{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T10:08:58Z","timestamp":1760609338653},"reference-count":94,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2021,1,25]],"date-time":"2021-01-25T00:00:00Z","timestamp":1611532800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,25]],"date-time":"2021-01-25T00:00:00Z","timestamp":1611532800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Ambient Intell Human Comput"],"published-print":{"date-parts":[[2021,11]]},"DOI":"10.1007\/s12652-020-02746-w","type":"journal-article","created":{"date-parts":[[2021,1,25]],"date-time":"2021-01-25T04:58:51Z","timestamp":1611550731000},"page":"9953-9976","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A chaos-based constrained optimization algorithm"],"prefix":"10.1007","volume":"12","author":[{"given":"Javad","family":"Alikhani Koupaei","sequence":"first","affiliation":[]},{"given":"Marjan","family":"Firouznia","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,1,25]]},"reference":[{"issue":"5","key":"2746_CR1","doi-asserted-by":"publisher","first-page":"2932","DOI":"10.1016\/j.asoc.2012.03.068","volume":"13","author":"M Abdechiri","year":"2013","unstructured":"Abdechiri M, Meybodi MR, Bahrami H (2013) Gases brownian motion optimization: an algorithm for optimization (GBMO). Appl Soft Comput 13(5):2932\u20132946","journal-title":"Appl Soft Comput"},{"issue":"4","key":"2746_CR2","doi-asserted-by":"publisher","first-page":"2597","DOI":"10.1007\/s11071-016-3213-3","volume":"87","author":"M Abdechiri","year":"2017","unstructured":"Abdechiri M, Faez K, Amindavar H, Bilotta E (2017) The chaotic dynamics of high-dimensional systems. Nonlinear Dyn 87(4):2597\u20132610","journal-title":"Nonlinear Dyn"},{"issue":"6","key":"2746_CR3","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1016\/0375-9601(90)90136-C","volume":"144","author":"K Aihara","year":"1990","unstructured":"Aihara K, Takabe T, Toyoda M (1990) Chaotic neural networks. Phys Lett A 144(6):333\u2013340","journal-title":"Phys Lett A"},{"issue":"9","key":"2746_CR4","doi-asserted-by":"crossref","first-page":"2687","DOI":"10.1016\/j.amc.2010.03.114","volume":"216","author":"B Alatas","year":"2010","unstructured":"Alatas B (2010) Chaotic harmony search algorithms. Appl Math Comput 216(9):2687\u20132699","journal-title":"Appl Math Comput"},{"issue":"9","key":"2746_CR5","doi-asserted-by":"publisher","first-page":"3696","DOI":"10.1016\/j.cnsns.2010.12.025","volume":"16","author":"B Alatas","year":"2011","unstructured":"Alatas B (2011) Uniform Big Bang\u2013chaotic Big Crunch optimization. Commun Nonlinear Sci Numer Simul 16(9):3696\u20133703","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"2","key":"2746_CR6","doi-asserted-by":"publisher","first-page":"939","DOI":"10.1016\/j.chaos.2008.04.024","volume":"41","author":"B Alatas","year":"2009","unstructured":"Alatas B, Akin E (2009) Chaotically encoded particle swarm optimization algorithm and its applications. Chaos Soliton & Fractals 41(2):939\u2013950","journal-title":"Chaos Soliton & Fractals"},{"key":"2746_CR7","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1016\/j.chaos.2015.09.027","volume":"81","author":"JK Alikhani","year":"2015","unstructured":"Alikhani JK, Hosseini SMM (2015) A new hybrid algorithm based on chaotic maps for solving systems of nonlinear equations. Chaos Solitons Fractals 81:233\u2013245","journal-title":"Chaos Solitons Fractals"},{"key":"2746_CR8","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/j.engappai.2016.01.034","volume":"50","author":"JK Alikhani","year":"2016","unstructured":"Alikhani JK, Hosseini SMM, Ghaini FM (2016) A new optimization algorithm based on chaotic maps and golden section search method. Eng Appl Artif Intell 50:201\u2013214","journal-title":"Eng Appl Artif Intell"},{"key":"2746_CR9","doi-asserted-by":"publisher","first-page":"2495","DOI":"10.1016\/j.cma.2005.05.014","volume":"195","author":"A Amirjanov","year":"2006","unstructured":"Amirjanov A (2006) The development of a changing range genetic