Skip to main content
Log in

Chaotic oppositional sine–cosine method for solving global optimization problems

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

Abstract

This study proposed an improved sine–cosine algorithm (SCA) for global optimization tasks. The SCA is a meta-heuristic method ground on sine and cosine functions. It has found its application in many fields. However, SCA still has some shortcomings such as weak global search ability and low solution quality. In this study, the chaotic local search strategy and the opposition-based learning strategy are utilized to strengthen the exploration and exploitation capability of the basic SCA, and the improved algorithm is called chaotic oppositional SCA (COSCA). The COSCA was validated on a comprehensive set of 22 benchmark functions from classical 23 functions and CEC2014. Simulation experiments suggest that COSCA’s global optimization ability is significantly improved and superior to other algorithms. Moreover, COSCA is evaluated on three complex engineering problems with constraints. Experimental results show that COSCA can solve such problems more effectively than different algorithms.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Zhang X, Wang D, Zhou Z, Ma Y (2019) Robust low-rank tensor recovery with rectification and alignment. IEEE Trans Pattern Anal Mach Intell. https://doi.org/10.1109/TPAMI.2019.2929043

    Article  Google Scholar 

  2. Jiao S, Chong G, Huang C, Hu H, Wang M, Heidari AA, Chen H, Zhao X (2020) Orthogonally adapted Harris hawks optimization for parameter estimation of photovoltaic models. Energy 203:117804. https://doi.org/10.1016/j.energy.2020.117804

    Article  Google Scholar 

  3. Luo J, Chen H, Zhang Q, Xu Y, Huang H, Zhao X (2018) An improved grasshopper optimization algorithm with application to financial stress prediction. Appl Math Model 64:654–668. https://doi.org/10.1016/j.apm.2018.07.044

    Article  MathSciNet  MATH  Google Scholar 

  4. Yu H, Zhao N, Wang P, Chen H, Li C (2020) Chaos-enhanced synchronized bat optimizer. Appl Math Model 77:1201–1215. https://doi.org/10.1016/j.apm.2019.09.029

    Article  Google Scholar 

  5. Fan Y, Wang P, Asghar Heidari A, Wang M, Zhao X, Chen H, Li C (2020) Rationalized fruit fly optimization with sine cosine algorithm: a comprehensive analysis. Expert Syst Appl

  6. Fan Y, Wang P, Heidari AA, Wang M, Zhao X, Chen H, Li C (2020) Boosted hunting-based fruit fly optimization and advances in real-world problems. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2020.113502

    Article  Google Scholar 

  7. Zhang Y, Liu R, Wang X, Chen H, Li C (2020) Boosted binary Harris hawks optimizer and feature selection. Eng Comput. https://doi.org/10.1007/s00366-020-01028-5

    Article  Google Scholar 

  8. Chen H, Heidari AA, Chen H, Wang M, Pan Z, Gandomi AH (2020) Multi-population differential evolution-assisted Harris hawks optimization: framework and case studies. Future Gener Comput Syst 111:175–198. https://doi.org/10.1016/j.future.2020.04.008

    Article  Google Scholar 

  9. Ridha HM, Heidari AA, Wang M, Chen H (2020) Boosted mutation-based Harris hawks optimizer for parameters identification of single-diode solar cell models. Energy Convers Manag 209:112660. https://doi.org/10.1016/j.enconman.2020.112660

    Article  Google Scholar 

  10. Zhang H, Heidari AA, Wang M, Zhang L, Chen H, Li C (2020) Orthogonal Nelder–Mead moth flame method for parameters identification of photovoltaic modules. Energy Convers Manag 211:112764. https://doi.org/10.1016/j.enconman.2020.112764

    Article  Google Scholar 

  11. Nguyen H, Moayedi H, Sharifi A, Amizah WJW, Safuan ARA (2019) Proposing a novel predictive technique using M5Rules-PSO model estimating cooling load in energy-efficient building system. Eng Comput 35:1–11. https://doi.org/10.1007/s00366-019-00735-y

