SpringerLink
Log in

Chaotic arithmetic optimization algorithm

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Arithmetic Optimization Algorithm (AOA) is a meta-heuristic algorithm. Its main idea is to use the distribution behavior of the four main mathematical operators of addition(A), subtraction(S), multiplication(M) and division(D). Chaotic map** strategy was introduced into the optimization process of AOA. Firstly, ten chaotic maps are separately embedded into two parameter Arithmetic Optimization Accelerator (MOA) and Arithmetic Optimization Probability (MOP) that affect the exploration and balance of AOA so as to enhance its ergodicity and non-repeatability, and improve its convergence speed and accuracy. Then a combination test was carried out by embedding ten chaotic maps into MOA and MOP at the same time, and their advantages and disadvantages were compared with the chaotic maps embedded separately. 26 benchmark functions in CEC-BC-2017 are used to examine the performance of the proposed chaotic arithmetic optimization algorithm (CAOA). Finally, four engineering design issues are optimized, involving three-bar truss design problem, welded beam design problem, pressure vessel design problem and spring design problem. The experimental results reveal that CAOA can obviously solve the function optimization and engineering optimization problems. AOA based on the chaotic interference factors has the merit of balancing the exploration and exploitation in the optimization process and enhances the convergence accuracy.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

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

Similar content being viewed by others

References

  1. Abualigaha L, Diabat A, Mirjalili S et al (2021) The arithmetic optimization algorithm. Comp Methods Appl Mech Eng 376:113609

    Article  MathSciNet  MATH  Google Scholar 

  2. Dutta T, Bhattacharyya S, Dey S, Platos J (2020) Border collie optimization. IEEE Access 8:109177–109197

    Article  Google Scholar 

  3. S Arora, P Anand (2018) Chaotic grasshopper optimization algorithm for global optimization. Neural Comp Appl

  4. Yang X-S, Gandomi AH, Talatahari S, Alavi AH (eds) (2012) Metaheuristics in water, geotechnical and transport engineering.Elsevier, Newnes

  5. Abualigah L, Diabat A (2020) A comprehensive survey of the grasshopper optimization algorithm: results, variants, and applications. Neural Comput. Appl.:1–24

  6. Shahrzad Saremi,Seyedali Mirjalili,Andrew Lewis (2014) Biogeography-based optimisation with chaos. Neural Comput & Applic

  7. Kallioras NA, Lagaros ND, Avtzis DN (2018) Pity beetle algorithm–a new metaheuristic inspired by the behavior of bark beetles. AdvEng Softw 121:147–166

    Article  Google Scholar 

  8. Talatahari S, Azizi M (2021) Chaos game optimization: a novel metaheuristic algorithm. Artif Intell Rev 54:917–1004

    Article  Google Scholar 

  9. Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S (2020) Equilibrium optimizer: a novel optimization algorithm. Knowl-Based Syst 191:105190

    Article  Google Scholar 

  10. Sadollah A, Sayyaadi H, Lee HM, Kim JH et al (2018) Mine blast harmony search: a new hybrid optimization method for improving exploration and exploitation capabilities. Appl Soft Comput 68:548–564

    Article  Google Scholar 

  11. Gholizadeh S, Danesh M, Gheyratmand C (2020) A new newton metaheuristic algorithm for discrete performance-based design optimization of steel moment frames. Comput Struct 234:106250

    Article  Google Scholar 

  12. Abualigah L (2020) Group search optimizer: a nature-inspired meta-heuristic optimization algorithm with its results, variants, and applications. Neural Comput Appl:1–24

  13. Jordehi AR (2014) Particle swarm optimisation for dynamic optimisation problems:a review. Neural Comput Appl:1–10

  14. El-Shorbagy MA, El-Refaey AM (2020) Hybridization of grasshopper optimization algorithm with genetic algorithm for solving system of non-linear equations. IEEE Access 8:220944–220961

    Article  Google Scholar 

  15. et al (2021) A novel algorithm for global optimization: rat swarm optimizer. J Ambient Intell Human Comput 12:8457–8482Dhiman, G., Garg, M., Nagar, A.et al A novel algorithm for global optimization: rat swarm optimizer. J Ambient Intell Human Comput 12, 8457–8482 (2021)

