{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T07:10:05Z","timestamp":1780989005032,"version":"3.54.1"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"17","license":[{"start":{"date-parts":[[2020,3,4]],"date-time":"2020-03-04T00:00:00Z","timestamp":1583280000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,3,4]],"date-time":"2020-03-04T00:00:00Z","timestamp":1583280000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1007\/s00521-020-04815-9","type":"journal-article","created":{"date-parts":[[2020,3,4]],"date-time":"2020-03-04T06:14:54Z","timestamp":1583302494000},"page":"14227-14239","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":98,"title":["A chaotic optimization method based on logistic-sine map for numerical function optimization"],"prefix":"10.1007","volume":"32","author":[{"given":"Fahrettin Burak","family":"Demir","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T\u00fcrker","family":"Tuncer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adnan Fatih","family":"Kocamaz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,3,4]]},"reference":[{"issue":"2","key":"4815_CR1","first-page":"162","volume":"16","author":"J Deuri","year":"2018","unstructured":"Deuri J, Sathya SS (2018) Cricket chirping algorithm: an efficient meta-heuristic for numerical function optimisation. Int J Comput Sci Eng 16(2):162\u2013172","journal-title":"Int J Comput Sci Eng"},{"key":"4815_CR2","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/j.measurement.2015.02.052","volume":"68","author":"M Canayaz","year":"2015","unstructured":"Canayaz M, Karc\u0131 A (2015) Investigation of cricket behaviours as evolutionary computation for system design optimization problems. Measurement 68:225\u2013235","journal-title":"Measurement"},{"key":"4815_CR3","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"},{"issue":"24","key":"4815_CR4","doi-asserted-by":"publisher","first-page":"5434","DOI":"10.1016\/j.ijleo.2015.09.098","volume":"126","author":"F \u00d6zkaynak","year":"2015","unstructured":"\u00d6zkaynak F (2015) A novel method to improve the performance of chaos based evolutionary algorithms. Optik 126(24):5434\u20135438","journal-title":"Optik"},{"issue":"1","key":"4815_CR5","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/s10462-016-9459-9","volume":"46","author":"\u015e Do\u011fan","year":"2016","unstructured":"Do\u011fan \u015e (2016) A new data hiding method based on chaos embedded genetic algorithm for color image. Artif Intell Rev 46(1):129\u2013143","journal-title":"Artif Intell Rev"},{"issue":"1","key":"4815_CR6","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1080\/00051144.2018.1498205","volume":"59","author":"G Ozmen Koca","year":"2018","unstructured":"Ozmen Koca G, Dogan S, Yilmaz H (2018) A multi-objective route planning model based on genetic algorithm for cuboid surfaces. Automatika 59(1):120\u2013130","journal-title":"Automatika"},{"key":"4815_CR7","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1016\/j.knosys.2015.07.027","volume":"88","author":"J Niu","year":"2015","unstructured":"Niu J, Zhong W, Liang Y, Luo N, Qian F (2015) Fruit fly optimization algorithm based on differential evolution and its application on gasification process operation optimization. Knowl Based Syst 88:253\u2013263","journal-title":"Knowl Based Syst"},{"key":"4815_CR8","volume-title":"Ant colony optimization","author":"M Dorigo","year":"2010","unstructured":"Dorigo M, Birattari M (2010) Ant colony optimization. Springer, Berlin"},{"issue":"3","key":"4815_CR9","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/s10898-007-9149-x","volume":"39","author":"D Karaboga","year":"2007","unstructured":"Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459\u2013471","journal-title":"J Glob Optim"},{"key":"4815_CR10","unstructured":"Yang X-S, Deb S (2009) Cuckoo search via L\u00e9vy flights. In: 2009 world congress on nature and biologically \u0131nspired computing (NaBIC). IEEE, pp 210\u2013214"},{"key":"4815_CR11","unstructured":"Yang X-S (2010) Firefly algorithm, stochastic test functions and design optimisation. Preprint arXiv:10031409"},{"key":"4815_CR12","unstructured":"Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, pp 