algorithm. Comput Methods Appl Mech Eng 195:2495\u20132508","journal-title":"Comput Methods Appl Mech Eng"},{"key":"2746_CR10","volume-title":"Introduction to optimum design","author":"JS Arora","year":"1989","unstructured":"Arora JS (1989) Introduction to optimum design. McGraw-Hill, New York"},{"issue":"3\u20134","key":"2746_CR11","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/BF01743964","volume":"9","author":"JS Arora","year":"1995","unstructured":"Arora JS, Elwakeil OA, Chahande AI, Hsieh CC (1995) Global optimization methods for engineering applications: a review. Struct Optim 9(3\u20134):137\u2013159","journal-title":"Struct Optim"},{"issue":"4","key":"2746_CR12","doi-asserted-by":"publisher","first-page":"1301","DOI":"10.1016\/j.engappai.2012.08.005","volume":"26","author":"SM Ashrafi","year":"2013","unstructured":"Ashrafi SM, Dariane AB (2013) Performance evaluation of an improved harmony search algorithm for numerical optimization: Melody Search (MS). Eng Appl Artif Intell 26(4):1301\u20131321","journal-title":"Eng Appl Artif Intell"},{"key":"2746_CR13","unstructured":"Aslimani N, Talbi E-G, Ellaia R (2020) Tornado: an autonomous chaotic algorithm for large scale global optimization,\u00a0HAL Id: hal-02499326,\u00a0https:\/\/hal.inria.fr\/hal-02499326v2"},{"key":"2746_CR14","unstructured":"Belegundu AD (1982) A study of mathematical programming methods for structural optimization. PhD thesis, Department of civil and Environmental Engineering, University of Iowa."},{"key":"2746_CR15","doi-asserted-by":"crossref","unstructured":"Bernardino HS, Barbosa HJC, Lemonge ACC (2007) A hybrid genetic algorithm for constrained optimization problems in mechanical engineering. In: 2007 IEEE Congress on evolutionary computation, pp 646\u201353","DOI":"10.1109\/CEC.2007.4424532"},{"issue":"4","key":"2746_CR16","first-page":"613","volume":"14","author":"L Bing","year":"1997","unstructured":"Bing L, Weisun J (1997) Chaos optimization method and its application. Control Theory Appl 14(4):613\u2013615","journal-title":"Control Theory Appl"},{"issue":"3","key":"2746_CR17","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1109\/MCAS.2002.1167624","volume":"2","author":"M Bucolo","year":"2002","unstructured":"Bucolo M, Caponetto R, Fortuna L, Frasca M, Rizzo A (2002) Does chaos work better than noise? Circuits Syst Mag 2(3):4\u201319","journal-title":"Circuits Syst Mag"},{"issue":"1","key":"2746_CR18","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1080\/03052150802344535","volume":"41","author":"TY Chen","year":"2009","unstructured":"Chen TY, Chen HC (2009) Mixed\u2013discrete structural optimization using a rank-niche evolution strategy. Eng Optim 41(1):39\u201358","journal-title":"Eng Optim"},{"key":"2746_CR19","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/j.apm.2019.02.004","volume":"71","author":"H Chen","year":"2019","unstructured":"Chen H, Xu Y, Wang M, Zhao X (2019) A balanced whale optimization algorithm for constrained engineering design problems. Appl Math Model 71:45\u201359","journal-title":"Appl Math Model"},{"issue":"2","key":"2746_CR20","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/S0166-3615(99)00046-9","volume":"41","author":"CAC Coello","year":"2000","unstructured":"Coello CAC (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41(2):113\u2013127","journal-title":"Comput Ind"},{"issue":"3","key":"2746_CR21","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/S1474-0346(02)00011-3","volume":"16","author":"CAC Coello","year":"2002","unstructured":"Coello CAC, Montes EM (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inform 16(3):193\u2013203","journal-title":"Adv Eng Inform"},{"issue":"2","key":"2746_CR22","doi-asserted-by":"publisher","first-page":"412","DOI":"10.1016\/j.eswa.2013.07.067","volume":"41","author":"E Cuevas","year":"2014","unstructured":"Cuevas E, Cienfuegos M (2014) A new algorithm inspired in the behavior of the social-spider for constrained optimization. Expert Syst Appl 41(2):412\u2013425","journal-title":"Expert Syst