{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T15:23:39Z","timestamp":1772119419994,"version":"3.50.1"},"reference-count":71,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,12,23]],"date-time":"2024-12-23T00:00:00Z","timestamp":1734912000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,12,23]],"date-time":"2024-12-23T00:00:00Z","timestamp":1734912000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Science and Engineering Research Board (SERB), Government of India","award":["MTR\/2021\/000264"],"award-info":[{"award-number":["MTR\/2021\/000264"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2025,1]]},"DOI":"10.1007\/s00500-024-10339-4","type":"journal-article","created":{"date-parts":[[2024,12,23]],"date-time":"2024-12-23T03:29:57Z","timestamp":1734924597000},"page":"157-194","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Quadratic and Lagrange interpolation-based butterfly optimization algorithm for numerical optimization and engineering design problem"],"prefix":"10.1007","volume":"29","author":[{"given":"Sushmita","family":"Sharma","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3475-018X","authenticated-orcid":false,"given":"Apu Kumar","family":"Saha","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sanjoy","family":"Chakraborty","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Suman","family":"Deb","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saroj Kumar","family":"Sahoo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,12,23]]},"reference":[{"key":"10339_CR1","first-page":"1","volume":"86","author":"L Abualigah","year":"2023","unstructured":"Abualigah L, Oliva D, Jia H, Gul F, Khodadadi N, Hussien AG, Zitar RA (2023) Improved prairie dog optimization algorithm by dwarf mongoose optimization algorithm for optimization problems. Multimed Tools Appl 86:1\u201341","journal-title":"Multimed Tools Appl"},{"key":"10339_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2022.116516","volume":"195","author":"I Ahmadianfar","year":"2022","unstructured":"Ahmadianfar I, Heidari AA, Noshadian S, Chen H, Gandomi AH (2022) INFO: an efficient optimization algorithm based on weighted mean of vectors. Expert Syst Appl 195:116516. https:\/\/doi.org\/10.1016\/j.eswa.2022.116516","journal-title":"Expert Syst Appl"},{"key":"10339_CR3","doi-asserted-by":"publisher","unstructured":"Alsattar H, Zaidan A, Bahaa B (2020) Novel meta-heuristic bald eagle search optimisation algorithm. Artif Intell Rev.https:\/\/doi.org\/10.1007\/s10462-019-09732-5","DOI":"10.1007\/s10462-019-09732-5"},{"key":"10339_CR4","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.eswa.2018.08.051","volume":"116","author":"S Arora","year":"2019","unstructured":"Arora S, Anand P (2019) Binary butterfly optimization approaches for feature selection. Expert Syst Appl 116:147\u2013160","journal-title":"Expert Syst Appl"},{"issue":"3","key":"10339_CR5","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1007\/s00500-018-3102-4","volume":"23","author":"S Arora","year":"2019","unstructured":"Arora S, Singh S (2019) Butterfly optimization algorithm: a novel approach for global optimization. Soft Comput 23(3):715\u2013734","journal-title":"Soft Comput"},{"key":"10339_CR6","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/s40430-017-0927-1","volume":"40","author":"S Arora","year":"2018","unstructured":"Arora S, Singh S, Yetilmezsoy K (2018) A modified butterfly optimization algorithm for mechanical design optimization problems J. Braz Soc Mech Sci Eng 40:21","journal-title":"Braz Soc Mech Sci Eng"},{"key":"10339_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2020.113702","volume":"161","author":"Q Askari","year":"2020","unstructured":"Askari Q, Saeed M, Younas I (2020) Heap-based optimizer inspired by corporate rank hierarchy for global optimization. Expert Syst Appl 161:113702. https:\/\/doi.org\/10.1016\/j.eswa.2020.113702","journal-title":"Expert