65\u201374"},{"key":"4815_CR13","unstructured":"Chu S-C, Tsai P-W, Pan J-S (2006) Cat swarm optimization. In: Pacific Rim international conference on artificial intelligence. Springer, pp 854\u2013858"},{"issue":"5","key":"4815_CR14","doi-asserted-by":"publisher","first-page":"973","DOI":"10.1109\/TEVC.2009.2011992","volume":"13","author":"S He","year":"2009","unstructured":"He S, Wu QH, Saunders J (2009) Group search optimizer: an optimization algorithm inspired by animal searching behavior. IEEE Trans Evol Comput 13(5):973\u2013990","journal-title":"IEEE Trans Evol Comput"},{"issue":"4","key":"4815_CR15","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/s10462-016-9486-6","volume":"47","author":"S Akyol","year":"2017","unstructured":"Akyol S, Alatas B (2017) Plant intelligence based metaheuristic optimization algorithms. Artif Intell Rev 47(4):417\u2013462","journal-title":"Artif Intell Rev"},{"key":"4815_CR16","doi-asserted-by":"crossref","unstructured":"Boschetti MA, Maniezzo V, Roffilli M, R\u00f6hler AB (2009) Matheuristics: optimization, simulation and control. In: International workshop on hybrid metaheuristics. Springer, pp 171\u2013177","DOI":"10.1007\/978-3-642-04918-7_13"},{"key":"4815_CR17","unstructured":"Ozbay F, Alatas B (2016) Review of musics based computational intelligence algorithms. In: 1st international conference on engineering technology and applied sciences. Afyon Kocatepe University, pp 663\u2013669"},{"key":"4815_CR18","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":"4815_CR19","first-page":"47","volume":"4","author":"FB Demir","year":"2019","unstructured":"Demir FB, Tuncer T, Kocamaz AF (2019) Lojistik-Gauss Harita Tabanl\u0131 Yeni Bir Kaotik S\u00fcr\u00fc Optimizasyon Y\u00f6ntemi. Anatolian Science-Bilgisayar Bilimleri Dergisi 4:47\u201353","journal-title":"Anatolian Science-Bilgisayar Bilimleri Dergisi"},{"issue":"8","key":"4815_CR20","doi-asserted-by":"publisher","first-page":"4385","DOI":"10.1007\/s00521-018-3343-2","volume":"31","author":"S Arora","year":"2019","unstructured":"Arora S, Anand P (2019) Chaotic grasshopper optimization algorithm for global optimization. Neural Comput Appl 31(8):4385\u20134405","journal-title":"Neural Comput Appl"},{"key":"4815_CR21","doi-asserted-by":"publisher","first-page":"1373","DOI":"10.1007\/s10462-019-09704-9","volume":"53","author":"EV Altay","year":"2019","unstructured":"Altay EV, Alatas B (2019) Bird swarm algorithms with chaotic mapping. Artif Intell Rev 53:1373\u20131414","journal-title":"Artif Intell Rev"},{"key":"4815_CR22","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1016\/j.solener.2019.01.026","volume":"180","author":"N Pourmousa","year":"2019","unstructured":"Pourmousa N, Ebrahimi SM, Malekzadeh M, Alizadeh M (2019) Parameter estimation of photovoltaic cells using improved Lozi map based chaotic optimization algorithm. Sol Energy 180:180\u2013191","journal-title":"Sol Energy"},{"key":"4815_CR23","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1016\/j.knosys.2019.02.010","volume":"172","author":"MA Elaziz","year":"2019","unstructured":"Elaziz MA, Mirjalili S (2019) A hyper-heuristic for improving the initial population of whale optimization algorithm. Knowl Based Syst 172:42\u201363","journal-title":"Knowl Based Syst"},{"key":"4815_CR24","doi-asserted-by":"publisher","first-page":"1201","DOI":"10.1016\/j.apm.2019.09.029","volume":"77","author":"H Yu","year":"2019","unstructured":"Yu H, Zhao N, Wang P, Chen H, Li C (2019) Chaos-enhanced synchronized bat optimizer. Appl Math Model 77:1201\u20131215","journal-title":"Appl Math Model"},{"issue":"1","key":"4815_CR25","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/s00521-017-2988-6","volume":"31","author":"GI Sayed","year":"2019","unstructured":"Sayed GI, Hassanien AE, Azar AT (2019) Feature selection via a novel chaotic crow search algorithm. Neural Comput Appl 31(1):171\u2013188","journal-title":"Neural Comput Appl"},{"key":"4815_CR26","doi-asserted-by":"publisher","first-page":"22023","DOI":"10.1007\/s11042-019-7453-3","volume":"78","author":"Y Luo","year":"2019","unstructured":"Luo Y, Yu J, Lai W, Liu L (2019) A