Appl"},{"key":"2746_CR23","volume-title":"Optimization for engineering design: algorithms and examples","author":"K Deb","year":"1995","unstructured":"Deb K (1995) Optimization for engineering design: algorithms and examples. Prentice-Hall, New Delhi"},{"key":"2746_CR24","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1016\/S0045-7825(99)00389-8","volume":"186","author":"K Deb","year":"2000","unstructured":"Deb K (2000) Anefficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Engrg 186:311\u2013338","journal-title":"Comput Methods Appl Mech Engrg"},{"key":"2746_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-020-04815-9","author":"FB Demir","year":"2020","unstructured":"Demir FB, Tuncer T, Kocamaz AF (2020) A chaotic optimization method based on logistic-sine map for numerical function optimization. Neural Comput Appl. https:\/\/doi.org\/10.1007\/s00521-020-04815-9","journal-title":"Neural Comput Appl"},{"key":"2746_CR26","volume-title":"An introduction to chaotic dynamical systems","author":"RL Devaney","year":"1987","unstructured":"Devaney RL (1987) An introduction to chaotic dynamical systems. Addison-Wesley, Boston"},{"issue":"2","key":"2746_CR27","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/S0045-7949(99)00084-X","volume":"75","author":"F Erbatur","year":"2000","unstructured":"Erbatur F, Hasan\u00e7ebi O, T\u00fct\u00fcnc\u00fc I, K\u0131l\u0131\u00e7 H (2000) Optimal design of planar and space structures with genetic algorithms. Comput Struct 75(2):209\u2013224","journal-title":"Comput Struct"},{"issue":"33","key":"2746_CR28","doi-asserted-by":"publisher","first-page":"3080","DOI":"10.1016\/j.cma.2008.02.006","volume":"197","author":"M Fesanghary","year":"2008","unstructured":"Fesanghary M, Mahdavi M, Minary-Jolandan M, Alizadeh Y (2008) Hybridizing harmony search algorithm with sequential quadratic programming for engineering optimization problems. Comput Methods Appl Mech Eng 197(33):3080\u20133091","journal-title":"Comput Methods Appl Mech Eng"},{"key":"2746_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jvcir.2018.02.014","volume":"53","author":"M Firouznia","year":"2018","unstructured":"Firouznia M, Faez K, Amindavar H, Alikhani Koupaei J (2018) Chaotic particle filter for visual object tracking. J Vis Commun Image Rep 53:1\u201312","journal-title":"J Vis Commun Image Rep"},{"key":"2746_CR30","volume-title":"A Collection of test problems for constrained Global optimization. Lecture notes in computer Science","author":"C Floundas","year":"1987","unstructured":"Floundas C, Pardalos P (1987) A Collection of test problems for constrained Global optimization. Lecture notes in computer Science. Springer-Verlag, Berlin"},{"issue":"23","key":"2746_CR31","doi-asserted-by":"publisher","first-page":"2325","DOI":"10.1016\/j.compstruc.2011.08.002","volume":"89","author":"AH Gandomi","year":"2011","unstructured":"Gandomi AH, Yang XS, Alavi AH (2011) Mixed variable structural optimization using firefly algorithm. Comput Struct 89(23):2325\u20132336","journal-title":"Comput Struct"},{"issue":"1","key":"2746_CR32","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/j.cnsns.2012.06.009","volume":"18","author":"AH Gandomi","year":"2013","unstructured":"Gandomi AH, Yang XS, Talatahari S, Alavi AH (2013) Firefly algorithm with chaos. Commun Nonlinear Sci Numer Simul 18(1):89\u201398","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"2746_CR33","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.amc.2015.11.001","volume":"274","author":"H Garg","year":"2016","unstructured":"Garg H (2016) A hybrid PSO-GA algorithm for constrained optimization problems. Appl Math Comput 274:292\u2013305","journal-title":"Appl Math Comput"},{"key":"2746_CR34","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1016\/j.ins.2018.11.041","volume":"478","author":"H Garg","year":"2019","unstructured":"Garg H (2019) A hybrid GSA-GA algorithm for constrained optimization problems. Inf Sci 478:499\u2013523","journal-title":"Inf