Syst Appl"},{"key":"10339_CR8","doi-asserted-by":"crossref","unstructured":"Ayg\u00fcl K, Cikan M, Demirdelen T, Tumay M (2019) Butterfly optimization algorithm based maximum power point tracking of photovoltaic systems under partial shading condition. Energy Sour Part A Recov Utiliz Environ Effects: 1\u201319","DOI":"10.1080\/15567036.2019.1677818"},{"issue":"7","key":"10339_CR9","doi-asserted-by":"publisher","first-page":"3785","DOI":"10.1007\/s00500-022-07530-w","volume":"27","author":"A Bendahmane","year":"2023","unstructured":"Bendahmane A, Tlemsani R (2023) Unknown area exploration for robots with energy constraints using a modified Butterfly Optimization Algorithm. Soft Comput 27(7):3785\u20133804","journal-title":"Soft Comput"},{"key":"10339_CR10","doi-asserted-by":"crossref","unstructured":"Chakraborty S, Sharma S, Saha AK, Saha A (2022) A novel improved whale optimization algorithm to solve numerical optimization and real-world applications. Artif Intell Rev:1-112","DOI":"10.1007\/s10462-021-10114-z"},{"key":"10339_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2021.107779","volume":"236","author":"S Chakraborty","year":"2022","unstructured":"Chakraborty S, Nama S, Saha AK (2022b) An improved symbiotic organisms search algorithm for higher dimensional optimization problems. Knowl Based Syst 236:107779","journal-title":"Knowl Based Syst"},{"issue":"1","key":"10339_CR12","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1002\/int.22617","volume":"37","author":"S Chakraborty","year":"2022","unstructured":"Chakraborty S, Saha AK, Chakraborty R, Saha M, Nama S (2022c) HSWOA: an ensemble of hunger games search and whale optimization algorithm for global optimization. Int J Intell Syst 37(1):52\u2013104","journal-title":"Int J Intell Syst"},{"issue":"11","key":"10339_CR13","doi-asserted-by":"publisher","first-page":"7245","DOI":"10.1007\/s00500-023-07920-8","volume":"27","author":"P Chakraborty","year":"2023","unstructured":"Chakraborty P, Sharma S, Saha AK (2023) Convergence analysis of butterfly optimization algorithm. Soft Comput 27(11):7245\u20137257","journal-title":"Soft Comput"},{"key":"10339_CR15","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/j.aej.2022.12.045","volume":"68","author":"A Chhabra","year":"2023","unstructured":"Chhabra A, Hussien AG, Hashim FA (2023) Improved bald eagle search algorithm for global optimization and feature selection. Alex Eng J 68:141\u2013180","journal-title":"Alex Eng J"},{"key":"10339_CR16","doi-asserted-by":"crossref","unstructured":"Deng W, Li K, Zhao H (2023) A flight arrival time prediction method based on cluster clustering-based modular with deep neural network. IEEE Trans Intell Transp Syst","DOI":"10.1109\/TITS.2023.3338251"},{"key":"10339_CR17","doi-asserted-by":"publisher","first-page":"88026","DOI":"10.1109\/ACCESS.2020.2993148","volume":"8","author":"Y Fan","year":"2020","unstructured":"Fan Y, Shao J, Sun G, Shao X (2020) A self-adaption butterfly optimization algorithm for numerical optimization problems. IEEE Access 8:88026\u201388041","journal-title":"IEEE Access"},{"key":"10339_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.enconman.2020.113115","volume":"220","author":"A Fathy","year":"2020","unstructured":"Fathy A (2020) Butterfly optimization algorithm based methodology for enhancing the shaded photovoltaic array extracted power via reconfiguration process. Energy Convers Manage 220:113115","journal-title":"Energy Convers Manage"},{"key":"10339_CR19","doi-asserted-by":"crossref","unstructured":"Gaber T, Awad AA, Ali AF (2019) Feature selection method based on chaotic maps and butterfly optimization algorithm. In: International Conference on Artificial Intelligence and Computer Vision (AICV\u20192020)","DOI":"10.1007\/978-3-030-44289-7_16"},{"key":"10339_CR20","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2023.110269","volume":"139","author":"B