    Article  Google Scholar 

  12. Yuan C, Moayedi H (2019) The performance of six neural-evolutionary classification techniques combined with multi-layer perception in two-layered cohesive slope stability analysis and failure recognition. Eng Comput 36:1–10. https://doi.org/10.1007/s00366-019-00791-4

    Article  Google Scholar 

  13. Xi W, Li G, Moayedi H, Nguyen H (2019) A particle-based optimization of artificial neural network for earthquake-induced landslide assessment in Ludian county. China Geomat Nat Hazards Risk 10:1750–1771

    Article  Google Scholar 

  14. Wang B, Moayedi H, Ahmad SAR, Nguyen H (2019) Feasibility of a novel predictive technique based on artificial neural network optimized with particle swarm optimization estimating pullout bearing capacity of helical piles. Eng Comput 36:1–10. https://doi.org/10.1007/s00366-019-00764-7

    Article  Google Scholar 

  15. Tien Bui D, MaM Abdullahi, Ghareh S, Moayedi H, Nguyen H (2019) Fine-tuning of neural computing using whale optimization algorithm for predicting compressive strength of concrete. Eng Comput. https://doi.org/10.1007/s00366-019-00850-w

    Article  Google Scholar 

  16. Moayedi H, Hayati S (2018) Modelling and optimization of ultimate bearing capacity of strip footing near a slope by soft computing methods. Appl Soft Comput 66:208–219. https://doi.org/10.1016/j.asoc.2018.02.027

    Article  Google Scholar 

  17. Kennedy J (2010) Particle swarm optimization. In: Sammut C, Webb GI (eds) Encyclopedia of machine learning. Springer, Boston, pp 760–766. https://doi.org/10.1007/978-0-387-30164-8_630

    Chapter  Google Scholar 

  18. Moayedi H, Foong LK, Nguyen H, Bui DT, Jusoh WAW, Rashid ASA (2019) Optimizing ANN models with PSO for predicting short building seismic response. Eng Comput 35:1–16. https://doi.org/10.1007/s00366-019-00733-0

    Article  Google Scholar 

  19. Luo Z, Bui X-N, Nguyen H, Moayedi H (2019) A novel artificial intelligence technique for analyzing slope stability using PSO-CA model. Eng Comput. https://doi.org/10.1007/s00366-019-00839-5

    Article  Google Scholar 

  20. Liu W, Moayedi H, Nguyen H, Lyu Z, Bui DT (2019) Proposing two new metaheuristic algorithms of ALO-MLP and SHO-MLP in predicting bearing capacity of circular footing located on horizontal multilayer soil. Eng Comput. https://doi.org/10.1007/s00366-019-00897-9

    Article  Google Scholar 

  21. Ding Z, Nguyen H, Bui X-N, Zhou J, Moayedi H (2019) Computational intelligence model for estimating intensity of blast-induced ground vibration in a mine based on imperialist competitive and extreme gradient boosting algorithms. Nat Resour Res. https://doi.org/10.1007/s11053-019-09548-8

    Article  Google Scholar 

  22. 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 

  23. Zhao X, Zhang X, Cai Z, Tian X, Wang X, Huang Y, Chen H, Hu L (2019) Chaos enhanced grey wolf optimization wrapped ELM for diagnosis of paraquat-poisoned patients. Comput Biol Chem 78:481–490. https://doi.org/10.1016/j.compbiolchem.2018.11.017

    Article  Google Scholar 

  24. Wang M, Chen H, Li H, Cai Z, Zhao X, Tong C, Li J, Xu X (2017) Grey wolf optimization evolving kernel extreme learning machine: application to bankruptcy prediction. Eng Appl Artif Intell 63:54–68. https://doi.org/10.1016/j.engappai.2017.05.003

    Article  Google Scholar 

  25. Mirjalili S, Lewis A (2016) The Whale optimization algorithm. Adv Eng Softw 95:51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008

    Article  Google Scholar 

  26. Wang M, Chen H (2019) Chaotic multi-swarm whale optimizer boosted support vector machine for medical diagnosis. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2019.105946

    Article  Google Scholar 

  27. Luo J, Chen H, Heidari AA, Xu Y, Zhang Q, Li C (2019) Multi-strategy boosted mutative whale-inspired optimization approaches. Appl Math Model 73:109–123. https://doi.org/10.1016/j.apm.2019.03.046