Sci"},{"key":"2746_CR35","doi-asserted-by":"publisher","first-page":"884","DOI":"10.1016\/j.cma.2013.10.019","volume":"268","author":"W Gong","year":"2014","unstructured":"Gong W, Cai Z, Liang D (2014) Engineering optimization by means of an improved constrained differential evolution. Comput Methods Appl Mech Eng 268:884\u2013904","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"4","key":"2746_CR36","doi-asserted-by":"publisher","first-page":"348","DOI":"10.1504\/IJVD.2001.005210","volume":"26","author":"L Gu","year":"2001","unstructured":"Gu L, Yang RJ, Tho CH, Makowskit M, Faruquet OY, Li YL (2001) Optimisation and robustness for crashworthiness of side impact. Int J Veh Des 26(4):348\u2013360","journal-title":"Int J Veh Des"},{"issue":"1","key":"2746_CR37","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.amc.2012.05.062","volume":"219","author":"T Hamaizia","year":"2012","unstructured":"Hamaizia T, Lozi R, Hamri NE (2012) Fast chaotic optimization algorithm based on locally averaged strategy and multifold chaotic attractor. Appl Math Comput 219(1):188\u2013196","journal-title":"Appl Math Comput"},{"issue":"4","key":"2746_CR38","first-page":"479","volume":"2","author":"O Hasancebi","year":"2012","unstructured":"Hasancebi O, Azad SK (2012) An efficient metaheuristic algorithm for engineering optimization: SOPT. Int J Optim Civil Eng 2(4):479\u2013487","journal-title":"Int J Optim Civil Eng"},{"issue":"7","key":"2746_CR39","first-page":"900","volume":"48","author":"D He","year":"2001","unstructured":"He D, He C, Jiang LG, Zhu HW, Hu GR (2001) Chaotic characteristics of a one-dimensional iterative map with infinite collapses. Circuits Syst 48(7):900\u2013906","journal-title":"Circuits Syst"},{"issue":"5","key":"2746_CR40","doi-asserted-by":"publisher","first-page":"3169","DOI":"10.1016\/j.chaos.2009.04.019","volume":"42","author":"YY He","year":"2009","unstructured":"He YY, Zhou JZ, Xiang XQ, Chen H, Qin H (2009) Comparison of different chaotic maps in particle swarm optimization algorithm for long-term cascaded hydroelectric system scheduling. Chaos Solitons Fractals 42(5):3169\u20133176","journal-title":"Chaos Solitons Fractals"},{"key":"2746_CR41","volume-title":"Chaos and nonlinear dynamics: an introduction for scientists and engineers","author":"RC Hilborn","year":"2004","unstructured":"Hilborn RC (2004) Chaos and nonlinear dynamics: an introduction for scientists and engineers. Oxford University Press, Oxford"},{"key":"2746_CR42","volume-title":"Applied nonlinear programming","author":"DM Himmelblau","year":"1972","unstructured":"Himmelblau DM (1972) Applied nonlinear programming. McGraw-Hill, New York"},{"issue":"1","key":"2746_CR43","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/j.amc.2006.07.105","volume":"186","author":"FZ Huang","year":"2007","unstructured":"Huang FZ, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186(1):340\u2013356","journal-title":"Appl Math Comput"},{"key":"2746_CR44","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1016\/j.ins.2012.01.017","volume":"222","author":"G Jia","year":"2013","unstructured":"Jia G, Wang Y, Cai Z, Jin Y (2013) An improved (\u03bc+ \u03bb)-constrained differential evolution for constrained optimization. Inf Sci 222:302\u2013322","journal-title":"Inf Sci"},{"issue":"4","key":"2746_CR45","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1080\/019697298125678","volume":"29","author":"BLW Jiang","year":"1998","unstructured":"Jiang BLW (1998) Optimizing complex functions by chaos search. Cybern Syst 29(4):409\u2013419","journal-title":"Cybern Syst"},{"key":"2746_CR46","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/0960-0779(95)80030-K","volume":"6","author":"T Kapitaniak","year":"1995","unstructured":"Kapitaniak T (1995) Continuous control and synchronization in chaotic systems. Chaos Solitons Fractals 6:237\u2013244","journal-title":"Chaos Solitons Fractals"},{"key":"2746_CR47","unstructured":"Karaboga D, (2005) An idea based on honey bee swarm for numerical optimization, Technical report-tr06, Erciyes University, Engineering Faculty, Computer Engineering Department."