Gonzalez-Sanchez","year":"2023","unstructured":"Gonzalez-Sanchez B, Vega-Rodr\u00edguez MA, Santander-Jim\u00e9nez S (2023) A multi-objective butterfly optimization algorithm for protein encoding. Appl Soft Comput 139:110269","journal-title":"Appl Soft Comput"},{"key":"10339_CR21","first-page":"1","volume":"37","author":"Y Guo","year":"2020","unstructured":"Guo Y, Liu X, Chen L (2020) Improved butterfly optimisation algorithm based on guiding weight and population restart. J Exp Theor Artif Intell 37:1\u201319","journal-title":"J Exp Theor Artif Intell"},{"issue":"1","key":"10339_CR22","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1080\/0952813X.2020.1725651","volume":"33","author":"Y Guo","year":"2021","unstructured":"Guo Y, Liu X, Chen L (2021) Improved butterfly optimisation algorithm based on guiding weight and population restart. J Exp Theor Artif Intell 33(1):127\u2013145","journal-title":"J Exp Theor Artif Intell"},{"key":"10339_CR23","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1016\/j.aej.2023.12.050","volume":"87","author":"K He","year":"2024","unstructured":"He K, Zhang Y, Wang YK, Zhou RH, Zhang HZ (2024) EABOA: enhanced adaptive butterfly optimization algorithm for numerical optimization and engineering design problems. Alex Eng J 87:543\u2013573","journal-title":"Alex Eng J"},{"key":"10339_CR24","doi-asserted-by":"crossref","unstructured":"Huang Q, Zhang K, Song J, Zhang Y, Shi J (2018) Adaptive differential evolution with a lagrange interpolation argument algorithm. Inform Sci:472","DOI":"10.1016\/j.ins.2018.09.004"},{"issue":"19","key":"10339_CR25","doi-asserted-by":"publisher","first-page":"13951","DOI":"10.1007\/s00500-023-08468-3","volume":"27","author":"AG Hussien","year":"2023","unstructured":"Hussien AG, Khurma RA, Alzaqebah A, Amin M, Hashim FA (2023) Novel memetic of beluga whale optimization with self-adaptive exploration\u2013exploitation balance for global optimization and engineering problems. Soft Comput 27(19):13951\u201313989","journal-title":"Soft Comput"},{"issue":"7","key":"10339_CR26","doi-asserted-by":"publisher","first-page":"3887","DOI":"10.1007\/s00500-022-07592-w","volume":"27","author":"B Irmak","year":"2023","unstructured":"Irmak B, Karakoyun M, G\u00fclc\u00fc \u015e (2023) An improved butterfly optimization algorithm for training the feed-forward artificial neural networks. Soft Comput 27(7):3887\u20133905","journal-title":"Soft Comput"},{"key":"10339_CR27","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1017\/CBO9780511778025.008","volume":"1","author":"D Izzo","year":"2010","unstructured":"Izzo D (2010) Global optimization and space pruning for spacecraft trajectory design. Spacecr Traject Optim 1:178\u2013200","journal-title":"Spacecr Traject Optim"},{"key":"10339_CR28","doi-asserted-by":"crossref","unstructured":"Jalali SMJ, Ahmadian S, Kebria PM, Khosravi A, Lim CP, Nahavandi S (2019) Evolving artificial neural networks using butterfly optimization algorithm for data classification. In: International Conference on Neural Information Processing (pp. 596\u2013607). Springer, Cham.","DOI":"10.1007\/978-3-030-36708-4_49"},{"key":"10339_CR29","doi-asserted-by":"crossref","unstructured":"Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN'95\u2014International Conference on Neural Networks 4:1942\u20131948","DOI":"10.1109\/ICNN.1995.488968"},{"key":"10339_CR30","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1016\/j.future.2020.03.055","volume":"111","author":"S Li","year":"2020","unstructured":"Li S, Chen H, Wang M, Heidari AA, Mirjalili S (2020) Slime mould algorithm: a new method for stochastic optimization. Fut Gen Comput Syst 111:300\u2013323. https:\/\/doi.org\/10.1016\/j.future.2020.03.055","journal-title":"Fut Gen Comput Syst"},{"issue":"14","key":"10339_CR31","doi-asserted-by":"publisher","first-page":"14263","DOI":"10.1109\/JSEN.2022.3179165","volume":"22","author":"X