    Article  MathSciNet  MATH  Google Scholar 

  28. Chen H, Yang C, Heidari AA, Zhao X (2019) An efficient double adaptive random spare reinforced whale optimization algorithm. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2019.113018

    Article  Google Scholar 

  29. Dorigo M, Birattari M (2010) Ant colony optimization. Springer, Berlin

    Google Scholar 

  30. Moayedi H, Mu’azu MA, Foong LK (2019) Novel swarm-based approach for predicting the cooling load of residential buildings based on social behavior of elephant herds. Energy Build 206:109579. https://doi.org/10.1016/j.enbuild.2019.109579

    Article  Google Scholar 

  31. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39:459–471. https://doi.org/10.1007/s10898-007-9149-x

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  33. Yang X-S, Deb S (2009) Cuckoo search via Lévy flights. In: 2009 World congress on nature & biologically inspired computing (NaBIC)

  34. Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: algorithm and applications. Future Gener Comput Syst 97:849–872. https://doi.org/10.1016/j.future.2019.02.028

    Article  Google Scholar 

  35. Chen H, Jiao S, Wang M, Heidari AA, Zhao X (2019) Parameters identification of photovoltaic cells and modules using diversification-enriched Harris hawks optimization with chaotic drifts. J Clean Prod. https://doi.org/10.1016/j.jclepro.2019.118778

    Article  Google Scholar 

  36. Li S, Chen H, Wang M, Heidari AA, Mirjalili S (2020) Slime mould algorithm: a new method for stochastic optimization. Future Gener Comput Syst 111:300–323. https://doi.org/10.1016/j.future.2020.03.055

    Article  Google Scholar 

  37. Zhang X, Xu Y, Yu C, Heidari AA, Li S, Chen H, Li C (2020) Gaussian mutational chaotic fruit fly-built optimization and feature selection. Expert Syst Appl 141:112976. https://doi.org/10.1016/j.eswa.2019.112976

    Article  Google Scholar 

  38. Zhang Q, Chen H, Heidari AA, Zhao X, Xu Y, Wang P, Li Y, Li C (2019) Chaos-induced and mutation-driven schemes boosting salp chains-inspired optimizers. IEEE Access 7:31243–31261. https://doi.org/10.1109/access.2019.2902306

    Article  Google Scholar 

  39. Xu Y, Chen H, Luo J, Zhang Q, Jiao S, Zhang X (2019) Enhanced Moth-flame optimizer with mutation strategy for global optimization. Inf Sci 492:181–203. https://doi.org/10.1016/j.ins.2019.04.022

    Article  MathSciNet  Google Scholar 

  40. Xu Y, Chen H, Heidari AA, Luo J, Zhang Q, Zhao X, Li C (2019) An efficient chaotic mutative moth-flame-inspired optimizer for global optimization tasks. Expert Syst Appl 129:135–155. https://doi.org/10.1016/j.eswa.2019.03.043

    Article  Google Scholar 

  41. Xu X, Chen H-l (2014) Adaptive computational chemotaxis based on field in bacterial foraging optimization. Soft Comput 18:797–807

    Article  Google Scholar 

  42. Chen H, Zhang Q, Luo J, Xu Y, Zhang X (2019) An enhanced bacterial foraging optimization and its application for training kernel extreme learning machine. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2019.105884

    Article  Google Scholar 

  43. Chen H, Li S, Asghar Heidari A, Wang P, Li J, Yang Y, Wang M, Huang C (2020) Efficient multi-population outpost fruit fly-driven optimizers: framework and advances in support vector machines. Expert Syst Appl 142:112999. https://doi.org/10.1016/j.eswa.2019.112999

    Article  Google Scholar 

  44. Shen L, Chen H, Yu Z, Kang W, Zhang B, Li H, Yang B, Liu D (2016) Evolving support vector machines using fruit fly optimization for medical data classification. Knowl-Based Syst 96:61–75. https://doi.org/10.1016/j.knosys.2016.01.002

