Abstract
Harris Hawk’s Optimizer (HHO) is a recently developed meta-heuristics search algorithm with inherent capability to explore global minima and maxima. However, the local search of the basic HHO algorithm is sluggish and has slow convergence rate due to its poor exploitation capability. In the present work, exploration and exploitation phase of HHO have been improved using a chaotic variant of the present optimizer. The proposed chaotic variant has been simulated and tested for 23 standard test functions and 10 different engineering design optimization problems of real life. To check the efficacy of the proposed algorithm, the test results of the proposed CHHO algorithm have been compared with others recently developed and well-known classical optimizers, such as PSO, DE, SSA, MVO, GWO, DE, MFO, SCA, CS, TSA, PSO-DE, GA, HS, Ray and Sain, MBA, ACO, MMA, etc. The experimental results reveal that the suggested method outperforms on most of the test functions and engineering design challenges with superior convergence.
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References
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
Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1:28–39. https://doi.org/10.1109/MCI.2006.329691
Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Perth A (ed) Proceedings of IEEE international conference of neural network. Springer, Cham, pp 1942–1948
Karaboga D, Gorkemli B, Ozturk C, Karaboga N (2014) A comprehensive survey: artificial bee colony (ABC) algorithm and applications. Artif Intell Rev 42:21–57. https://doi.org/10.1007/s10462-012-9328-0
Yang XS (2010) A new metaheuristic bat-inspired algorithm. Nature inspired ooperative strategies for optimization (NICSO 2010). Springer, Cham, p 65
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
Gandomi AH, Alavi AH (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17:4831–4845. https://doi.org/10.1016/j.cnsns.2012.05.010
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 110–111:151–166. https://doi.org/10.1016/j.compstruc.2012.07.010
Li X, Zhang J, Yin M (2014) Animal migration optimization: an optimization algorithm inspired by animal migration behavior. Neural Comput Appl 24:1867–1877. https://doi.org/10.1007/s00521-013-1433-8
Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition, 2007 IEEE Congr. Evol Comput CEC 2007:4661–4667. https://doi.org/10.1109/CEC.2007.4425083
Cohen AI, Yoshimura M (1983) A branch-and-bound algorithm for unit commitment. IEEE Trans Power Appar Syst 102:444–451
Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris Hawks optimization: algorithm and applications. Futur Gener Comput Syst 97:849–872. https://doi.org/10.1016/j.future.2019.02.028
Kazarlis SA, Bakirtzis AG, Petridis V (1996) A genetic algorithm solution to the unit commitment problem. IEEE Trans Power Syst 11:83–92. https://doi.org/10.1109/59.485989
Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359
Hamdani H, Radi B, El Hami A (2019) Optimization of solder joints in embedded mechatronic systems via Kriging-assisted CMA-ES algorithm. Int J Simul Multidiscip Des Optim 10:A3. https://doi.org/10.1051/smdo/2019002
Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci (Ny) 179:2232–2248. https://doi.org/10.1016/j.ins.2009.03.004
Kaveh A (2016) Advances in metaheuristic algorithms for optimal design of structures, 2nd edn. Springer, Cham. https://doi.org/10.1007/978-3-319-46173-1
Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27:495–513. https://doi.org/10.1007/s00521-015-1870-7
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
Glover F, Melián B (2003) Tabu search. Intel Artif 7:43–57. https://doi.org/10.4114/ia.v7i19.714
Satapathy SC, Naik A, Parvathi K (2013) A teaching learning based optimization based on orthogonal design for solving global optimization problems. Springerplus 2:1–12. https://doi.org/10.1186/2193-1801-2-130
Mirjalili S, Jangir P, Saremi S (2017) Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems. Appl Intell 46:79–95. https://doi.org/10.1007/s10489-016-0825-8