novel chaotic image encryption algorithm based on improved baker map and logistic map. Multimed Tools Appl 78:22023\u201322043","journal-title":"Multimed Tools Appl"},{"issue":"8","key":"4815_CR27","doi-asserted-by":"publisher","first-page":"790","DOI":"10.3390\/e21080790","volume":"21","author":"S Zhu","year":"2019","unstructured":"Zhu S, Wang G, Zhu C (2019) A secure and fast image encryption scheme based on double chaotic s-boxes. Entropy 21(8):790","journal-title":"Entropy"},{"key":"4815_CR28","doi-asserted-by":"publisher","DOI":"10.1007\/s11042-018-7144-5","author":"S Pan","year":"2019","unstructured":"Pan S, Wei J, Hu S (2019) A novel image encryption algorithm based on hybrid chaotic mapping and intelligent learning in financial security system. Multimed Tools Appl https:\/\/doi.org\/10.1007\/s11042-018-7144-5","journal-title":"Multimed Tools Appl"},{"key":"4815_CR29","unstructured":"Anter AM, Zhang Z (2019) Adaptive Neuro-fuzzy inference system-based chaotic swarm intelligence hybrid model for recognition of mild cognitive impairment from resting-state fMRI. In: International workshop on predictive intelligence in medicine. Springer, pp 23\u201333"},{"issue":"1","key":"4815_CR30","doi-asserted-by":"publisher","first-page":"013132","DOI":"10.1063\/1.5048299","volume":"29","author":"G Fuertes","year":"2019","unstructured":"Fuertes G, Vargas M, Alfaro M, Soto-Garrido R, Sabattin J, Peralta MA (2019) Chaotic genetic algorithm and the effects of entropy in performance optimization. Chaos Interdiscip J Nonlinear Sci 29(1):013132","journal-title":"Chaos Interdiscip J Nonlinear Sci"},{"issue":"2","key":"4815_CR31","doi-asserted-by":"publisher","first-page":"146","DOI":"10.3390\/math7020146","volume":"7","author":"Y Sun","year":"2019","unstructured":"Sun Y, Gao Y, Shi X (2019) Chaotic multi-objective particle swarm optimization algorithm incorporating clone immunity. Mathematics 7(2):146","journal-title":"Mathematics"},{"key":"4815_CR32","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1016\/j.sigpro.2018.03.010","volume":"149","author":"Z Hua","year":"2018","unstructured":"Hua Z, Jin F, Xu B, Huang H (2018) 2D logistic-sine-coupling map for image encryption. Sig Process 149:148\u2013161","journal-title":"Sig Process"},{"key":"4815_CR33","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.ins.2014.11.018","volume":"297","author":"Z Hua","year":"2015","unstructured":"Hua Z, Zhou Y, Pun C-M, Chen CP (2015) 2D sine logistic modulation map for image encryption. Inf Sci 297:80\u201394","journal-title":"Inf Sci"},{"issue":"7","key":"4815_CR34","first-page":"3166","volume":"217","author":"G Zhu","year":"2010","unstructured":"Zhu G, Kwong S (2010) Gbest-guided artificial bee colony algorithm for numerical function optimization. Appl Math Comput 217(7):3166\u20133173","journal-title":"Appl Math Comput"},{"issue":"3","key":"4815_CR35","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1007\/s00500-013-1073-z","volume":"18","author":"H Zhang","year":"2014","unstructured":"Zhang H, Zhu Y, Chen H (2014) Root growth model: a novel approach to numerical function optimization and simulation of plant root system. Soft Comput 18(3):521\u2013537","journal-title":"Soft Comput"},{"issue":"16","key":"4815_CR36","doi-asserted-by":"publisher","first-page":"3508","DOI":"10.1016\/j.ins.2011.04.024","volume":"181","author":"F Kang","year":"2011","unstructured":"Kang F, Li J, Ma Z (2011) Rosenbrock artificial bee colony algorithm for accurate global optimization of numerical functions. Inf Sci 181(16):3508\u20133531","journal-title":"Inf Sci"},{"key":"4815_CR37","unstructured":"Gordon VS, Whitley D (1993) Serial and parallel genetic algorithms as function optimizers. In: ICGA, pp 177\u2013183"},{"key":"4815_CR38","unstructured":"Potter MA, De Jong KA (1994) A cooperative coevolutionary approach to function optimization. In: International conference on parallel problem solving from nature. Springer, pp 249\u2013257"},{"key":"4815_CR39","doi-asserted-by":"crossref","unstructured":"Das S, Konar A, Chakraborty UK (2005) Improved differential evolution algorithms for handling noisy optimization problems. In: 2005 IEEE congress on evolutionary