Solving 0–1 knapsack problems by chaotic monarch butterfly optimization algorithm with Gaussian mutation
Recently, inspired by the migration behavior of monarch butterflies in nature, a metaheuristic optimization algorithm, called monarch butterfly optimization (MBO), was proposed. In the present study, a novel chaotic MBO algorithm (CMBO) is proposed, in which chaos theory is introduced in order to en...
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| Published in | Memetic computing Vol. 10; no. 2; pp. 135 - 150 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.06.2018
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1865-9284 1865-9292 |
| DOI | 10.1007/s12293-016-0211-4 |
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| Abstract | Recently, inspired by the migration behavior of monarch butterflies in nature, a metaheuristic optimization algorithm, called monarch butterfly optimization (MBO), was proposed. In the present study, a novel chaotic MBO algorithm (CMBO) is proposed, in which chaos theory is introduced in order to enhance its global optimization ability. Here, 12 one-dimensional classical chaotic maps are used to tune two main migration processes of monarch butterflies. Meanwhile, applying Gaussian mutation operator to some worst individuals can effectively prevent premature convergence of the optimization process. The performance of CMBO is verified and analyzed by three groups of large-scale 0–1 knapsack problems instances. The results show that the introduction of appropriate chaotic map and Gaussian perturbation can significantly improve the solution quality together with the overall performance of the proposed CMBO algorithm. The proposed CMBO can outperform the standard MBO and other eight state-of-the-art canonical algorithms. |
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| AbstractList | Recently, inspired by the migration behavior of monarch butterflies in nature, a metaheuristic optimization algorithm, called monarch butterfly optimization (MBO), was proposed. In the present study, a novel chaotic MBO algorithm (CMBO) is proposed, in which chaos theory is introduced in order to enhance its global optimization ability. Here, 12 one-dimensional classical chaotic maps are used to tune two main migration processes of monarch butterflies. Meanwhile, applying Gaussian mutation operator to some worst individuals can effectively prevent premature convergence of the optimization process. The performance of CMBO is verified and analyzed by three groups of large-scale 0–1 knapsack problems instances. The results show that the introduction of appropriate chaotic map and Gaussian perturbation can significantly improve the solution quality together with the overall performance of the proposed CMBO algorithm. The proposed CMBO can outperform the standard MBO and other eight state-of-the-art canonical algorithms. |
| Author | Yang, Juan Lu, Mei Feng, Yanhong Zhao, Xiang-Jun Wu, Congcong |
| Author_xml | – sequence: 1 givenname: Yanhong surname: Feng fullname: Feng, Yanhong email: qinfyh@163.com organization: School of Information Engineering, Hebei GEO University – sequence: 2 givenname: Juan surname: Yang fullname: Yang, Juan organization: School of Mathematical Sciences, Kaili University – sequence: 3 givenname: Congcong surname: Wu fullname: Wu, Congcong organization: School of Information Engineering, Hebei GEO University – sequence: 4 givenname: Mei surname: Lu fullname: Lu, Mei organization: School of Computer Science and Technology, Jiangsu Normal University – sequence: 5 givenname: Xiang-Jun surname: Zhao fullname: Zhao, Xiang-Jun organization: School of Computer Science and Technology, Jiangsu Normal University |