},{"key":"2746_CR48","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.cad.2014.12.007","volume":"63","author":"AH Kashan","year":"2015","unstructured":"Kashan AH (2015) An effective algorithm for constrained optimization based on optics inspired optimization (OIO). Comput Aided Des 63:52\u201371","journal-title":"Comput Aided Des"},{"key":"2746_CR49","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1016\/j.advengsoft.2013.09.006","volume":"67","author":"A Kaveh","year":"2014","unstructured":"Kaveh A, Sheikholeslami R, Talatahari S, Keshvari-Ilkhichi M (2014) Chaotic swarming particles: a new method for size optimization of truss structures. Adv Eng Softw 67:136\u2013147","journal-title":"Adv Eng Softw"},{"key":"2746_CR50","first-page":"1942","volume":"4","author":"J Kennedy","year":"1995","unstructured":"Kennedy J, Eberhart R (1995) Particle swarm optimization. IEEE Int Conf Neural Netw 4:1942\u20131948","journal-title":"IEEE Int Conf Neural Netw"},{"issue":"3","key":"2746_CR51","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1090\/S0002-9939-1953-0055639-3","volume":"4","author":"J Kiefer","year":"1953","unstructured":"Kiefer J (1953) Sequential minimax search for a maximum. Proc Am Math Soc 4(3):502\u2013506","journal-title":"Proc Am Math Soc"},{"issue":"4598","key":"2746_CR52","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1126\/science.220.4598.671","volume":"220","author":"S Kirkpatrick","year":"1983","unstructured":"Kirkpatrick S, Vecchi MP (1983) Optimization by simmulated annealing. Science 220(4598):671\u2013680","journal-title":"Science"},{"key":"2746_CR53","doi-asserted-by":"crossref","unstructured":"Kohda T, Tsuneda A, Sakae T, (1992) Chaotic binary sequences by Chebyshev maps and their correlation properties. In: Spread Spectrum Techniques and Applications, ISSTA 92, IEEE Second International Symposium, pp 63\u201366","DOI":"10.1109\/ISSSTA.1992.665630"},{"issue":"1","key":"2746_CR54","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1162\/evco.1999.7.1.19","volume":"7","author":"S Koziel","year":"1999","unstructured":"Koziel S, Michalewicz Z (1999) Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evol Comput 7(1):19\u201344","journal-title":"Evol Comput"},{"issue":"1","key":"2746_CR55","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1137\/S1052623496303470","volume":"9","author":"JC Lagarias","year":"1998","unstructured":"Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the nelder-mead simplex method in low dimensions. SIAM J Optim 9(1):112\u2013147","journal-title":"SIAM J Optim"},{"issue":"36","key":"2746_CR56","doi-asserted-by":"publisher","first-page":"3902","DOI":"10.1016\/j.cma.2004.09.007","volume":"194","author":"KS Lee","year":"2005","unstructured":"Lee KS, Geem ZW (2005) A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194(36):3902\u20133933","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"5","key":"2746_CR57","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1002\/nme.899","volume":"59","author":"AC Lemonge","year":"2004","unstructured":"Lemonge AC, Barbosa HJ (2004) An adaptive penalty scheme for genetic algorithms in structural optimization. Int J Numer Meth Eng 59(5):703\u2013736","journal-title":"Int J Numer Meth Eng"},{"key":"2746_CR58","volume-title":"Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real parameter optimization","author":"JJ Liang","year":"2006","unstructured":"Liang JJ, Runarsson TP, Mezura-Montes E, Clerc M, Suganthan PN, Coello CAC, Deb K (2006) Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real parameter optimization. Nanyang Technological University, Singapore"},{"key":"2746_CR59","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-30528-9","volume-title":"Global optimization: from theory to implementation","author":"L Liberti","year":"2006","unstructured":"Liberti L, Maculan N (2006) Global optimization: from theory to implementation. Springer Science and Business