computation. IEEE, pp 1691\u20131698","DOI":"10.1109\/CEC.2005.1554892"},{"issue":"6","key":"4815_CR40","doi-asserted-by":"publisher","first-page":"1423","DOI":"10.1007\/s00521-014-1629-6","volume":"25","author":"S Mirjalili","year":"2014","unstructured":"Mirjalili S, Wang G-G, Coelho LDS (2014) Binary optimization using hybrid particle swarm optimization and gravitational search algorithm. Neural Comput Appl 25(6):1423\u20131435","journal-title":"Neural Comput Appl"},{"issue":"1","key":"4815_CR41","first-page":"13","volume":"6","author":"GG Tejani","year":"2019","unstructured":"Tejani GG, Savsani VJ, Patel VK, Mirjalili S (2019) An improved heat transfer search algorithm for unconstrained optimization problems. J Comput Des Eng 6(1):13\u201332","journal-title":"J Comput Des Eng"},{"key":"4815_CR42","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/j.advengsoft.2017.07.002","volume":"114","author":"S Mirjalili","year":"2017","unstructured":"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\u2013191","journal-title":"Adv Eng Softw"},{"key":"4815_CR43","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":"4815_CR44","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.advengsoft.2017.01.004","volume":"105","author":"S Saremi","year":"2017","unstructured":"Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30\u201347","journal-title":"Adv Eng Softw"},{"key":"4815_CR45","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","volume":"69","author":"S Mirjalili","year":"2014","unstructured":"Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46\u201361","journal-title":"Adv Eng Softw"},{"issue":"2","key":"4815_CR46","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1007\/s00521-015-1870-7","volume":"27","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27(2):495\u2013513","journal-title":"Neural Comput Appl"},{"key":"4815_CR47","doi-asserted-by":"publisher","first-page":"3445","DOI":"10.1007\/s13042-019-00931-8","volume":"10","author":"N Al-Madi","year":"2019","unstructured":"Al-Madi N, Faris H, Mirjalili S (2019) Binary multi-verse optimization algorithm for global optimization and discrete problems. Int J Mach Learn Cybern 10:3445\u20133465","journal-title":"Int J Mach Learn Cybern"},{"key":"4815_CR48","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/j.knosys.2017.10.011","volume":"139","author":"K Chen","year":"2018","unstructured":"Chen K, Zhou F, Liu A (2018) Chaotic dynamic weight particle swarm optimization for numerical function optimization. Knowl Based Syst 139:23\u201340","journal-title":"Knowl Based Syst"},{"issue":"11","key":"4815_CR49","doi-asserted-by":"publisher","first-page":"3316","DOI":"10.1016\/j.cnsns.2010.01.009","volume":"15","author":"M Jaberipour","year":"2010","unstructured":"Jaberipour M, Khorram E (2010) Two improved harmony search algorithms for solving engineering optimization problems. Commun Nonlinear Sci Numer Simul 15(11):3316\u20133331","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"4815_CR50","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.advengsoft.2015.11.004","volume":"92","author":"MD Li","year":"2016","unstructured":"Li MD, Zhao H, Weng XW, Han T (2016) A novel nature-inspired algorithm for optimization: virus colony search. Adv Eng Softw 92:65\u201388","journal-title":"Adv Eng Softw"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-020-04815-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-020-04815-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-020-04815-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,4]],"date-time":"2021-03-04T00:47:25Z","timestamp":1614818845000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-020-04815-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,4]]},"references-count":50,"journal-issue":{"issue":"17","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["4815"],"URL":"https:\/\/doi.org\/10.1007\/s00521-020-04815-9","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,4]]},"assertion":[{"value":"13 May 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 February 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 March 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}