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| Cites_doi | 10.1109/ISCBI.2015.8 10.1007/s00521-012-1304-8 10.1016/j.chaos.2007.09.063 10.1016/j.neucom.2013.08.031 10.1016/j.chaos.2006.04.057 10.1109/NABIC.2009.5393690 10.1007/s00521-015-2135-1 10.1016/j.amc.2010.03.114 10.1109/ICEC.1995.489178 10.1007/s12293-015-0162-1 10.1103/PhysRevLett.64.821 10.1360/crad20070905 10.1016/j.ins.2014.02.123 10.1007/s10878-014-9717-1 10.1109/4235.687885 10.1007/s12293-016-0180-7 10.1016/j.amc.2006.09.087 10.1007/s00521-015-1923-y 10.1504/IJBIC.2013.053507 10.1016/j.procs.2010.04.160 10.1080/03052150500384759 10.1016/j.eswa.2007.02.002 10.1504/IJBIC.2016.081335 10.1007/s10898-007-9149-x 10.1023/A:1008202821328 10.1504/IJBIC.2015.10004283 10.1504/IJBIC.2015.073165 |
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| Keywords | Monarch butterfly optimization 0–1 Knapsack problems Gaussian mutation operator Chaotic maps |
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| References | WangGGGandomiAHAlaviAHStud krill herd algorithmNeurocomputing201412836337010.1016/j.neucom.2013.08.031 Tawhid MA, Ali AF (2016) A simplex social spider algorithm for solving integer programming and minimax problems. Mem Comput 1–20. doi:10.1007/s12293-016-0180-7 Gharooni-FardGMoein-DarbariFDeldariHMorvaridiAScheduling of scientific workflows using a chaos-genetic algorithmProc Comput Sci2010111445145410.1016/j.procs.2010.04.160 RudolphGLocal convergence rates of simple evolutionary algorithms with Cauchy mutationsIEEE Trans Evol Comput199714249258119499710.1109/4235.687885 WangGGGuoLHWangHQIncorporating mutation scheme into krill herd algorithm for global numerical optimizationNeural Comput Appl2014243–485387110.1007/s00521-012-1304-8 MathewsGBOn the partition of numbers. Introduction to analysis of the infinite1988New YorkSpringer WangGGGuoLHGandomiAHChaotic krill herd algorithmInf Sci20142741734319802610.1016/j.ins.2014.02.123 Wang GG, Deb S, Coelho LDS (2015) Elephant herding optimization. In: 2015 3rd International symposium on computational and business intelligence (ISCBI 2015), Bali, Indonesia, pp 1–5 StornRPriceKDifferential evolution-a simple and efficient heuristic for global optimization over continuous spacesJ Glob Optim1997114341359147955310.1023/A:1008202821328 MartelloSTothPKnapsack problems: algorithms and computer implementations1990AmsterdamWiley0708.68002 He YC, Zhang XL, Li WB et al (2016) Algorithms for randomized time-varying knapsack problems. J Comb Optim 31(1):95–117 KarabogaDBasturkBA powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithmJ Glob Optim2007393459471234617810.1007/s10898-007-9149-x Hinterding R (1995) Gaussian mutation and self-adaption for numeric genetic algorithms. In: Evolutionary computation, IEEE international conference on Feng YH, Wang GG, Deb S et al (2015) Solving 0–1 Knapsack problem by a novel binary monarch butterfly optimization. Neural Comput Appl 1–16. doi:10.1007/s00521-015-2135-1 Wang GG, Deb S, Cui ZH (2015) Monarch butterfly optimization. Neural Comput Appl 1–20. doi:10.1007/s00521-015-1923-y EusuffMLanseyKPashaFShuffled frog-leaping algorithm: a memetic metaheuristic for discrete optimizationEng Optim2006382129154220478310.1080/03052150500384759 YangXSNature-inspired metaheuristic algorithms2010FromeLuniver Press PatvardhanCBansalSSrivastavAQuantum-inspired evolutionary algorithm for difficult knapsack problemsMemetic Comput20157213515510.1007/s12293-015-0162-1 HeYCSongJMZhangJMGouHYResearch on genetic algorithms for solving static and dynamic knapsack problemsAppl Res Comput201532410111015 Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: Proceeding of world