Wild horse optimizer: a new meta-heuristic algorithm for solving engineering optimization problems

Nowadays, the design of optimization algorithms is very popular to solve problems in various scientific fields. The optimization algorithms usually inspired by the natural behaviour of an agent, which can be humans, animals, plants, or a physical or chemical agent. Most of the algorithms proposed in...

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Published in:	Engineering with computers Vol. 38; no. Suppl 4; pp. 3025 - 3056
Main Authors:	Naruei, Iraj, Keynia, Farshid
Format:	Journal Article
Language:	English
Published:	London Springer London 01.10.2022 Springer Nature B.V
Subjects:	Algorithms Animals CAE) and Design Calculus of Variations and Optimal Control; Optimization Classical Mechanics Computer Science Computer-Aided Engineering (CAD Control Design optimization Heuristic methods Horses Math. Applications in Chemistry Mathematical and Computational Engineering Optimization algorithms Original Article Source code Systems Theory Optimization techniques Meta-heuristic algorithm Horse algorithm Wild horse optimizer
ISSN:	0177-0667, 1435-5663
Online Access:	Get full text
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Abstract	Nowadays, the design of optimization algorithms is very popular to solve problems in various scientific fields. The optimization algorithms usually inspired by the natural behaviour of an agent, which can be humans, animals, plants, or a physical or chemical agent. Most of the algorithms proposed in the last decade inspired by animal behaviour. In this article, we present a new optimizer algorithm called the wild horse optimizer (WHO), which is inspired by the social life behaviour of wild horses. Horses usually live in groups that include a stallion and several mares and foals. Horses exhibit many behaviours, such as grazing, chasing, dominating, leading, and mating. A fascinating behaviour that distinguishes horses from other animals is the decency of horses. Horse decency behaviour is such that the foals of the horse leave the group before reaching puberty and join other groups. This departure is to prevent the father from mating with the daughter or siblings. The main inspiration for the proposed algorithm is the decency behaviour of the horse. The proposed algorithm was tested on several sets of test functions such as CEC2017 and CEC2019 and compared with popular and new optimization methods. The results showed that the proposed algorithm presented very competitive results compared to other algorithms. The source code is currently available for public from: https://www.mathworks.com/matlabcentral/fileexchange/90787-wild-horse-optimizer .
AbstractList	Nowadays, the design of optimization algorithms is very popular to solve problems in various scientific fields. The optimization algorithms usually inspired by the natural behaviour of an agent, which can be humans, animals, plants, or a physical or chemical agent. Most of the algorithms proposed in the last decade inspired by animal behaviour. In this article, we present a new optimizer algorithm called the wild horse optimizer (WHO), which is inspired by the social life behaviour of wild horses. Horses usually live in groups that include a stallion and several mares and foals. Horses exhibit many behaviours, such as grazing, chasing, dominating, leading, and mating. A fascinating behaviour that distinguishes horses from other animals is the decency of horses. Horse decency behaviour is such that the foals of the horse leave the group before reaching puberty and join other groups. This departure is to prevent the father from mating with the daughter or siblings. The main inspiration for the proposed algorithm is the decency behaviour of the horse. The proposed algorithm was tested on several sets of test functions such as CEC2017 and CEC2019 and compared with popular and new optimization methods. The results showed that the proposed algorithm presented very competitive results compared to other algorithms. The source code is currently available for public from: https://www.mathworks.com/matlabcentral/fileexchange/90787-wild-horse-optimizer . Nowadays, the design of optimization algorithms is very popular to solve problems in various scientific fields. The optimization algorithms usually inspired by the natural behaviour of an agent, which can be humans, animals, plants, or a physical or chemical agent. Most of the algorithms proposed in the last decade inspired by animal behaviour. In this article, we present a new optimizer algorithm called the wild horse optimizer (WHO), which is inspired by the social life behaviour of wild horses. Horses usually live in groups that include a stallion and several mares and foals. Horses exhibit many behaviours, such as grazing, chasing, dominating, leading, and mating. A fascinating behaviour that distinguishes horses from other animals is the decency of horses. Horse decency behaviour is such that the foals of the horse leave the group before reaching puberty and join other groups. This departure is to prevent the father from mating with the daughter or siblings. The main inspiration for the proposed algorithm is the decency behaviour of the horse. The proposed algorithm was tested on several sets of test functions such as CEC2017 and CEC2019 and compared with popular and new optimization methods. The results showed that the proposed algorithm presented very competitive results compared to other algorithms. The source code is currently available for public from: https://www.mathworks.com/matlabcentral/fileexchange/90787-wild-horse-optimizer.