Saremi S, Mirjalili S, Lewis A (2014) Biogeography-based optimisation with chaos. Neural Comput Appl 25:1077–1097. https://doi.org/10.1007/s00521-014-1597-x
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
Hashim FA, Hussain K, Houssein EH, Mabrouk MS, Al-Atabany W (2021) Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems. Appl Intell 51:1531–1551. https://doi.org/10.1007/s10489-020-01893-z
Hu K, Jiang H, Ji CG, Pan Z (2021) A modified butterfly optimization algorithm: an adaptive algorithm for global optimization and the support vector machine. Expert Syst 38:1–18. https://doi.org/10.1111/exsy.12642
Bala Krishna A, Saxena S, V.K, (2021) Kamboj, hSMA-PS: a novel memetic approach for numerical and engineering design challenges. Springer, London. https://doi.org/10.1007/s00366-021-01371-1
Abualigah L, Yousri D, Abd Elaziz M, Ewees AA, Al-qaness MAA, Gandomi AH (2021) Aquila optimizer: a novel meta-heuristic optimization algorithm. Comput Ind Eng 157:107250. https://doi.org/10.1016/j.cie.2021.107250
Xu Z, Gui W, Heidari AA, Liang G, Chen H, Wu C, Turabieh H, Mafarja M (2021) Spiral motion mode embedded grasshopper optimization algorithm: design and analysis. IEEE Access 9:71104–71132. https://doi.org/10.1109/access.2021.3077616
Neshat M, Nezhad MM, Abbasnejad E, Mirjalili S, Groppi D, Heydari A, Tjernberg LB, Astiaso Garcia D, Alexander B, Shi Q, Wagner M (2021) Wind turbine power output prediction using a new hybrid neuro-evolutionary method. Energy 229:120617. https://doi.org/10.1016/j.energy.2021.120617
Kaur A, Singh L, Dhillon JS (2021) Modified Krill Herd algorithm for constrained economic load dispatch problem. Int J Ambient Energy. https://doi.org/10.1080/01430750.2021.1888798
Nandi A, Kamboj VK (2021) A meliorated Harris Hawks Optimizer for combinatorial unit commitment problem with photovoltaic applications. J Electr Syst Inf Technol. https://doi.org/10.1186/s43067-020-00026-3
Yang Y, Chen H, Heidari AA, Gandomi AH (2021) Hunger games search: Visions, conception, implementation, deep analysis, perspectives, and towards performance shifts. Expert Syst Appl 177:114864. https://doi.org/10.1016/j.eswa.2021.114864
Osaba E, Yang X-S (2021) Soccer-inspired metaheuristics: systematic review of recent research and applications. Appl Optim Swarm Intell. https://doi.org/10.1007/978-981-16-0662-5_5
Barshandeh S, Piri F, Sangani SR (2020) HMPA: an innovative hybrid multi-population algorithm based on artificial ecosystem-based and Harris Hawks optimization algorithms for engineering problems. Springer, London. https://doi.org/10.1007/s00366-020-01120-w
Li S, Chen H, Wang M, Heidari AA, Mirjalili S (2020) Slime mould algorithm: a new method for stochastic optimization. Futur Gener Comput Syst. https://doi.org/10.1016/j.future.2020.03.055
Faramarzi A, Heidarinejad M, Mirjalili S, Gandomi AH (2020) Marine predators algorithm: a nature-inspired metaheuristic. Expert Syst Appl 152:113377. https://doi.org/10.1016/j.eswa.2020.113377
Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris Hawks optimization: algorithm and applications. Futur Gener Comput Syst. https://doi.org/10.1016/j.future.2019.02.028
Chen X, Tianfield H, Li K, SC, (2019) Self-adaptive differential artificial bee colony algorithm for global optimization problems. Swarm Evol Comput. https://doi.org/10.1016/j.swevo.2019.01.003
Shadravan S, Naji HR, Bardsiri VK (2019) The Sailfish Optimizer: a novel nature-inspired metaheuristic algorithm for solving constrained engineering optimization problems. Eng Appl Artif Intell 80:20–34. https://doi.org/10.1016/j.engappai.2019.01.001
Pierezan J (2018) Coyote optimization algorithm : a new metaheuristic for global optimization problems. In: 2018 IEEE Congress on Evolutionary Computation, pp 1–8
Sulaiman MH, Mustaffa Z, Saari MM, Daniyal H, Mohamad AJ, Othman MR (2019) Barnacles mating optimizer algorithm for optimization mohd. Springer, Singapore. https://doi.org/10.1007/978-981-13-3708-6
Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191. https://doi.org/10.1016/j.advengsoft.2017.07.002
Tabari A, Ahmad A (2017) Accept e us cr t. Comput Chem Eng. https://doi.org/10.1016/j.compchemeng.2017.01.046
Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47. https://doi.org/10.1016/j.advengsoft.2017.01.004
Singh N, Singh SB (2017) A novel hybrid GWO-SCA approach for optimization problems. Eng Sci Technol an Int J 20:1586–1601. https://doi.org/10.1016/j.jestch.2017.11.001
Gohil NB, Dwivedi VV (2017) A review on lion optimization : nature inspired evolutionary algorithm. Int J Adv Manag Technol Eng Sci 7:340–352
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
Gray B (2015) W. optimization, author’ s accepted manuscript binary gray wolf optimization approaches for feature selection. Neurocomputing. https://doi.org/10.1016/j.neucom.2015.06.083
Shahriar MS, Rana MJ, Asif MA, Hasan MM, Hawlader MM (2015) Optimization of Unit Commitment Problem for wind-thermal generation using Fuzzy optimization technique. In 2015 International conference on advances in electrical engineering (ICAEE). IEEE, pp 88–92
Huang L, Ding S, Yu S, Wang J, Lu K (2016) Chaos-enhanced Cuckoo search optimization algorithms for global optimization. Appl Math Model 40:3860–3875. https://doi.org/10.1016/j.apm.2015.10.052
Ghasemi M, Ghavidel S, Akbari E, Vahed AA (2014) Solving non-linear, non-smooth and non-convex optimal power flow problems using chaotic invasive weed optimization algorithms based on chaos. Energy 73:340–353. https://doi.org/10.1016/j.energy.2014.06.026
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
Wang GG, Guo L, Gandomi AH, Hao GS, Wang H (2014) Chaotic Krill Herd algorithm. Inf Sci (Ny) 274:17–34. https://doi.org/10.1016/j.ins.2014.02.123
Gandomi AH (2014) Interior search algorithm (ISA): a novel approach for global optimization. ISA Trans 53:1168–1183. https://doi.org/10.1016/j.isatra.2014.03.018
Mohseni S, Gholami R, Zarei N, Zadeh AR (2014) Competition over resources: a new optimization algorithm based on animals behavioral ecology. Proc Int Conf Intell Netw Collab Syst. https://doi.org/10.1109/INCoS.2014.55
Ghaemi M, Feizi-Derakhshi MR (2014) Forest optimization algorithm. Expert Syst Appl 41:6676–6687. https://doi.org/10.1016/j.eswa.2014.05.009
Salimi H (2015) Stochastic fractal search: a powerful metaheuristic algorithm. Knowl-Based Syst 75:1–18. https://doi.org/10.1016/j.knosys.2014.07.025
Kuo HC, Lin CH (2013) Cultural evolution algorithm for global optimizations and its applications. J Appl Res Technol 11:510–522. https://doi.org/10.1016/S1665-6423(13)71558-X
Alabool HM, Alarabiat D, Abualigah L, Heidari AA (2021) Harris hawks optimization: a comprehensive review of recent variants and applications. Springer, London. https://doi.org/10.1007/s00521-021-05720-5
Yıldız AR, Yıldız BS, Sait SM, Li X (2019) The Harris hawks, grasshopper and multi-verse optimization algorithms for the selection of optimal machining parameters in manufacturing operations. Mater Test 61:725–733. https://doi.org/10.3139/120.111377
Abbasi A, Firouzi B, Sendur P (2021) On the application of Harris Hawks Optimization (HHO) algorithm to the design of microchannel heat sinks. Eng Comput 37:1409–1428. https://doi.org/10.1007/s00366-019-00892-0
Moayedi H, Osouli A, Nguyen H, Rashid ASA (2021) A novel Harris hawks’ Optimization and k-fold cross-validation predicting slope stability. Eng Comput 37:369–379. https://doi.org/10.1007/s00366-019-00828-8
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. Futur Gener Comput Syst 111:175–198. https://doi.org/10.1016/j.future.2020.04.008
Firouzi B, Abbasi A, Sendur P (2021) Improvement of the computational efficiency of metaheuristic algorithms for Improvement of the computational efficiency of metaheuristic algorithms for the crack detection of cantilever beams using hybrid methods. Eng Optim. https://doi.org/10.1080/0305215X.2021.1919887