Media, Berlin"},{"issue":"2","key":"2746_CR60","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","volume":"20","author":"EN Lorenz","year":"1963","unstructured":"Lorenz EN (1963) Deterministic non-periodic flow. J Atmos Sci 20(2):130\u2013141","journal-title":"J Atmos Sci"},{"issue":"4","key":"2746_CR61","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1016\/S0960-0779(03)00033-X","volume":"18","author":"Z Lu","year":"2003","unstructured":"Lu Z, Shieh LS, Chen G (2003) On robust control of uncertain chaotic systems: a sliding-mode synthesis via chaotic optimization. Chaos Solitons Fractals 18(4):819\u2013827","journal-title":"Chaos Solitons Fractals"},{"issue":"4","key":"2746_CR62","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1631\/jzus.2006.A0539","volume":"7","author":"HJ Lu","year":"2006","unstructured":"Lu HJ, Zhang HM, Ma LH (2006) A new optimization algorithm based on chaos. J Zhejiang Univ Sci A 7(4):539\u2013542","journal-title":"J Zhejiang Univ Sci A"},{"issue":"2","key":"2746_CR63","doi-asserted-by":"crossref","first-page":"1567","DOI":"10.1016\/j.amc.2006.11.033","volume":"188","author":"M Mahdavi","year":"2007","unstructured":"Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567\u20131579","journal-title":"Appl Math Comput"},{"issue":"4","key":"2746_CR64","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1109\/TEVC.2009.2033582","volume":"14","author":"R Mallipeddi","year":"2010","unstructured":"Mallipeddi R, Suganthan P, Suganthan N (2010) Ensemble of constraint handling techniques. IEEE Trans Evol Comput 14(4):561\u2013579","journal-title":"IEEE Trans Evol Comput"},{"issue":"5560","key":"2746_CR65","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1038\/261459a0","volume":"261","author":"RM May","year":"1976","unstructured":"May RM (1976) Simple mathematical models with very complicated dynamics. Nature 261(5560):459\u2013467","journal-title":"Nature"},{"issue":"5","key":"2746_CR66","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1080\/03052150701364022","volume":"39","author":"E Mezura-Montes","year":"2007","unstructured":"Mezura-Montes E, Coello CA, Vel\u00e1zquez-Reyes J, Mu\u00f1oz-D\u00e1vila L (2007) Multiple trial vectors in differential evolution for engineering design. Eng Optim 39(5):567\u2013589","journal-title":"Eng Optim"},{"issue":"3","key":"2746_CR67","first-page":"284","volume":"6","author":"M Misaghi","year":"2019","unstructured":"Misaghi M, Yaghoobi M (2019) Improved invasive weed optimization algorithm (IWO) based on chaos theory for optimal design of PID controller. J Comput Des Eng 6(3):284\u2013295","journal-title":"J Comput Des Eng"},{"key":"2746_CR68","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1016\/j.neucom.2012.07.064","volume":"148","author":"B Niu","year":"2015","unstructured":"Niu B, Wang J, Wang H (2015) Bacterial-inspired algorithms for solving constrained optimization problems. Neurocomputing 148:54\u201362","journal-title":"Neurocomputing"},{"key":"2746_CR69","volume-title":"Numerical optimization","author":"J Nocedal","year":"2006","unstructured":"Nocedal J, Wright SJ (2006) Numerical optimization. Springer Science and Business Media, New York"},{"key":"2746_CR70","first-page":"63","volume-title":"Calculus: labs for matlab","author":"KM O'Connor","year":"2005","unstructured":"O\u2019Connor KM (2005) Calculus: labs for matlab. Jones and Bartlett publishers, Burlington, pp 63\u201364"},{"issue":"11","key":"2746_CR71","doi-asserted-by":"publisher","first-page":"1196","DOI":"10.1103\/PhysRevLett.64.1196","volume":"64","author":"E Ott","year":"1990","unstructured":"Ott E, Grebogi C, Yorke JA (1990) Controlling chaos. Phys Rev Lett 64(11):1196\u20131199","journal-title":"Phys Rev Lett"},{"issue":"8","key":"2746_CR72","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1103\/PhysRevLett.64.821","volume":"64","author":"LM Pecora","year":"1990","unstructured":"Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821\u2013824","journal-title":"Phys Rev Lett"},{"key":"2746_CR73","doi-asserted-by":"publisher","first-page":"110472","DOI":"10.1109\/ACCESS.2019.2931910","volume":"7","author":"W