Author	Keynia, Farshid Naruei, Iraj
Author_xml	– sequence: 1 givenname: Iraj surname: Naruei fullname: Naruei, Iraj organization: Department Engineering, Kerman Branch, Islamic Azad University – sequence: 2 givenname: Farshid orcidid: 0000-0002-9027-7315 surname: Keynia fullname: Keynia, Farshid email: f.keynia@kgut.ac.ir organization: Department of Energy Management and Optimization, Institute of Science and High Technology and Environmental Sciences, Graduate University of Advanced Technology
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ContentType	Journal Article
Copyright	The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021.
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References	MirjaliliSMoth-flame optimization algorithm: a novel nature-inspired heuristic paradigmKnowl-Based Syst20158922824910.1016/j.knosys.2015.07.006 ChongEKPŻakSHAn introduction to optimization2008HobokenWiley10.1002/97811180333401140.90041 KaurSAwasthiLKSangalALDhimanGTunicate Swarm Algorithm: a new bio-inspired based metaheuristic paradigm for global optimizationEng Appl Artif Intell20209010354110.1016/j.engappai.2020.103541 DréoJMetaheuristics for hard optimization2006Berlin/HeidelbergSpringer-Verlag1118.90058 YangX-SFirefly algorithm, Lévy flights and global optimizationResearch and development in intelligent systems XXVI2010LondonSpringer20921810.1007/978-1-84882-983-1_15 MirjaliliSMirjaliliSMHatamlouAMulti-verse optimizer: a nature-inspired algorithm for global optimizationNeural Comput Appl20162749551310.1007/s00521-015-1870-7 RaoSSEngineering optimization: theory and practice1996New Age International Publishers HeidariAAMirjaliliSFarisHHarris hawks optimization: algorithm and applicationsFuture Gener Comput Syst20199784987210.1016/j.future.2019.02.028 RashediENezamabadi-pourHSaryazdiSGSA: a gravitational search algorithmInf Sci (NY)20091792232224810.1016/j.ins.2009.03.0041177.90378 AljarahIMafarjaMHeidariAAAsynchronous accelerating multi-leader salp chains for feature selectionAppl Soft Comput20187196497910.1016/j.asoc.2018.07.040 KocisGRGrossmannIEGlobal optimization of nonconvex mixed-integer nonlinear programming (MINLP) problems in process synthesisInd Eng Chem Res1988271407142110.1021/ie00080a013 MirjaliliSGandomiAHMirjaliliSZSalp Swarm algorithm: a bio-inspired optimizer for engineering design problemsAdv Eng Softw201711416319110.1016/j.advengsoft.2017.07.002 AnitaYAKumarNArtificial electric field algorithm for engineering optimization problemsExpert Syst Appl202014911330810.1016/j.eswa.2020.113308 Nowacki H (1973) Optimization in pre-contract ship design. In: International Conference on Computer Applications in the Automation of Shipyard Operation and ShipDesign, pp 1–12 PriceKVAwadNHAliMZPNSThe 100-digit challenge: problem definitions and evaluation criteria for the 100-digit challenge special session and competition on single objective numerical optimization2018Sch Elect Electron Eng, Nanyang Technol Univ, Singapore, Tech Rep HollandJHGenetic algorithms understand genetic algorithmsSurprise1967961121510.2307/24939139 MirjaliliSThe ant lion optimizerAdv Eng Softw201583809810.1016/j.advengsoft.2015.01.010 MillerRDennistoRHInterband dominance in feral horsesZ Tierpsychol201051414710.1111/j.1439-0310.1979.tb00670.x WolpertDHMacreadyWGNo free lunch theorems for optimizationIEEE Trans Evol Comput19971678210.1109/4235.585893 KumarAWuGAliMZA test-suite of non-convex constrained optimization problems from the real-world and some baseline resultsSwarm Evol Comput20205610069310.1016/j.swevo.2020.100693 BeightlerCSPDApplied geometric programming1976Wiley0344.90034 AbdullahJMAhmedTFitness dependent