Wei Y, Lv H, Chen M, Wang M, Heidari AA, Chen H, Li C (2020) Predicting entrepreneurial intention of students: an extreme learning machine with gaussian barebone Harris Hawks optimizer. IEEE Access 8:76841–76855. https://doi.org/10.1109/ACCESS.2020.2982796
Qu C, He W, Peng X, Peng X (2020) Harris Hawks optimization with information exchange. Appl Math Model 84:52–75. https://doi.org/10.1016/j.apm.2020.03.024
Elkadeem MR, Abd Elaziz M, Ullah Z, Wang S, Sharshir SW (2019) Optimal planning of renewable energy-integrated distribution system considering uncertainties. IEEE Access. 7:164887–164907. https://doi.org/10.1109/ACCESS.2019.2947308
Ebrahimzadeh R, Jampour M (2013) Chaotic genetic algorithm based on lorenz chaotic system for optimization problems. Int J Intell Syst Appl 5:19–24. https://doi.org/10.5815/ijisa.2013.05.03
Ji Y, Tu J, Zhou H, Gui W, Liang G, Chen H, Wang M (2020) An adaptive chaotic sine cosine algorithm for constrained and unconstrained optimization. Complexity. https://doi.org/10.1155/2020/6084917
Afrabandpey H, Ghaffari M, Mirzaei A, Safayani M (2014) A novel Bat Algorithm based on chaos for optimization tasks, 2014 Iran. Conf Intell Syst ICIS. https://doi.org/10.1109/IranianCIS.2014.6802527
Kohli M, Arora S (2018) Chaotic grey wolf optimization algorithm for constrained optimization problems. J Comput Des Eng 5:458–472. https://doi.org/10.1016/j.jcde.2017.02.005
Chuang LY, Hsiao CJ, Yang CH (2011) Chaotic particle swarm optimization for data clustering. Expert Syst Appl 38:14555–14563. https://doi.org/10.1016/j.eswa.2011.05.027
Kaur G, Arora S (2018) Chaotic whale optimization algorithm. J Comput Des Eng 5:275–284. https://doi.org/10.1016/j.jcde.2017.12.006
Ewees AA, Elaziz MA (2020) Performance analysis of Chaotic Multi-Verse Harris Hawks Optimization: a case study on solving engineering problems. Eng Appl Artif Intell 88:103370. https://doi.org/10.1016/j.engappai.2019.103370
Barshandeh S, Haghzadeh M (2020) A new hybrid chaotic atom search optimization based on tree-seed algorithm and Levy flight for solving optimization problems. Springer, London. https://doi.org/10.1007/s00366-020-00994-0
Dhawale D, Kamboj VK (2020) HHHO-IGWO: A new hybrid harris hawks optimizer for solving global optimization problems. Proc Int Conf Comput Autom Knowl Manag. https://doi.org/10.1109/ICCAKM46823.2020.9051509
Fu W, Shao K, Tan J, Wang K (2020) Fault diagnosis for rolling bearings based on composite multiscale fine-sorted dispersion entropy and SVM with hybrid mutation SCA-HHO algorithm optimization. IEEE Access 8:13086–13104. https://doi.org/10.1109/ACCESS.2020.2966582
Kamboj VK, Nandi A, Bhadoria A, Sehgal S (2020) An intensify Harris Hawks Optimizer for numerical and engineering optimization problems. Appl Soft Comput J 89:106018. https://doi.org/10.1016/j.asoc.2019.106018
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
Hu H, Ao Y, Bai Y, Cheng R, Xu T (2020) An improved Harris’s Hawks Optimization for SAR target recognition and stock market index prediction. IEEE Access 8:65891–65910. https://doi.org/10.1109/ACCESS.2020.2985596
Selim A, Kamel S, Alghamdi AS, Jurado F (2020) Optimal placement of DGs in distribution system using an improved harris hawks optimizer based on single- and multi-objective approaches. IEEE Access 8:52815–52829. https://doi.org/10.1109/ACCESS.2020.2980245
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
Zhong C, Wang M, Dang C, Ke W, Guo S (2020) First-order reliability method based on Harris Hawks Optimization for high-dimensional reliability analysis. Struct Multidiscip Optim 62:1951–1968. https://doi.org/10.1007/s00158-020-02587-3
Fan Q, Chen Z, Xia Z (2020) A novel quasi-reflected Harris hawks optimization algorithm for global optimization problems. Soft Comput 24:14825–14843. https://doi.org/10.1007/s00500-020-04834-7
Essa FA, Abd Elaziz M, Elsheikh AH (2020) An enhanced productivity prediction model of active solar still using artificial neural network and Harris Hawks optimizer. Appl Therm Eng 170:115020. https://doi.org/10.1016/j.applthermaleng.2020.115020