  16. Hashim FA, Hussain K, Houssein EH et al (2021) Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems. Appl Intell 51:1531–1551

    Article  Google Scholar 

  17. Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S (2020) Equilibrium optimizer: a novel optimization algorithm. Knowledge-Based Syst 191

  18. Abualigah L, Shehab M, Alshinwan M, Mirjalili S, Abd Elaziz M (2020) Ant lion optimizer: a comprehensive survey of its variants and applications. Arch Comput Methods Eng 28:1397–1416

    Article  MathSciNet  Google Scholar 

  19. Assiri AS, Hussien AG, Amin M (2020) Ant lion optimization: variants, hybrids, and applications. IEEE Access 8:77746–77764

    Article  Google Scholar 

  20. Wang Y, Gao S, Yu Y, Wang Z, Cheng J, Yuki T (2020) A gravitational search algorithm with chaotic neural oscillators. IEEE Access 8:25938–25948

    Article  Google Scholar 

  21. Mahamed GH, Omran MM (2008) Global-best harmony search. Appl Math Comput 198(2)

  22. Beyer H, Sendhoff B (2017) Simplify your covariance matrix adaptation evolution strategy. IEEE Trans Evol Comp 21(5):746–759

    Article  Google Scholar 

  23. Arora S, Singh S (2019) Butterfly optimization algorithm: a novel approach for global optimization. Soft Comput 23:715–734

    Article  Google Scholar 

  24. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer [J]. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  25. Abualigah L, Diabat A (2020) A comprehensive survey of the grasshopper optimization algorithm: results, variants, and applications. Neural Comput & Applic 32:15533–15556

    Article  Google Scholar 

  26. Eskandari S, Javidi MM (2020) A novel hybrid bat algorithm with a fast clustering-based hybridization. Evol Intel 13:427–442

    Article  Google Scholar 

  27. Chen H, Li W, Yang X (2020) A whale optimization algorithm with chaos mechanism based on quasi-opposition for global optimization problems. Expert Syst Appl 158:113612

    Article  Google Scholar 

  28. Saha S, Mukherjee V (2018) A novel chaos-integrated symbiotic organisms search algorithm for global optimization. Soft Comput 22:3797–3816

    Article  Google Scholar 

  29. Gandomi A, Yang X-S, Talatahari S, Alavi A (2013) Firefly algorithm with chaos. Commun Nonlinear Sci Numer Simul 18(1):89–98

    Article  MathSciNet  MATH  Google Scholar 

  30. Kaur A, Pal SK, Singh AP (2018) New chaotic flower pollination algorithm for unconstrained non-linear optimization functions[J]. Int J Syst Assur Eng Manag 9(4):853–865

  31. Yu H (2020) Nannan Zhao, Pengjun Wang, Huiling Chen, Chengye Li, chaos-enhanced synchronized bat optimizer, applied mathematical modelling, volume 77. Part 2:1201–1215

    Google Scholar 

  32. D Prayogo (2021) Chaotic coyote algorithm applied to truss optimization problems, Comp Struct,242, Juliano Pierezan, Leandro dos Santos Coelho, Viviana Cocco Mariani, Emerson Hochsteiner de Vasconcelos Segundo

  33. Sanaj MS, Joe Prathap PM (2020) Nature inspired chaotic squirrel search algorithm (CSSA) for multi objective task scheduling in an IAAS cloud computing atmosphere. Eng Sci Technol Int J 23(4)

  34. Heidari AA, Abbaspour RA, Jordehi AR (2017) An efficient chaotic water cycle algorithm for optimization tasks. Neural Comput Appl 28(1):57–85

    Article  Google Scholar 

  35. Gupta S, Deep K (2018) An opposition-based chaotic Grey wolf optimizer for global optimisation tasks[J]. J Exp Theor Artif Intell 31:1–29

    Google Scholar 

  36. Saha S, Mukherjee V (2017) A novel quasi-oppositional chaotic antlion optimizer for global optimization[J]. Appl Intell 48(9):2628–2660

    Article  Google Scholar 

  37. Gandomi AH, Yun GJ, Yang X-S, Talatahari S (2013) Chaos enhanced accelerated particle swarm optimization. Commun Nonlinear Sci Numer Simul 18(2):327–340