congress on nature and biologically inspired computing (NaBIC 2009), IEEE Publications, pp 210–214 Wang GG, Deb S, Coelho LDS (2015) Earthworm optimization algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Int J Bio-Inspir Comput (accepted) WangGGDebSGandomiAHChaotic cuckoo searchSoft Comput20155114 CoelhoLDSMarianiVCUse of chaotic sequences in a biologically inspired algorithm for engineering design optimizationExpert Syst Appl20083431905191310.1016/j.eswa.2007.02.002 AlatasBChaotic harmony search algorithmsAppl Math Comput2010216268726991193.65094 AlatasBAkinEOzerABChaos embedded particle swarm optimization algorithmsChaos Solit Fract200940417151734253125910.1016/j.chaos.2007.09.063 Wang GG, Deb S, Gao XZ, Coelho LDS (2016) A new metaheuristic optimization algorithm motivated by elephant herding behavior. Int J Bio-Inspir Comput (accepted) YangDXLiGChengGDOn the efficiency of chaos optimization algorithms for global optimizationChaos Solit Fract200734413661375228678010.1016/j.chaos.2006.04.057 TavazoeiMSHaeriMComparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithmsAppl Math Comput20071871076108523231141114.65335 HeYCWangXZKouYZA binary differential evolution algorithm with hybrid encodingJ Comput Res Dev20074491476148410.1360/crad20070905 CuiZHFanSZengJArtificial plant optimization algorithm with three-period photosynthesisInt J Bio-Inspir Comput20135213313910.1504/IJBIC.2013.053507 PecoraLCarrollTSynchronization in chaotic systemPhys Rev Lett199064821103826310.1103/PhysRevLett.64.821 KarthikeyanSAsokanPNickolasSPageTA hybrid discrete firefly algorithm for solving multi-objective flexible job shop scheduling problemsInt J Bio-Inspir Comput20157638640110.1504/IJBIC.2015.073165 S Karthikeyan (211_CR3) 2015; 7 M Eusuff (211_CR10) 2006; 38 211_CR27 211_CR2 ZH Cui (211_CR9) 2013; 5 211_CR6 G Rudolph (211_CR26) 1997; 1 211_CR5 211_CR4 R Storn (211_CR15) 1997; 11 G Gharooni-Fard (211_CR20) 2010; 1 B Alatas (211_CR19) 2009; 40 YC He (211_CR28) 2007; 44 YC He (211_CR29) 2015; 32 LDS Coelho (211_CR25) 2008; 34 MS Tavazoei (211_CR24) 2007; 187 S Martello (211_CR30) 1990 B Alatas (211_CR18) 2010; 216 211_CR31 211_CR13 211_CR12 211_CR11 DX Yang (211_CR17) 2007; 34 C Patvardhan (211_CR32) 2015; 7 XS Yang (211_CR1) 2010 GB Mathews (211_CR23) 1988 L Pecora (211_CR16) 1990; 64 GG Wang (211_CR22) 2014; 274 GG Wang (211_CR7) 2014; 24 D Karaboga (211_CR14) 2007; 39 GG Wang (211_CR8) 2014; 128 GG Wang (211_CR21) 2015; 5 |
| References_xml | – reference: WangGGGuoLHGandomiAHChaotic krill herd algorithmInf Sci20142741734319802610.1016/j.ins.2014.02.123 – reference: MartelloSTothPKnapsack problems: algorithms and computer implementations1990AmsterdamWiley0708.68002 – reference: YangDXLiGChengGDOn the efficiency of chaos optimization algorithms for global optimizationChaos Solit Fract200734413661375228678010.1016/j.chaos.2006.04.057 – reference: WangGGGandomiAHAlaviAHStud krill herd algorithmNeurocomputing201412836337010.1016/j.neucom.2013.08.031 – reference: MathewsGBOn the partition of numbers. Introduction to analysis of the infinite1988New YorkSpringer – reference: YangXSNature-inspired metaheuristic algorithms2010FromeLuniver Press – reference: KarabogaDBasturkBA powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithmJ Glob Optim2007393459471234617810.1007/s10898-007-9149-x – reference: Hinterding R (1995) Gaussian mutation and self-adaption for numeric genetic algorithms. In: Evolutionary computation, IEEE international conference on – reference: PecoraLCarrollTSynchronization in chaotic systemPhys Rev Lett199064821103826310.1103/PhysRevLett.64.821 – reference: Tawhid MA, Ali AF (2016) A simplex social spider algorithm for solving