    Article  Google Scholar 

  45. Zhou G, Moayedi H, Bahiraei M, Lyu Z (2020) Employing artificial bee colony and particle swarm techniques for optimizing a neural network in prediction of heating and cooling loads of residential buildings. J Clean Prod 254:120082

    Article  Google Scholar 

  46. Qiao W, Moayedi H, Foong KL (2020) Nature-inspired hybrid techniques of IWO, DA, ES, GA, and ICA, validated through a k-fold validation process predicting monthly natural gas consumption. Energy Build. https://doi.org/10.1016/j.enbuild.2020.110023

    Article  Google Scholar 

  47. Moayedi H, Gör M, Lyu Z, Bui DT (2020) Herding behaviors of grasshopper and Harris hawk for hybridizing the neural network in predicting the soil compression coefficient. Measurement 152:107389. https://doi.org/10.1016/j.measurement.2019.107389

    Article  Google Scholar 

  48. Moayedi H, Gör M, Khari M, Foong LK, Bahiraei M, Bui DT (2020) Hybridizing four wise neural-metaheuristic paradigms in predicting soil shear strength. Measurement 156:107576

    Article  Google Scholar 

  49. Nguyen H, Mehrabi M, Kalantar B, Moayedi H, Mu’azu MA (2019) Potential of hybrid evolutionary approaches for assessment of geo-hazard landslide susceptibility mapping. Geomat Nat Hazards Risk 10:1667–1693

    Article  Google Scholar 

  50. Moayedi H, Tien Bui D, Gör M, Pradhan B, Jaafari A (2019) The feasibility of three prediction techniques of the artificial neural network, adaptive neuro-fuzzy inference system, and hybrid particle swarm optimization for assessing the safety factor of cohesive slopes. ISPRS Int J Geo-Inf 8:391

    Article  Google Scholar 

  51. Moayedi H, Osouli A, Tien Bui D, Foong LK (2019) Spatial landslide susceptibility assessment based on novel neural-metaheuristic geographic information system based ensembles. Sensors 19:4698

    Article  Google Scholar 

  52. Moayedi H, Mehrabi M, Kalantar B, Mu’azu MA MA, Rashid ASA, Foong LK, Nguyen H (2019) Novel hybrids of adaptive neuro-fuzzy inference system (ANFIS) with several metaheuristic algorithms for spatial hazard assessment of seismic-induced landslide. Geomat Nat Hazards Risk. https://doi.org/10.1080/19475705.2019.1650126

    Article  Google Scholar 

  53. Moayedi H, Hayati S (2018) Applicability of a CPT-based neural network solution in predicting load-settlement responses of bored pile. Int J Geomech 18:06018009. https://doi.org/10.1061/%28ASCE%29GM.1943-5622.0001125

    Article  Google Scholar 

  54. Moayedi H, Rezaei A (2017) An artificial neural network approach for under-reamed piles subjected to uplift forces in dry sand. Neural Comput Appl 31:327–336. https://doi.org/10.1007/s00521-017-2990-z

    Article  Google Scholar 

  55. 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 

  56. Das S, Bhattacharya A, Chakraborty AK (2017) Solution of short-term hydrothermal scheduling using sine cosine algorithm. Soft Comput. https://doi.org/10.1007/s00500-017-2695-3

    Article  MATH  Google Scholar 

  57. Nayak DR, Dash R, Majhi B, Wang S (2018) Combining extreme learning machine with modified sine cosine algorithm for detection of pathological brain. Comput Electr Eng 68:366–380. https://doi.org/10.1016/j.compeleceng.2018.04.009

    Article  Google Scholar 

  58. Reddy KS, Panwar LK, Panigrahi B, Kumar R (2018) A new binary variant of sine-cosine algorithm: development and application to solve profit-based unit commitment problem. Arab J Sci Eng 43:4041–4056. https://doi.org/10.1007/s13369-017-2790-x

    Article  Google Scholar 

  59. Li S, Fang H, Liu X (2018) Parameter optimization of support vector regression based on sine cosine algorithm. Expert Syst Appl 91:63–77. https://doi.org/10.1016/j.eswa.2017.08.038