    Article  MathSciNet  MATH  Google Scholar 

  38. Arora S, Singh S (2017) An improved butterfly optimization algorithm with chaos. J Intell Fuzzy Syst 32(1):1079–1088

    Article  MATH  Google Scholar 

  39. Han X, Chang X (2013) An intelligent noise reduction method for chaotic signals based on genetic algorithms and lifting wavelet transforms. Inf Sci 218:103–118

    Article  Google Scholar 

  40. Coelho LDS (2009) Reliability–redundancy optimization by means of a chaotic differential evolution approach. Chaos Solitons Fractals 41:594–602

    Article  MATH  Google Scholar 

  41. Lu Y, Zhou J, Qin H, Wang Y, Zhang Y (2011) Chaotic differential evolution methods for dynamic economic dispatch with valve-point effects. Eng Appl Artif Intell 24:378–387

    Article  Google Scholar 

  42. Pan Q-K, Wang L, Gao L (2011) A chaotic harmony search algorithm for the flow shop scheduling problem with limited buffers. Appl Soft Comput 11:5270–5280

    Article  Google Scholar 

  43. Ahmed A. Ewees, Mohamed Abd Elaziz, Zakaria Alameer, Haiwang Ye, Zhang Jianhua, Improving multilayer perceptron neural network using chaotic grasshopper optimization algorithm to forecast iron ore price volatility, Resources Policy, 65, 2020, 101555

  44. Talatahari S, Farahmand Azar B, Sheikholeslami R, Gandomi A (2012) Imperialist competitive algorithm combined with chaos for global optimization. CommunNonlinear Sci Numer Simul 17:1312–1319

    Article  MathSciNet  MATH  Google Scholar 

  45. Talatahari S, Kaveh A, Sheikholeslami R (2011) An efficient charged system search using chaos for global optimization problems. Int J Optim Civil Eng 2:305–325

    Google Scholar 

  46. Alatas B (2011) Uniform big bang–chaotic big crunch optimization. Commun Nonlinear Sci Numer Simul 16:3696–3703

    Article  MATH  Google Scholar 

  47. Wu B., Fan S. (2011) Improved artificial bee Colony algorithm with chaos. In: Yu Y., Yu Z., Zhao J. (eds) Computer Science for Environmental Engineering and EcoInformatics. CSEEE 2011. Communications in Computer and Information Science, vol 158. Springer, Berlin, Heidelberg

  48. Jordehi AR (2015) A chaotic artificial immune system optimisation algorithm for solving global continuous optimisation problems. Neural Comput Appl 26(4):827–833

    Article  Google Scholar 

  49. Chuang L-Y, Tsai S-W, Yang C-H (2011) Chaotic catfish particle swarm optimization for solving global numerical optimization problems. Appl Math Comput 217(16):6900–6916

    MathSciNet  MATH  Google Scholar 

  50. Saremi S, Mirjalili S, Lewis A (2014) Biogeography-based optimisation with chaos. Neural Comput Appl 25(5):1077–1097

    Article  Google Scholar 

  51. Han X, Chang X (2012) A chaotic digital secure communication based on a modified gravitational search algorithm filter. Inf Sci 208:14–27

    Article  Google Scholar 

  52. Niknam T, Narimani MR, Jabbari M et al (2011) A modified shuffle frog lea** algorithm for multi-objective optimal power flow. Energy 36:6420–6432

    Article  Google Scholar 

  53. Prasad D, Mukherjee A, Shankar G, Mukherjee V (2017) Application of chaotic whale optimisation algorithm for transient stability constrained optimal power flow. IET Sci, Meas Technol

  54. Gandomi AH, Yang X-S (2014) Chaotic bat algorithm. J. Comput. Sci. 5(2):224–232

    Article  MathSciNet  Google Scholar 

  55. Mukherjee A, Mukherjee V (2015) Solution of optimal reactive power dispatch by chaotic krill herd algorithm. IET Gener. Transm. Distrib 9(15):2351–2362

    Article  Google Scholar 

  56. Zhu S, Zhu C, Cui H, Wang W (2019) A class of quadratic polynomial chaotic maps and its application in cryptography. IEEE Access 7:34141–34152