optimizer: inspired by the bee swarming reproductive processIEEE Access20197434734348610.1109/ACCESS.2019.2907012 SquiresVRDawsGTLeadership and dominance relationships in Merino and Border Leicester sheepAppl Anim Ethol1975126327410.1016/0304-3762(75)90019-X Klingel H (1975) Social organization and reproduction in equids. J Reprod Fertil Suppl 7–11 SaremiSMirjaliliSLewisAGrasshopper optimisation algorithm: theory and applicationAdv Eng Softw2017105304710.1016/j.advengsoft.2017.01.004 Eberhart R, Kennedy J (2002) A new optimizer using particle swarm theory. In: MHS’95. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science. IEEE, pp 39–43 Welsh DA, University D (1975) Population, behavioural and grazing ecology of the horses of Sable Island, Nova Scotia. PhD thesis, Dalhousie University CarsonKWood-GushDGMEquine behaviour: I. A review of the literature on social and dam—Foal behaviourAppl Anim Ethol19831016517810.1016/0304-3762(83)90138-4 WellsSMGoldschmidt-RothschildBSocial behaviour and relationships in a herd of camargue horsesZ Tierpsychol20104936338010.1111/j.1439-0310.1979.tb00299.x MirjaliliSSCA: a sine cosine algorithm for solving optimization problemsKnowl-Based Syst20169612013310.1016/j.knosys.2015.12.022 Awad NH, MZ. Ali JJ, Liang BY, Qu PS (2016) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective real-parameter numerical optimization. Tech Rep MautnerDHApplied nonlinear programming1972McGraw-Hill Co MirjaliliSLewisAThe whale optimization algorithmAdv Eng Softw201695516710.1016/j.advengsoft.2016.01.008 Awad NH, Ali MZ, Suganthan PN, Liang JJ, Qu BY (2017) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective real-parameter numerical optimization. In: 2017 IEEE Congress on Evolutionary Computation (CEC) Samareh MoosaviSHBardsiriVKPoor and rich optimization algorithm: a new human-based and multi populations algorithmEng Appl Artif Intell20198616518110.1016/j.engappai.2019.08.025 KocisGRGrossmannIEA modelling and decomposition strategy for the minlp optimization of process flowsheetsComput Chem Eng19891379781910.1016/0098-1354(89)85053-7 GuptaSTiwariRNairSBMulti-objective design optimisation of rolling bearings using genetic algorithmsMech Mach Theory2007421418144310.1016/j.mechmachtheory.2006.10.0021188.74082 MirjaliliSMirjaliliSMLewisAGrey wolf optimizerAdv Eng Softw201469466110.1016/j.advengsoft.2013.12.007 CarsonKWood-GushDGMEquine behaviour: II. A review of the literature on feeding, eliminative and resting behaviourAppl Anim Ethol19831017919010.1016/0304-3762(83)90139-6 BelegunduADAroraJSA study of mathematical programming methods for structural optimization. Part I: theoryInt J Numer Methods Eng1985211583159910.1002/nme.16202109040585.73159 MafarjaMAljarahIHeidariAAEvolutionary population dynamics and grasshopper optimization approaches for feature selection problemsKnowl-Based Syst2018145254510.1016/j.knosys.2017.12.037 Feist JD, McCullough DR (1975) Reproduction in feral horses. J Reprod Fertil Suppl (23):13–18. PMID:1060766 HousseinEHSaadMRHashimFALévy flight distribution: a new metaheuristic algorithm for solving engineering optimization problemsEng Appl Artif Intell20209410373110.1016/j.engappai.2020.103731 FloudasCACiricARGrossmannIEAutomatic synthesis of optimum heat exchanger network configurationsAIChE J19863227629010.1002/aic.690320215 K Carson (1438_CR24) 1983; 10 YA Anita (1438_CR17) 2020; 149 EH Houssein (1438_CR18) 2020; 94 S Mirjalili (1438_CR21) 2015; 89 M Mafarja (1438_CR3) 2018; 145 S Mirjalili (1438_CR13) 2017; 114 R Miller (1438_CR28) 2010; 51 SH Samareh Moosavi (1438_CR14) 2019; 86 S Saremi (1438_CR31) 2017; 105 EKP Chong (1438_CR1) 2008 S