article  Google Scholar 

  60. Kannan B, Kramer SN (1994) An augmented Lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. J Mech Des 116(2):405–411

    Article  Google Scholar 

  61. Sandgren E (1990) Nonlinear integer and discrete programming in mechanical design. J Mech Des 112(2):223–229. https://doi.org/10.1115/1.2912596

  62. Deb K (1991) Optimal design of a welded beam via genetic algorithms. AIAA J 29(11):2013–2015

    Article  Google Scholar 

  63. Ragsdell KM, Phillips DT (1976) Optimal Design of a Class of welded structures using geometric programming. J Eng Ind 98(3):1021–1025. https://doi.org/10.1115/1.3438995

    Article  Google Scholar 

  64. Coello Coello CA (2000) Constraint-handling using an evolutionary multiobjective optimization technique. Civ Eng Syst 17(4):319–346

    Article  Google Scholar 

  65. Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2):311–338. https://doi.org/10.1016/S0045-7825(99)00389-8

    Article  MATH  Google Scholar 

  66. Lee KS, Geem ZW (2005) A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194(36–38):3902–3933

    Article  Google Scholar 

  67. Ku KJ, Rao S, Chen L (1998) Taguchi-aided search method for design optimization of engineering systems. Eng Optim 30(1):1–23

    Article  Google Scholar 

  68. Wang L, L-p L (2010) An effective differential evolution with level comparison for constrained engineering design. Struct Multidiscip Optim 41(6):947–963. https://doi.org/10.1007/s00158-009-0454-5

    Article  Google Scholar 

  69. Zhang M, Luo W, Wang X (2008) Differential evolution with dynamic stochastic selection for constrained optimization. Inf Sci 178(15):3043–3074

    Article  Google Scholar 

  70. Wang Y, Cai Z, Zhou Y, Fan Z (2009) Constrained optimization based on hybrid evolutionary algorithm and adaptive constraint-handling technique. Struct Multidiscip Optim 37(4):395–413

    Article  Google Scholar 

  71. Ray T, Liew KM (2003) Society and civilization: an optimization algorithm based on the simulation of social behavior. IEEE Trans Evol Comput 7(4):386–396

    Article  Google Scholar 

  72. Mezura-Montes E, Coello CA, Reyes JV (2006) Increasing successful offspring and diversity in differential evolution for engineering design. Proceedings of the seventh international conference on adaptive computing in design and manufacture (ACDM 2006), pp 131–139

  73. Akay B, Karaboga D (2012) Artificial bee colony algorithm for large-scale problems and engineering design optimization. J Intell Manuf 23(4):1001–1014. https://doi.org/10.1007/s10845-010-0393-4

    Article  Google Scholar 

Download references

Acknowledgments

The first author gratefully acknowledges the financial support of the Ministry of Human Resource Development, Government of India, for carrying out this study.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dilip Kumar Pratihar.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

Sample Matlab code of the proposed Bonobo Optimizer (BO) to solve Sphere function with 4 decision variables.

figure afigure afigure a

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Das, A.K., Pratihar, D.K. Bonobo optimizer (BO): an intelligent heuristic with self-adjusting parameters over continuous spaces and its applications to engineering problems. Appl Intell 52, 2942–2974 (2022). https://doi.org/10.1007/s10489-021-02444-w

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-021-02444-w

Keywords

Navigation