Li","year":"2022","unstructured":"Li X, Zhao H, Yu L, Chen H, Deng W, Deng W (2022) Feature extraction using parameterized multisynchrosqueezing transform. IEEE Sens J 22(14):14263\u201314272","journal-title":"IEEE Sens J"},{"key":"10339_CR32","doi-asserted-by":"publisher","first-page":"498","DOI":"10.1016\/j.matcom.2022.08.020","volume":"204","author":"Y Li","year":"2023","unstructured":"Li Y, Yu X, Liu J (2023a) An opposition-based butterfly optimization algorithm with adaptive elite mutation in solving complex high-dimensional optimization problems. Math Comput Simul 204:498\u2013528","journal-title":"Math Comput Simul"},{"key":"10339_CR33","doi-asserted-by":"publisher","first-page":"21489","DOI":"10.1109\/JIOT.2023.3295763","volume":"10","author":"X Li","year":"2023","unstructured":"Li X, Zhao H, Deng W (2023) BFOD: blockchain-based privacy protection and security sharing scheme of flight operation data. IEEE Internet Things J 10:21489","journal-title":"IEEE Internet Things J"},{"key":"10339_CR34","doi-asserted-by":"publisher","first-page":"16693","DOI":"10.1109\/JIOT.2024.3354942","volume":"11","author":"X Li","year":"2024","unstructured":"Li X, Zhao H, Deng W (2024) IOFL: intelligent optimization-based federated learning for non-IID data. IEEE Internet Things J 11:16693","journal-title":"IEEE Internet Things J"},{"issue":"2","key":"10339_CR35","doi-asserted-by":"publisher","first-page":"1399","DOI":"10.1007\/s11831-022-09843-3","volume":"30","author":"SN Makhadmeh","year":"2023","unstructured":"Makhadmeh SN, Al-Betar MA, Abasi AK, Awadallah MA, Doush IA, Alyasseri ZAA, Alomari OA (2023) Recent advances in butterfly optimization algorithm, its versions and applications. Arch Comput Methods Eng 30(2):1399\u20131420","journal-title":"Arch Comput Methods Eng"},{"key":"10339_CR36","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1016\/j.knosys.2015.07.006","volume":"89","author":"S Mirjalili","year":"2015","unstructured":"Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl Based Syst 89:228\u2013249","journal-title":"Knowl Based Syst"},{"key":"10339_CR37","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.knosys.2015.12.022","volume":"96","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120\u2013133","journal-title":"Knowl-Based Syst"},{"key":"10339_CR38","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.advengsoft.2016.01.008","volume":"95","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51\u201367","journal-title":"Adv Eng Softw"},{"key":"10339_CR39","doi-asserted-by":"publisher","first-page":"163","DOI":"10.5267\/j.dsl.2018.7.002","volume":"8","author":"S Nama","year":"2019","unstructured":"Nama S, Saha AK (2019) A novel hybrid backtracking search optimization algorithm for continuous function Optimization. Decis Sci Lett 8:163\u2013174","journal-title":"Decis Sci Lett"},{"key":"10339_CR40","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1007\/s12293-016-0194-1","volume":"9","author":"S Nama","year":"2017","unstructured":"Nama S, Saha AK, Ghosh S (2017) A hybrid symbiosis organisms search algorithm and its application to real world problems. Memetic Comp 9:261\u2013280","journal-title":"Memetic Comp"},{"key":"10339_CR42","doi-asserted-by":"publisher","DOI":"10.1111\/coin.12290","author":"S Nama","year":"2020","unstructured":"Nama S, Saha AK, Sharma S (2020) A novel improved symbiotic organisms search algorithm. Comput Intell. https:\/\/doi.org\/10.1111\/coin.12290","journal-title":"Comput Intell"},{"key":"10339_CR43","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2023.101304","volume":"79","author":"S Nama","year":"2023","unstructured":"Nama S, Saha AK, Chakraborty S, Gandomi AH, Abualigah L (2023) Boosting particle swarm optimization by backtracking search algorithm for optimization problems. Swarm Evol Comput 79:101304","journal-title":"Swarm Evol