Mirjalili (1438_CR8) 2014; 69 1438_CR25 1438_CR6 S Mirjalili (1438_CR32) 2016; 96 A Kumar (1438_CR35) 2020; 56 1438_CR26 CA Floudas (1438_CR36) 1986; 32 AD Belegundu (1438_CR39) 1985; 21 1438_CR20 SM Wells (1438_CR27) 2010; 49 J Dréo (1438_CR2) 2006 S Mirjalili (1438_CR11) 2016; 95 1438_CR40 S Kaur (1438_CR19) 2020; 90 DH Wolpert (1438_CR22) 1997; 1 AA Heidari (1438_CR15) 2019; 97 JM Abdullah (1438_CR16) 2019; 7 GR Kocis (1438_CR38) 1989; 13 I Aljarah (1438_CR4) 2018; 71 CSPD Beightler (1438_CR43) 1976 S Mirjalili (1438_CR12) 2016; 27 K Carson (1438_CR23) 1983; 10 KV Price (1438_CR34) 2018 S Mirjalili (1438_CR10) 2015; 83 S Gupta (1438_CR42) 2007; 42 VR Squires (1438_CR29) 1975; 1 DH Mautner (1438_CR44) 1972 X-S Yang (1438_CR7) 2010 SS Rao (1438_CR41) 1996 E Rashedi (1438_CR9) 2009; 179 1438_CR33 GR Kocis (1438_CR37) 1988; 27 1438_CR30 JH Holland (1438_CR5) 1967; 96
References_xml	– reference: BelegunduADAroraJSA study of mathematical programming methods for structural optimization. Part I: theoryInt J Numer Methods Eng1985211583159910.1002/nme.16202109040585.73159 – reference: ChongEKPŻakSHAn introduction to optimization2008HobokenWiley10.1002/97811180333401140.90041 – reference: KocisGRGrossmannIEGlobal optimization of nonconvex mixed-integer nonlinear programming (MINLP) problems in process synthesisInd Eng Chem Res1988271407142110.1021/ie00080a013 – reference: Klingel H (1975) Social organization and reproduction in equids. J Reprod Fertil Suppl 7–11 – reference: KaurSAwasthiLKSangalALDhimanGTunicate Swarm Algorithm: a new bio-inspired based metaheuristic paradigm for global optimizationEng Appl Artif Intell20209010354110.1016/j.engappai.2020.103541 – reference: MirjaliliSGandomiAHMirjaliliSZSalp Swarm algorithm: a bio-inspired optimizer for engineering design problemsAdv Eng Softw201711416319110.1016/j.advengsoft.2017.07.002 – reference: Feist JD, McCullough DR (1975) Reproduction in feral horses. J Reprod Fertil Suppl (23):13–18. PMID:1060766 – reference: MillerRDennistoRHInterband dominance in feral horsesZ Tierpsychol201051414710.1111/j.1439-0310.1979.tb00670.x – reference: FloudasCACiricARGrossmannIEAutomatic synthesis of optimum heat exchanger network configurationsAIChE J19863227629010.1002/aic.690320215 – reference: RashediENezamabadi-pourHSaryazdiSGSA: a gravitational search algorithmInf Sci (NY)20091792232224810.1016/j.ins.2009.03.0041177.90378 – reference: MirjaliliSThe ant lion optimizerAdv Eng Softw201583809810.1016/j.advengsoft.2015.01.010 – reference: KumarAWuGAliMZA test-suite of non-convex constrained optimization problems from the real-world and some baseline resultsSwarm Evol Comput20205610069310.1016/j.swevo.2020.100693 – reference: AnitaYAKumarNArtificial electric field algorithm for engineering optimization problemsExpert Syst Appl202014911330810.1016/j.eswa.2020.113308 – reference: WellsSMGoldschmidt-RothschildBSocial behaviour and relationships in a herd of camargue horsesZ Tierpsychol20104936338010.1111/j.1439-0310.1979.tb00299.x – reference: MafarjaMAljarahIHeidariAAEvolutionary population dynamics and grasshopper optimization approaches for feature selection problemsKnowl-Based Syst2018145254510.1016/j.knosys.2017.12.037 – reference: MirjaliliSLewisAThe whale optimization algorithmAdv Eng Softw201695516710.1016/j.advengsoft.2016.01.008 – reference: Eberhart R, Kennedy J (2002) A new optimizer using particle swarm theory. 