integer programming and minimax problems. Mem Comput 1–20. doi:10.1007/s12293-016-0180-7 – reference: CoelhoLDSMarianiVCUse of chaotic sequences in a biologically inspired algorithm for engineering design optimizationExpert Syst Appl20083431905191310.1016/j.eswa.2007.02.002 – reference: EusuffMLanseyKPashaFShuffled frog-leaping algorithm: a memetic metaheuristic for discrete optimizationEng Optim2006382129154220478310.1080/03052150500384759 – reference: HeYCSongJMZhangJMGouHYResearch on genetic algorithms for solving static and dynamic knapsack problemsAppl Res Comput201532410111015 – reference: Wang GG, Deb S, Coelho LDS (2015) Elephant herding optimization. In: 2015 3rd International symposium on computational and business intelligence (ISCBI 2015), Bali, Indonesia, pp 1–5 – reference: StornRPriceKDifferential evolution-a simple and efficient heuristic for global optimization over continuous spacesJ Glob Optim1997114341359147955310.1023/A:1008202821328 – reference: WangGGGuoLHWangHQIncorporating mutation scheme into krill herd algorithm for global numerical optimizationNeural Comput Appl2014243–485387110.1007/s00521-012-1304-8 – reference: Wang GG, Deb S, Cui ZH (2015) Monarch butterfly optimization. Neural Comput Appl 1–20. doi:10.1007/s00521-015-1923-y – reference: Wang GG, Deb S, Gao XZ, Coelho LDS (2016) A new metaheuristic optimization algorithm motivated by elephant herding behavior. Int J Bio-Inspir Comput (accepted) – reference: PatvardhanCBansalSSrivastavAQuantum-inspired evolutionary algorithm for difficult knapsack problemsMemetic Comput20157213515510.1007/s12293-015-0162-1 – reference: Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: Proceeding of world congress on nature and biologically inspired computing (NaBIC 2009), IEEE Publications, pp 210–214 – reference: Wang GG, Deb S, Coelho LDS (2015) Earthworm optimization algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Int J Bio-Inspir Comput (accepted) – reference: Gharooni-FardGMoein-DarbariFDeldariHMorvaridiAScheduling of scientific workflows using a chaos-genetic algorithmProc Comput Sci2010111445145410.1016/j.procs.2010.04.160 – reference: AlatasBChaotic harmony search algorithmsAppl Math Comput2010216268726991193.65094 – reference: He YC, Zhang XL, Li WB et al (2016) Algorithms for randomized time-varying knapsack problems. J Comb Optim 31(1):95–117 – reference: CuiZHFanSZengJArtificial plant optimization algorithm with three-period photosynthesisInt J Bio-Inspir Comput20135213313910.1504/IJBIC.2013.053507 – reference: TavazoeiMSHaeriMComparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithmsAppl Math Comput20071871076108523231141114.65335 – reference: RudolphGLocal convergence rates of simple evolutionary algorithms with Cauchy mutationsIEEE Trans Evol Comput199714249258119499710.1109/4235.687885 – reference: KarthikeyanSAsokanPNickolasSPageTA hybrid discrete firefly algorithm for solving multi-objective flexible job shop scheduling problemsInt J Bio-Inspir Comput20157638640110.1504/IJBIC.2015.073165 – reference: Feng YH, Wang GG, Deb S et al (2015) Solving 0–1 Knapsack problem by a novel binary monarch butterfly optimization. Neural Comput Appl 1–16. doi:10.1007/s00521-015-2135-1 – reference: AlatasBAkinEOzerABChaos embedded particle swarm optimization algorithmsChaos Solit Fract200940417151734253125910.1016/j.chaos.2007.09.063 – reference: HeYCWangXZKouYZA binary differential evolution algorithm with hybrid encodingJ Comput Res Dev20074491476148410.1360/crad20070905 – reference: WangGGDebSGandomiAHChaotic cuckoo searchSoft Comput20155114 – volume-title: On the partition of numbers. Introduction to analysis of the infinite year: 1988 ident: 211_CR23 – ident: 211_CR6 doi: 10.1109/ISCBI.2015.8 – volume: 24 start-page: 853 issue: 3–4 year: 2014 ident: 211_CR7 publication-title: Neural Comput Appl doi: 10.1007/s00521-012-1304-8 – volume: 40 start-page: 1715 issue: 4 year: 2009 ident: 211_CR19 publication-title: Chaos Solit Fract doi: 10.1016/j.chaos.2007.09.063 – volume: 128 start-page: 363 year: 2014 ident: 211_CR8 publication-title: Neurocomputing doi: 10.1016/j.neucom.2013.08.031 – volume: 34 start-page: 1366 issue: 4 year: 2007 ident: 211_CR17 publication-title: Chaos Solit Fract doi: 10.1016/j.chaos.2006.04.057 – ident: 211_CR2 doi: 10.1109/NABIC.2009.5393690 – ident: 211_CR13 doi: 10.1007/s00521-015-2135-1 – volume: 216 start-page: 2687 year: 2010 ident: 211_CR18 publication-title: Appl Math Comput doi: 10.1016/j.amc.2010.03.114 – volume-title: Nature-inspired metaheuristic algorithms year: 2010 ident: 211_CR1 – ident: 211_CR27 doi: 10.1109/ICEC.1995.489178 – volume: 7 start-page: 135 issue: 2 year: 2015 ident: 211_CR32 publication-title: Memetic Comput doi: 10.1007/s12293-015-0162-1 – volume: 64 start-page: 821 year: 1990 ident: 211_CR16 publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.64.821 – volume: 44 start-page: 1476 issue: 9 year: 2007 ident: 211_CR28 publication-title: J Comput Res Dev doi: 10.1360/crad20070905 – volume: 274 start-page: 17 year: 2014 ident: 211_CR22 publication-title: Inf Sci doi: 10.1016/j.ins.2014.02.123 – volume: 32 start-page: 1011 issue: 4 year: 2015 ident: 211_CR29 publication-title: Appl Res Comput – ident: 211_CR31 doi: 10.1007/s10878-014-9717-1 – volume: 1 start-page: 249 issue: 4 year: 1997 ident: 211_CR26 publication-title: IEEE Trans Evol Comput doi: 10.1109/4235.687885 – ident: 211_CR11 doi: 10.1007/s12293-016-0180-7 – volume: 187 start-page: 1076 year: 2007 ident: 211_CR24 publication-title: Appl Math Comput doi: 10.1016/j.amc.2006.09.087 – volume: 5 start-page: 1 year: 2015 ident: 211_CR21 publication-title: Soft Comput – volume-title: Knapsack problems: algorithms and computer implementations year: 1990 ident: 211_CR30 – ident: 211_CR12 doi: 10.1007/s00521-015-1923-y – volume: 5 start-page: 133 issue: 2 year: 2013 ident: 211_CR9 publication-title: Int J Bio-Inspir Comput doi: 10.1504/IJBIC.2013.053507 – volume: 1 start-page: 1445 issue: 1 year: 2010 ident: 211_CR20 publication-title: Proc Comput Sci doi: 10.1016/j.procs.2010.04.160 – volume: 38 start-page: 129 issue: 2 year: 2006 ident: 211_CR10 publication-title: Eng Optim doi: 10.1080/03052150500384759 – volume: 34 start-page: 1905 issue: 3 year: 2008 ident: 211_CR25 publication-title: Expert Syst Appl doi: 10.1016/j.eswa.2007.02.002 – ident: 211_CR5 doi: 10.1504/IJBIC.2016.081335 – volume: 39 start-page: 459 issue: 3 year: 2007 ident: 211_CR14 publication-title: J Glob Optim doi: 10.1007/s10898-007-9149-x – volume: 11 start-page: 341 issue: 4 year: 1997 ident: 211_CR15 publication-title: J Glob Optim doi: 10.1023/A:1008202821328 – ident: 211_CR4 doi: 10.1504/IJBIC.2015.10004283 – volume: 7 start-page: 386 issue: 6 year: 2015 ident: 211_CR3 publication-title: Int J Bio-Inspir Comput doi: 10.1504/IJBIC.2015.073165 |
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| SubjectTerms | Algorithms Applications of Mathematics Artificial Intelligence Bioinformatics Butterflies & moths Chaos theory Complex Systems Control Engineering Gaussian process Global optimization Heuristic methods Mathematical and Computational Engineering Mechatronics Migration Optimization algorithms Regular Research Paper Robotics |
| Title | Solving 0–1 knapsack problems by chaotic monarch butterfly optimization algorithm with Gaussian mutation |
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