Menesy AS, Sultan HM, Selim A, Ashmawy MG, Kamel S (2020) Developing and applying Chaotic Harris Hawks Optimization technique for extracting parameters of several proton exchange membrane fuel cell stacks. IEEE Access 8:1. https://doi.org/10.1109/ACCESS.2019.2961811
Yin Q, Cao B, Li X, Wang, B, Zhang, Q, Wei X (2020) An intelligent optimization algorithm for constructing a DNA storage code: NOL-HHO. Int J Mol Sci 21(6):2191
Li C, Li J, Chen H (2020) A meta-heuristic-based approach for Qos-aware service composition. IEEE Access 8:69579–69592. https://doi.org/10.1109/ACCESS.2020.2987078
Shehabeldeen TA, Elaziz MA, Elsheikh AH, Zhou J (2019) Modeling of friction stir welding process using adaptive neuro-fuzzy inference system integrated with Harris Hawks Optimizer. J Mater Res Technol 8:5882–5892. https://doi.org/10.1016/j.jmrt.2019.09.060
Birogul S (2019) Hybrid harris hawk optimization based on differential evolution (HHODE) algorithm for optimal power flow problem. IEEE Access 7:184468–184488. https://doi.org/10.1109/ACCESS.2019.2958279
Moayedi H, Abdullahi MM, Nguyen H, Rashid ASA (2021) Comparison of dragonfly algorithm and Harris hawks optimization evolutionary data mining techniques for the assessment of bearing capacity of footings over two-layer foundation soils. Eng Comput 37:437–447. https://doi.org/10.1007/s00366-019-00834-w
Rezaie H, Kazemi-Rahbar MH, Vahidi B, Rastegar H (2019) Solution of combined economic and emission dispatch problem using a novel chaotic improved harmony search algorithm. J Comput Des Eng 6:447–467. https://doi.org/10.1016/j.jcde.2018.08.001
Saxena A, Shekhawat S, Kumar R (2018) Application and development of enhanced chaotic grasshopper optimization algorithms. Model Simul Eng. https://doi.org/10.1155/2018/4945157
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
Gao ZM, Zhao J, Hu YR, Chen HF (2019) The improved harris hawk optimization algorithm with the tent map. IEEE Int Conf Electron Inf Technol Comput Eng. https://doi.org/10.1109/EITCE47263.2019.9095091
Bednarz JC (1988) Cooperative hunting in Harris’ Hawks (Parabuteo unicinctus). Science (80-) 239:1525–1527. https://doi.org/10.1126/science.239.4847.1525
Wang J, Wang D (2008) Particle swarm optimization with a leader and followers. Prog Nat Sci 18:1437–1443. https://doi.org/10.1016/j.pnsc.2008.03.029
Xie J, Zhou YQ, Chen H (2013) A bat algorithm based on Lévy flights trajectory, Moshi Shibie Yu Rengong Zhineng/Pattern Recognit. Artif Intell 26:829–837
Yang XS (2010) Firefly algorithm. In: Ch M (ed) Engineering optimization: an introduction with metaheuristic applications. John Wiley and Sons Inc, Hoboken, p 221
Kazarlis SA (1996) A genetic algorithm solution to the unit commitment problem. IEEE Trans Power Syst 11:83–92
Cuevas E, Echavarría A, Ramírez-Ortegón MA (2014) An optimization algorithm inspired by the States of Matter that improves the balance between exploration and exploitation. Appl Intell 40:256–272. https://doi.org/10.1007/s10489-013-0458-0
Yang XS, Karamanoglu M, He X (2014) Flower pollination algorithm: a novel approach for multiobjective optimization. Eng Optim 46(9):1222–1237
Jagodziński D, Arabas J (2017) A differential evolution strategy. In 2017 IEEE Congress on Evolutionary Computation (CEC), pp 1872–1876
Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98. https://doi.org/10.1016/j.advengsoft.2015.01.010
Dhawale D, Kamboj VK, Anand P (2021) An effective solution to numerical and multi-disciplinary design optimization problems using chaotic slime mold algorithm, Springer. London. https://doi.org/10.1007/s00366-021-01409-4
Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27:1053–1073. https://doi.org/10.1007/s00521-015-1920-1
Nezamabadi-pour H, Rostami-sharbabaki M, Maghfoori-Farsangi M (2008) Binary particle swarm optimization: challenges and new solutions. J Comput Soc Iran 6:21–32
Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179:2232
John H (1992) Holland, adaptation in natural and artificial systems. MIT Press, Cambridge