Comput"},{"key":"10339_CR44","doi-asserted-by":"crossref","unstructured":"Ni Q, Deng J (2014) Analysis of population diversity of dynamic probabilistic particle swarm optimization algorithms. Math Prob Eng","DOI":"10.1155\/2014\/762015"},{"key":"10339_CR45","doi-asserted-by":"crossref","unstructured":"Olorunda O, Engelbrecht AP (2008) Measuring exploration\/exploitation in particle swarms using swarm diversity. In: 2008 IEEE congress on evolutionary computation (IEEE world congress on computational intelligence) (1128\u20131134). IEEE","DOI":"10.1109\/CEC.2008.4630938"},{"key":"10339_CR46","doi-asserted-by":"publisher","first-page":"e27509","DOI":"10.1016\/j.heliyon.2024.e27509","volume":"10","author":"V Rajinikanth","year":"2024","unstructured":"Rajinikanth V, Biju R, Mittal N, Mittal V, Askar SS, Abouhawwash M (2024) COVID-19 detection in lung CT slices using brownian-butterfly-algorithm optimized lightweight deep features. Heliyon. 10:e27509","journal-title":"Heliyon."},{"issue":"1","key":"10339_CR47","first-page":"19","volume":"7","author":"R Rao","year":"2016","unstructured":"Rao R (2016) Jaya: a simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int J Ind Eng Comput 7(1):19\u201334","journal-title":"Int J Ind Eng Comput"},{"key":"10339_CR48","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2022.109326","volume":"251","author":"AK Saha","year":"2022","unstructured":"Saha AK (2022) Multi-population-based adaptive sine cosine algorithm with modified mutualism strategy for global optimization. Knowl-Based Syst 251:109326","journal-title":"Knowl-Based Syst"},{"issue":"5","key":"10339_CR49","doi-asserted-by":"publisher","first-page":"1522","DOI":"10.1007\/s42235-022-00207-y","volume":"19","author":"SK Sahoo","year":"2022","unstructured":"Sahoo SK, Saha AK (2022) A hybrid moth flame optimization algorithm for global optimization. J Bionic Eng 19(5):1522\u20131543","journal-title":"J Bionic Eng"},{"key":"10339_CR50","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.120367","volume":"227","author":"SK Sahoo","year":"2023","unstructured":"Sahoo SK, Houssein EH, Premkumar M, Saha AK, Emam MM (2023a) Self-adaptive moth flame optimizer combined with crossover operator and Fibonacci search strategy for COVID-19 CT image segmentation. Expert Syst Appl 227:120367","journal-title":"Expert Syst Appl"},{"issue":"4","key":"10339_CR51","doi-asserted-by":"publisher","first-page":"2811","DOI":"10.1007\/s10462-022-10218-0","volume":"56","author":"SK Sahoo","year":"2023","unstructured":"Sahoo SK, Saha AK, Nama S, Masdari M (2023b) An improved moth flame optimization algorithm based on modified dynamic opposite learning strategy. Artif Intell Rev 56(4):2811\u20132869","journal-title":"Artif Intell Rev"},{"key":"10339_CR53","doi-asserted-by":"publisher","first-page":"4761","DOI":"10.1016\/j.egyr.2023.11.032","volume":"10","author":"A Selim","year":"2023","unstructured":"Selim A, Hassan MH, Kamel S, Hussien AG (2023) Allocation of distributed generator in power networks through an enhanced jellyfish search algorithm. Energy Rep 10:4761\u20134780","journal-title":"Energy Rep"},{"issue":"7","key":"10339_CR54","doi-asserted-by":"publisher","first-page":"4809","DOI":"10.1007\/s00500-019-04234-6","volume":"24","author":"S Sharma","year":"2020","unstructured":"Sharma S, Saha AK (2020) m-MBOA: a novel butterfly optimization algorithm enhanced with mutualism scheme. Soft Comput 24(7):4809\u20134827","journal-title":"Soft Comput"},{"key":"10339_CR55","doi-asserted-by":"crossref","unstructured":"Sharma S, Saha AK (2021) BOSCA\u2014a hybrid butterfly optimization algorithm modified with sine cosine algorithm. In: Panigrahi CR, Pati B, Mohapatra P, Buyya R, Li KC (eds) Progress in advanced computing and intelligent engineering. advances in intelligent systems and computing, vol 