    Article  Google Scholar 

  57. Anupadma S, Dharshini BS, Roshini S, Singh JK (2020) Random selective block encryption technique for image cryptography using chaotic cryptography. 2020 Int Conf Emerging Trends Inform Technol Eng (ic-ETITE):1–5

  58. Banu SA, Amirtharajan R (2020) A robust medical image encryption in dual domain: chaos-DNA-IWT combined approach. Med Biol Eng Comput 58:1445–1458

    Article  Google Scholar 

  59. Yu WB (2017) Application of Chaos in Image Processing and Recognition. 2017 Int Conf Comp Syst Elec Control (ICCSEC):1108–1113

  60. Chithra A, Raja Mohamed I (2017) Synchronization and chaotic communication in nonlinear circuits with nonlinear coupling. J Comput Electron 16:833–844

    Article  Google Scholar 

  61. Naanaa A (2015) Fast chaotic optimization algorithm based on spatiotemporal maps for global optimization. Appl Math Comput 269:402–411

    MathSciNet  MATH  Google Scholar 

  62. Lu H, Wang X, Fei Z, Qiu M (2014) The effects of using chaotic map on improving the performance of multiobjective evolutionary algorithms. Math Prob Eng 2014:16–16

    Article  MathSciNet  MATH  Google Scholar 

  63. Khennaoui AA, Ouannas A, Boulaaras S, Pham VT, Taher Azar A (2020) A fractional map with hidden attractors: chaos and control. Eur Phys J Spec Top 229:1083–1093

    Article  Google Scholar 

  64. Yousri D, Allam D, Babu TS et al (2020) Fractional chaos maps with flower pollination algorithm for chaotic systems’ parameters identification. Neural Comput & Applic 32:16291–16327

    Article  Google Scholar 

  65. Zhuoran Z, Changqiang H, Hanqiao H, Shangqin T, Kangsheng D (April 2018) An optimization method: hummingbirds optimization algorithm. J Syst Eng Electron 29(2):386–404

    Article  Google Scholar 

  66. Houssein EH, Helmy BE-D, Elngar AA, Abdelminaam DS, Shaban H (2021) An improved tunicate swarm algorithm for global optimization and image segmentation. IEEE Access 9:56066–56092

    Article  Google Scholar 

  67. Kommadath R, Kotecha P (2017) Teaching learning based optimization with focused learning and its performance on CEC2017 functions[C]// evolutionary computation. IEEE:2397–2403

  68. Faramarzi A, Heidarinejad M, Mirjalili S, Gandomi AH (2020) Marine predators algorithm: a nature-inspired metaheuristic[J]. Expert Syst Appl 152:1–50

    Article  Google Scholar 

  69. Naruei I, Keynia F (2021) Wild horse optimizer: a new meta-heuristic algorithm for solving engineering optimization problems. Eng Comput

  70. Djenouri Y, Comuzzi M (2017) Combining Apriori heuristic and bio-inspired algorithms for solving the frequent itemsets mining problem. Inf Sci 420:1–15

    Article  Google Scholar 

  71. Liu X, Niu X, Fournier-Viger P (2021) Fast top-K association rule mining using rule generation property pruning. Appl Intell 51:2077–2093

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Basic Scientific Research Project of Institution of Higher Learning of Liaoning Province (Grant No. LJKZ0293), and the Project by Liaoning Provincial Natural Science Foundation of China (Grant No. 20180550700).

Author information

Authors and Affiliations

  1. School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan, 114044, China

    Xu-Dong Li, Jie-Sheng Wang, Wen-Kuo Hao, Min Zhang & Min Wang

Authors
  1. Xu-Dong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jie-Sheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wen-Kuo Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Min Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Min Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Xu-Dong Li participated in the data collection, analysis, algorithm simulation, and draft writing. Jie-Sheng Wang participated in the concept, design, interpretation and commented on the manuscript. Wen-Kuo Hao, Min Zhang and Min Wang participated in the critical revision of this paper.

Corresponding author

Correspondence to Jie-Sheng Wang.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this article.

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

Li, XD., Wang, JS., Hao, WK. et al. Chaotic arithmetic optimization algorithm. Appl Intell 52, 16718–16757 (2022). https://doi.org/10.1007/s10489-021-03037-3

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-021-03037-3

Keywords

Search

Navigation