    Article  Google Scholar 

  60. Chen H, Heidari AA, Zhao X, Zhang L, Chen H (2019) Advanced orthogonal learning-driven multi-swarm sine cosine optimization: framework and case studies. Expert Syst Appl 45:50

    Google Scholar 

  61. Chen H, Wang M, Zhao X (2020) A multi-strategy enhanced sine cosine algorithm for global optimization and constrained practical engineering problems. Appl Math Comput 369:124872. https://doi.org/10.1016/j.amc.2019.124872

    Article  MathSciNet  MATH  Google Scholar 

  62. Zhu W, Ma C, Zhao X, Wang M, Heidari AA, Chen H, Li C (2020) Evaluation of sino foreign cooperative education project using orthogonal sine cosine optimized kernel extreme learning machine. IEEE Access 8:61107–61123. https://doi.org/10.1109/ACCESS.2020.2981968

    Article  Google Scholar 

  63. Liu G, Jia W, Wang M, Heidari AA, Chen H, Luo Y, Li C (2020) Predicting cervical hyperextension injury: a covariance guided sine cosine support vector machine. IEEE Access 8:46895–46908. https://doi.org/10.1109/ACCESS.2020.2978102

    Article  Google Scholar 

  64. Huang H, Feng X, Heidari AA, Xu Y, Wang M, Liang G, Chen H, Cai X (2020) Rationalized sine cosine optimization with efficient searching patterns. IEEE Access 8:61471–61490. https://doi.org/10.1109/ACCESS.2020.2983451

    Article  Google Scholar 

  65. Chen H, Heidari AA, Zhao X, Zhang L, Chen H (2020) Advanced orthogonal learning-driven multi-swarm sine cosine optimization: framework and case studies. Expert Syst Appl 144:113113. https://doi.org/10.1016/j.eswa.2019.113113

    Article  Google Scholar 

  66. Tu J, Lin A, Chen H, Li Y, Li C (2019) Predict the entrepreneurial intention of fresh graduate students based on an adaptive support vector machine framework. Math Probl Eng 2019:1–16. https://doi.org/10.1155/2019/2039872

    Article  Google Scholar 

  67. Lin A, Wu Q, Heidari AA, Xu Y, Chen H, Geng W, Li Y, Li C (2019) Predicting intentions of students for master programs using a chaos-induced sine cosine-based Fuzzy K-Nearest Neighbor Classifier. IEEE Access 7:67235–67248. https://doi.org/10.1109/ACCESS.2019.2918026

    Article  Google Scholar 

  68. Chen H, Jiao S, Heidari AA, Wang M, Chen X, Zhao X (2019) An opposition-based sine cosine approach with local search for parameter estimation of photovoltaic models. Energy Convers Manag 195:927–942. https://doi.org/10.1016/j.enconman.2019.05.057

    Article  Google Scholar 

  69. Fan Y, Wang P, Heidari AA, Wang M, Zhao X, Chen H, Li C (2020) Rationalized fruit fly optimization with sine cosine algorithm: a comprehensive analysis. Expert Syst Appl 157:113486. https://doi.org/10.1016/j.eswa.2020.113486

    Article  Google Scholar 

  70. Abd Elaziz M, Oliva D, Xiong S (2017) An improved opposition-based sine cosine algorithm for global optimization. Expert Syst Appl 90:484–500. https://doi.org/10.1016/j.eswa.2017.07.043

    Article  Google Scholar 

  71. Turgut OE (2017) Thermal and economical optimization of a shell and tube evaporator using hybrid backtracking search—sine–cosine algorithm. Arab J Sci Eng 42:2105–2123. https://doi.org/10.1007/s13369-017-2458-6

    Article  Google Scholar 

  72. Nenavath H, Kumar Jatoth DR, Das DS (2018) A synergy of the sine-cosine algorithm and particle swarm optimizer for improved global optimization and object tracking. Swarm Evol Comput. https://doi.org/10.1016/j.swevo.2018.02.011

    Article  Google Scholar 

  73. Issa M, Hassanien AE, Oliva D, Helmi A, Ziedan I, Alzohairy A (2018) ASCA-PSO: adaptive sine cosine optimization algorithm integrated with particle swarm for pairwise local sequence alignment. Expert Syst Appl 99:56–70. https://doi.org/10.1016/j.eswa.2018.01.019