1198. Springer, Singapore","DOI":"10.1007\/978-981-15-6584-7_35"},{"issue":"6","key":"10339_CR57","doi-asserted-by":"publisher","first-page":"4573","DOI":"10.1007\/s10586-022-03649-5","volume":"25","author":"S Sharma","year":"2022","unstructured":"Sharma S, Saha AK, Roy S, Mirjalili S, Nama S (2022a) A mixed sine cosine butterfly optimization algorithm for global optimization and its application. Clust Comput 25(6):4573\u20134600","journal-title":"Clust Comput"},{"issue":"4","key":"10339_CR58","doi-asserted-by":"publisher","first-page":"1161","DOI":"10.1007\/s42235-022-00175-3","volume":"19","author":"S Sharma","year":"2022","unstructured":"Sharma S, Chakraborty S, Saha AK, Nama S, Sahoo SK (2022b) mLBOA: a modified butterfly optimization algorithm with Lagrange interpolation for global optimization. J Bionic Eng 19(4):1161\u20131176","journal-title":"J Bionic Eng"},{"issue":"2","key":"10339_CR59","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1007\/s42235-022-00288-9","volume":"20","author":"S Sharma","year":"2023","unstructured":"Sharma S, Khodadadi N, Saha AK, Gharehchopogh FS, Mirjalili S (2023) Non-dominated sorting advanced butterfly optimization algorithm for multi-objective problems J. Bionic Eng 20(2):819\u2013843","journal-title":"Bionic Eng"},{"key":"10339_CR60","doi-asserted-by":"publisher","first-page":"1040","DOI":"10.1016\/j.asoc.2015.09.033","volume":"38","author":"D Singh","year":"2016","unstructured":"Singh D, Agrawal S (2016) Self-organizing migrating algorithm with quadratic interpolation for solving large scale global optimization problems. Appl Soft Comput 38:1040\u20131048","journal-title":"Appl Soft Comput"},{"key":"10339_CR61","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2023.107532","volume":"128","author":"R Sowmya","year":"2024","unstructured":"Sowmya R, Premkumar M, Jangir P (2024) Newton-Raphson-based optimizer: a new population-based metaheuristic algorithm for continuous optimization problems. Eng Appl Artif Intell 128:107532. https:\/\/doi.org\/10.1016\/j.engappai.2023.107532","journal-title":"Eng Appl Artif Intell"},{"key":"10339_CR62","volume-title":"Psychophysics","author":"SS Stevens","year":"1975","unstructured":"Stevens SS (1975) Psychophysics. Transaction Publishers, Routledge"},{"issue":"4","key":"10339_CR63","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1023\/A:1008202821328","volume":"11","author":"R Storn","year":"1997","unstructured":"Storn R, Price K (1997) Differential evolution\u2014a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341\u2013359","journal-title":"J Glob Optim"},{"issue":"9","key":"10339_CR64","doi-asserted-by":"publisher","first-page":"3543","DOI":"10.1108\/EC-02-2020-0126","volume":"37","author":"D Ustun","year":"2020","unstructured":"Ustun D (2020) An enhanced adaptive butterfly optimization algorithm rigorously verified on engineering problems and implemented to ISAR image motion compensation. Eng Comput 37(9):3543\u20133566","journal-title":"Eng Comput"},{"key":"10339_CR65","unstructured":"Vink\u00f3 T, Izzo D (2008) Global optimisation heuristics and test problems for preliminary spacecraft trajectory design.\u00a0In: Advanced Concepts Team, ESATR ACT-TNT-MAD-GOHTPPSTD."},{"key":"10339_CR66","doi-asserted-by":"publisher","first-page":"3665","DOI":"10.1007\/s00366-020-01025-8","volume":"37","author":"Z Wang","year":"2021","unstructured":"Wang Z, Luo Q, Zhou Y (2021) Hybrid metaheuristic algorithm using butterfly and flower pollination base on mutualism mechanism for global optimization problems. Eng Comput 37:3665\u20133698","journal-title":"Eng Comput"},{"key":"10339_CR67","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2019.106704","volume":"134","author":"S Wenzel","year":"2020","unstructured":"Wenzel S, Riedl F, Engell S (2020) An efficient hierarchical market-like coordination algorithm for coupled production systems based on quadratic approximation. Comput Chem Eng 134:106704","journal-title":"Comput Chem