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A review of the literature on social and dam—Foal behaviourAppl Anim Ethol19831016517810.1016/0304-3762(83)90138-4 – reference: HousseinEHSaadMRHashimFALévy flight distribution: a new metaheuristic algorithm for solving engineering optimization problemsEng Appl Artif Intell20209410373110.1016/j.engappai.2020.103731 – reference: MautnerDHApplied nonlinear programming1972McGraw-Hill Co – reference: SquiresVRDawsGTLeadership and dominance relationships in Merino and Border Leicester sheepAppl Anim Ethol1975126327410.1016/0304-3762(75)90019-X – reference: PriceKVAwadNHAliMZPNSThe 100-digit challenge: problem definitions and evaluation criteria for the 100-digit challenge special session and competition on single objective numerical optimization2018Sch Elect Electron Eng, Nanyang Technol Univ, Singapore, Tech Rep – reference: HeidariAAMirjaliliSFarisHHarris hawks optimization: algorithm and applicationsFuture Gener Comput Syst20199784987210.1016/j.future.2019.02.028 – reference: SaremiSMirjaliliSLewisAGrasshopper optimisation algorithm: theory and applicationAdv Eng Softw2017105304710.1016/j.advengsoft.2017.01.004 – reference: MirjaliliSSCA: a sine cosine algorithm for solving optimization problemsKnowl-Based Syst20169612013310.1016/j.knosys.2015.12.022 – reference: KocisGRGrossmannIEA modelling and decomposition strategy for the minlp optimization of process flowsheetsComput Chem Eng19891379781910.1016/0098-1354(89)85053-7 – reference: RaoSSEngineering optimization: theory and practice1996New Age International Publishers – reference: AbdullahJMAhmedTFitness dependent optimizer: inspired by the bee swarming reproductive processIEEE Access20197434734348610.1109/ACCESS.2019.2907012 – reference: DréoJMetaheuristics for hard optimization2006Berlin/HeidelbergSpringer-Verlag1118.90058 – reference: MirjaliliSMoth-flame optimization algorithm: a novel nature-inspired heuristic paradigmKnowl-Based Syst20158922824910.1016/j.knosys.2015.07.006 – reference: Nowacki H (1973) Optimization in pre-contract ship design. 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A review of the literature on feeding, eliminative and resting behaviourAppl Anim Ethol19831017919010.1016/0304-3762(83)90139-6 – reference: HollandJHGenetic algorithms understand genetic algorithmsSurprise1967961121510.2307/24939139 – reference: GuptaSTiwariRNairSBMulti-objective design optimisation of rolling bearings using genetic algorithmsMech Mach Theory2007421418144310.1016/j.mechmachtheory.2006.10.0021188.74082 – reference: AljarahIMafarjaMHeidariAAAsynchronous accelerating multi-leader salp chains for feature selectionAppl Soft Comput20187196497910.1016/j.asoc.2018.07.040 – reference: Welsh DA, University D (1975) Population, behavioural and grazing ecology of the horses of Sable Island, Nova Scotia. PhD thesis, Dalhousie University – reference: Awad NH, Ali MZ, Suganthan PN, Liang JJ, Qu BY (2017) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective real-parameter numerical optimization. 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Snippet	Nowadays, the design of optimization algorithms is very popular to solve problems in various scientific fields. The optimization algorithms usually inspired by...
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SubjectTerms	Algorithms Animals CAE) and Design Calculus of Variations and Optimal Control; Optimization Classical Mechanics Computer Science Computer-Aided Engineering (CAD Control Design optimization Heuristic methods Horses Math. Applications in Chemistry Mathematical and Computational Engineering Optimization algorithms Original Article Source code Systems Theory
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Title	Wild horse optimizer: a new meta-heuristic algorithm for solving engineering optimization problems
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