    Article  Google Scholar 

  74. Chegini SN, Bagheri A, Najafi F (2018) PSOSCALF: a new hybrid PSO based on sine cosine algorithm and levy flight for solving optimization problems. Appl Soft Comput J 73:697–726. https://doi.org/10.1016/j.asoc.2018.09.019

    Article  Google Scholar 

  75. Nenavath H, Jatoth RK (2018) Hybridizing sine cosine algorithm with differential evolution for global optimization and object tracking. Appl Soft Comput J 62:1019–1043. https://doi.org/10.1016/j.asoc.2017.09.039

    Article  Google Scholar 

  76. Qu C, Zeng Z, Dai J, Yi Z, He W (2018) A modified sine-cosine algorithm based on neighborhood search and greedy levy mutation. Comput Intell Neurosci. https://doi.org/10.1155/2018/4231647

    Article  Google Scholar 

  77. Rizk-Allah RM (2018) An improved sine–cosine algorithm based on orthogonal parallel information for global optimization. Soft Comput. https://doi.org/10.1007/s00500-018-3355-y

    Article  Google Scholar 

  78. Zamli KZ, Din F, Ahmed BS, Bures M (2018) A hybrid Q-learning sine-cosine-based strategy for addressing the combinatorial test suite minimization problem. PLoS ONE. https://doi.org/10.1371/journal.pone.0195675

    Article  Google Scholar 

  79. Zhang J, Zhou Y, Luo Q (2018) An improved sine cosine water wave optimization algorithm for global optimization. J Intell Fuzzy Syst 34:2129–2141. https://doi.org/10.3233/JIFS-171001

    Article  Google Scholar 

  80. Gupta S, Deep K (2019) A hybrid self-adaptive sine cosine algorithm with opposition based learning. Expert Syst Appl 119:210–230. https://doi.org/10.1016/j.eswa.2018.10.050

    Article  Google Scholar 

  81. Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: González JR, Pelta DA, Cruz C, Terrazas G, Krasnogor N (eds) Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, pp 65–74. https://doi.org/10.1007/978-3-642-12538-6_6

    Chapter  Google Scholar 

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

    Article  MATH  Google Scholar 

  83. Yang X-S (2010) Firefly algorithm, stochastic test functions and design optimisation. arXiv preprint arXiv:1003.1409

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

    Article  MathSciNet  Google Scholar 

  85. Fister Jr I, Fister D, Yang X-S (2013) A hybrid bat algorithm. arXiv preprint arXiv:1303.6310

  86. Wang W, Liu X (2015) Melt index prediction by least squares support vector machines with an adaptive mutation fruit fly optimization algorithm. Chemometr Intell Lab Syst 141:79–87. https://doi.org/10.1016/j.chemolab.2014.12.007

    Article  Google Scholar 

  87. Li M-W, Geng J, Han D-F, Zheng T-J (2016) Ship motion prediction using dynamic seasonal RvSVR with phase space reconstruction and the chaos adaptive efficient FOA. Neurocomputing 174:661–680. https://doi.org/10.1016/j.neucom.2015.09.089

    Article  Google Scholar 

  88. Wang G-G, Deb S, Gandomi AH, Alavi AH (2016) Opposition-based krill herd algorithm with Cauchy mutation and position clamping. Neurocomputing 177:147–157. https://doi.org/10.1016/j.neucom.2015.11.018

    Article  Google Scholar 

  89. Jiao S, Chong G, Huang C, Hu H, Wang M, Heidari AA, Chen H, Zhao X (2020) Orthogonally adapted Harris Hawk Optimization for parameter estimation of photovoltaic models. Energy. https://doi.org/10.1016/j.energy.2020.117804

    Article  Google Scholar 

  90. Chen H, Jiao S, Wang M, Heidari AA, Zhao X (2020) Parameters identification of photovoltaic cells and modules using diversification-enriched Harris hawks optimization with chaotic drifts. J Clean Prod 244:118778. https://doi.org/10.1016/j.jclepro.2019.118778