Nakamura RYM, Pereira LAM, Costa KA, Rodrigues D, Papa JP, Yang XS (2012) BBA: A binary bat algorithm for feature selection Brazilian Symp. Comput Graph Image Process. https://doi.org/10.1109/SIBGRAPI.2012.47
Storn R, Price K (1997) Differential evolution: a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359. https://doi.org/10.1023/A:1008202821328
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
Ray T, Saini P (2001) Engineering design optimization using a swarm with an intelligent information sharing among individuals. Eng Optim 33:735–748. https://doi.org/10.1080/03052150108940941
Tsai JFA (2005) Global optimization of nonlinear fractional programming problems in engineering design. Eng Optim 37:399–409. https://doi.org/10.1080/03052150500066737
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 J 13:2592–2612. https://doi.org/10.1016/j.asoc.2012.11.026
Zhao W, Zhang Z, Wang L (2020) Manta ray foraging optimization: an effective bio-inspired optimizer for engineering applications. Eng Appl Artif Intell 87:103300. https://doi.org/10.1016/j.engappai.2019.103300
Niu B, Li L (2008) A novel PSO-DE-Based hybrid algorithm for global optimization. Lect Notes Comput Sci. https://doi.org/10.1007/978-3-540-85984-0_20
Hameed IA, Bye RT, Osen OL (2016) Grey wolf optimizer (GWO) for automated offshore crane design. IEEE Symp Ser Comput Intell. https://doi.org/10.1109/SSCI.2016.7849998
Deb K, Goyal M (1996) A combined genetic adaptive search (GeneAS) for engineering design. Comput Sci Inf 26:30–45
Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13:398–417. https://doi.org/10.1109/TEVC.2008.927706
Chickermane H, Gea HC (2002) Structural optimization using a new local approximation method. Int J Numer Methods Eng 39:829–846. https://doi.org/10.1002/(sici)1097-0207(19960315)39:5%3c829::aid-nme884%3e3.0.co;2-u
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
Mezura-Montes E, Coello Coello CA (2005) A simple multimembered evolution strategy to solve constrained optimization problems, IEEE Trans. Evol Comput 9:1–17. https://doi.org/10.1109/TEVC.2004.836819
Deb K (1990) Optimal design of a class of welded structures via genetic algorithms. Collect Tech Pap AIAA/ASME/ASCE/AHS/ASC Struct Dyn Mater Conf. https://doi.org/10.2514/6.1990-1179
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
Wu G, Pedrycz W, Suganthan PN, Mallipeddi R (2015) A variable reduction strategy for evolutionary algorithms handling equality constraints. Appl Soft Comput J 37:774–786. https://doi.org/10.1016/j.asoc.2015.09.007
Sadollah A, Eskandar H, Bahreininejad A, Kim JH (2015) Water cycle algorithm with evaporation rate for solving constrained and unconstrained optimization problems. Appl Soft Comput J 30:58–71. https://doi.org/10.1016/j.asoc.2015.01.050
Kamboj VK, Bhadoria A, Gupta N (2018) A novel hybrid GWO-PS algorithm for standard benchmark optimization problems. Ina Lett 3:217–241. https://doi.org/10.1007/s41403-018-0051-2
Lee KS, Geem ZW (2004) A new structural optimization method based on the harmony search algorithm. Comput Struct 82:781–798. https://doi.org/10.1016/j.compstruc.2004.01.002
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
Rao RV, Savsani VJ, Vakharia DP (2011) Teaching-learning-based optimization: A novel method for constrained mechanical design optimization problems. CAD Comput Aided Des 43:303–315. https://doi.org/10.1016/j.cad.2010.12.015
Savsani P, Savsani V (2016) Passing vehicle search (PVS): a novel metaheuristic algorithm. Appl Math Model 40:3951–3978. https://doi.org/10.1016/j.apm.2015.10.040
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Dhawale, D., Kamboj, V.K. & Anand, P. An improved Chaotic Harris Hawks Optimizer for solving numerical and engineering optimization problems. Engineering with Computers 39, 1183–1228 (2023). https://doi.org/10.1007/s00366-021-01487-4
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DOI: https://doi.org/10.1007/s00366-021-01487-4