Eng"},{"key":"10339_CR68","unstructured":"Wu G, Mallipeddi R, Suganthan P (2016) Problem definitions and evaluation criteria for the CEC 2017 competition and special session on constrained single objective real-parameter optimization. Nanyang Technol. Univ., Singapore, Tech. Rep, 1\u201318"},{"issue":"3","key":"10339_CR69","doi-asserted-by":"publisher","first-page":"1121","DOI":"10.2166\/hydro.2023.026","volume":"25","author":"Z Xiao","year":"2023","unstructured":"Xiao Z, Liang Z, Wang J, Li B, Hu Y, Wang J (2023) An improved butterfly optimization algorithm and its application in cascade hydropower generation operation. J Hydroinf 25(3):1121\u20131138","journal-title":"J Hydroinf"},{"issue":"4","key":"10339_CR70","doi-asserted-by":"publisher","first-page":"365","DOI":"10.3139\/120.111492","volume":"62","author":"BS Y\u0131ld\u0131z","year":"2020","unstructured":"Y\u0131ld\u0131z BS, Y\u0131ld\u0131z AR, Albak E\u0130, Abderazek H, Sait SM, Bureerat S (2020) Butterfly optimization algorithm for optimum shape design of automobile suspension components. Mater Test 62(4):365\u2013370","journal-title":"Mater Test"},{"key":"10339_CR71","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0154191","volume":"11","author":"K Zhang","year":"2016","unstructured":"Zhang K, Song J, Ni K, Li S (2016) Lagrange interpolation learning particle swarm optimization. PLoS One 11:e0154191. https:\/\/doi.org\/10.1371\/journal.pone.0154191","journal-title":"PLoS One"},{"key":"10339_CR72","doi-asserted-by":"publisher","first-page":"512","DOI":"10.1016\/j.mechmachtheory.2019.01.012","volume":"134","author":"K Zhang","year":"2019","unstructured":"Zhang K, Huang Q, Zhang Y, Song J, Shi J (2019) Hybrid Lagrange interpolation differential evolution algorithm for path synthesis. Mech Mach Theory 134:512\u2013540","journal-title":"Mech Mach Theory"},{"key":"10339_CR73","doi-asserted-by":"publisher","first-page":"67799","DOI":"10.1109\/ACCESS.2020.2985986","volume":"8","author":"B Zhang","year":"2020","unstructured":"Zhang B, Yang X, Hu B, Liu Z, Li Z (2020) OEbBOA: a novel improved binary butterfly optimization approaches with various strategies for feature selection. IEEE Access 8:67799\u201367812","journal-title":"IEEE Access"},{"key":"10339_CR74","first-page":"1","volume":"75","author":"H Zhao","year":"2023","unstructured":"Zhao H, Wu Y, Deng W (2023) An interpretable dynamic inference system based on fuzzy broad learning. IEEE Trans Instrument Measure 75:1","journal-title":"IEEE Trans Instrument Measure"},{"key":"10339_CR75","doi-asserted-by":"publisher","DOI":"10.1016\/j.applthermaleng.2019.114766","volume":"173","author":"Y Zhi","year":"2020","unstructured":"Zhi Y, Weiqing W, Haiyun W, Khodaei H (2020) Improved butterfly optimization algorithm for CCHP driven by PEMFC. Appl Therm Eng 173:114766","journal-title":"Appl Therm Eng"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-024-10339-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-024-10339-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-024-10339-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T22:57:22Z","timestamp":1739314642000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-024-10339-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,23]]},"references-count":71,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10339"],"URL":"https:\/\/doi.org\/10.1007\/s00500-024-10339-4","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-3291495\/v1","asserted-by":"object"}]},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,23]]},"assertion":[{"value":"15 June 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 December 2024","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors mention that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"The authors give their consent for the publication of the article once it is accepted.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}]}}