    Article  Google Scholar 

  91. Tang H, Xu Y, Lin A, Heidari AA, Wang M, Chen H, Luo Y, Li C (2020) Predicting green consumption behaviors of students using efficient firefly grey wolf-assisted K-nearest neighbor classifiers. IEEE Access 8:35546–35562. https://doi.org/10.1109/ACCESS.2020.2973763

    Article  Google Scholar 

  92. Li C, Zhou J, Xiao J, Xiao H (2012) Parameters identification of chaotic system by chaotic gravitational search algorithm. Chaos Solit Fract 45:539–547

    Article  Google Scholar 

  93. Jia D, Zheng G, Khan MK (2011) An effective memetic differential evolution algorithm based on chaotic local search. Inf Sci 181:3175–3187

    Article  Google Scholar 

  94. Chen H, Xu Y, Wang M, Zhao X (2019) A balanced whale optimization algorithm for constrained engineering design problems. Appl Math Model 71:45–59. https://doi.org/10.1016/j.apm.2019.02.004

    Article  MathSciNet  MATH  Google Scholar 

  95. Yu Y, Gao S, Cheng S, Wang Y, Song S, Yuan F (2018) CBSO: a memetic brain storm optimization with chaotic local search. Mem Comput 10:353–367

    Article  Google Scholar 

  96. Wang G-G, Guo L, Gandomi AH, Hao G-S, Wang H (2014) Chaotic krill herd algorithm. Inf Sci 274:17–34. https://doi.org/10.1016/j.ins.2014.02.123

    Article  MathSciNet  Google Scholar 

  97. 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 1:3–18

    Article  Google Scholar 

  98. 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 180:2044–2064

    Article  Google Scholar 

  99. Coello Coello CA (2002) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: A survey of the state of the art. Comput Methods Appl Mech Eng 191:1245–1287. https://doi.org/10.1016/S0045-7825(01)00323-1

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  101. 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

    Google Scholar 

  102. Mezura-Montes E, Coello CAC (2008) An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. Int J Gen Syst 37:443–473. https://doi.org/10.1080/03081070701303470

    Article  MathSciNet  MATH  Google Scholar 

  103. Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188:1567–1579. https://doi.org/10.1016/j.amc.2006.11.033

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  105. Coello Coello CA (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41:113–127. https://doi.org/10.1016/S0166-3615(99)00046-9

    Article  MATH  Google Scholar 

  106. Kaveh A, Khayatazad M (2012) A new meta-heuristic method: Ray Optimization. Comput Struct 112–113:283–294. https://doi.org/10.1016/j.compstruc.2012.09.003

    Article  Google Scholar 

  107. Lee KS, Geem ZW (2005) A new meta-heuristic algorithm for continuous engineering optimization: Harmony search theory and practice. Comput Methods Appl Mech Eng 194:3902–3933. https://doi.org/10.1016/j.cma.2004.09.007

    Article  MATH  Google Scholar 

  108. Ragsdell KM, Phillips DT (1976) Optimal design of a class of welded structures using geometric programming. J Manuf Sci Eng Trans ASME 98:1021–1025. https://doi.org/10.1115/1.3438995

    Article  Google Scholar 

  109. Wang GG (2003) Adaptive response surface method using inherited Latin hypercube design points. J Mech Des Trans ASME 125:210–220. https://doi.org/10.1115/1.1561044

    Article  Google Scholar 

  110. Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29:17–35. https://doi.org/10.1007/s00366-011-0241-y

    Article  Google Scholar 

  111. Cheng MY, 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 

Download references

Acknowledgements

This research was supported by Guangdong Natural Science Foundation (2018A030313339), MOE (Ministry of Education in China) Youth Fund Project of Humanities and Social Sciences (17YJCZH261), and Scientific Research Team Project of Shenzhen Institute of Information Technology (SZIIT2019KJ022).

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Mingjing Wang, Huiling Chen or Chengye Li.

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

Liang, X., Cai, Z., Wang, M. et al. Chaotic oppositional sine–cosine method for solving global optimization problems. Engineering with Computers 38, 1223–1239 (2022). https://doi.org/10.1007/s00366-020-01083-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-020-01083-y

Keywords

Navigation