Qiao","year":"2019","unstructured":"Qiao W, Yang Z (2019) Modified dolphin swarm algorithm based on chaotic maps for solving high-dimensional function optimization problems. IEEE Access 7:110472\u2013110486","journal-title":"IEEE Access"},{"issue":"2","key":"2746_CR74","first-page":"1","volume":"4","author":"AO Raouf","year":"2014","unstructured":"Raouf AO, Baset AM, El-henawy I (2014) A new hybrid flower pollination algorithm for solving constrained global optimization problems. Int J Appl 4(2):1\u201313","journal-title":"Int J Appl"},{"key":"2746_CR75","unstructured":"Reklaitis GV, Ravindran A, Ragsdell KM (1983) Engineering optimization: methods and applications. Wiley, New York, pp 43\u201347"},{"issue":"2","key":"2746_CR76","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1115\/1.2912596","volume":"112","author":"E Sandgren","year":"1990","unstructured":"Sandgren E (1990) Nonlinear integer and discrete programming in mechanical design optimization. J Mech Des 112(2):223\u2013229","journal-title":"J Mech Des"},{"issue":"2","key":"2746_CR77","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1080\/0952813X.2018.1430858","volume":"30","author":"GI Sayed","year":"2018","unstructured":"Sayed GI, Darwish A, Hassanien AE (2018) A new chaotic multi-verse optimization algorithm for solving engineering optimization problems. J Exp Theor Artif Intell 30(2):293\u2013317","journal-title":"J Exp Theor Artif Intell"},{"issue":"4","key":"2746_CR78","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/s00158-006-0032-z","volume":"32","author":"K Sedlaczek","year":"2006","unstructured":"Sedlaczek K, Eberhard P (2006) Using augmented Lagrangian particle swarm optimization for constrained problems in engineering. Struct Multidiscip Optim 32(4):277\u2013286","journal-title":"Struct Multidiscip Optim"},{"key":"2746_CR79","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1016\/j.engappai.2014.09.009","volume":"37","author":"Z Seif","year":"2015","unstructured":"Seif Z, Ahmadi MB (2015) An opposition-based algorithm for function optimization. Eng Appl Artif Intell 37:293\u2013306","journal-title":"Eng Appl Artif Intell"},{"issue":"4","key":"2746_CR80","doi-asserted-by":"publisher","first-page":"331","DOI":"10.14257\/ijhit.2014.7.4.28","volume":"7","author":"X Sun","year":"2014","unstructured":"Sun X, Wang F, Wen S (2014) An improved evolutionary strategy of genetic algorithm and a new method on generation of initial population when using genetic algorithms for solving constrained optimization problems. Int J Hybrid Inform Technol 7(4):331\u2013344","journal-title":"Int J Hybrid Inform Technol"},{"issue":"2","key":"2746_CR81","doi-asserted-by":"crossref","first-page":"1076","DOI":"10.1016\/j.amc.2006.09.087","volume":"187","author":"MS Tavazoei","year":"2007","unstructured":"Tavazoei MS, Haeri M (2007) Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms. Appl Math Comput 187(2):1076\u20131085","journal-title":"Appl Math Comput"},{"key":"2746_CR82","doi-asserted-by":"crossref","unstructured":"Tessema B, Yen G, (2006) A selfadaptive penalty function based algorithm for constrained optimization. In: Proceedings of the 2006 IEEE Congress on Evolutionary Computation, IEEE Press, Vancouver, BC, Canada, pp 246\u2013253","DOI":"10.1109\/CEC.2006.1688315"},{"issue":"2","key":"2746_CR83","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1061\/(ASCE)0733-9445(1995)121:2(301)","volume":"121","author":"PB Thanedar","year":"1995","unstructured":"Thanedar PB, Vanderplaats GN (1995) Survey of discrete variable optimization for structural design. J Struct Eng 121(2):301\u2013306","journal-title":"J Struct Eng"},{"issue":"9","key":"2746_CR84","doi-asserted-by":"publisher","first-page":"3349","DOI":"10.1007\/s00500-015-1726-1","volume":"20","author":"GG Wang","year":"2016","unstructured":"Wang GG, Deb S, Gandomi AH, Zhang Z, Alavi AH (2016) Chaotic cuckoo search. Soft Comput 20(9):3349\u20133362","journal-title":"Soft Comput"},{"key":"2746_CR85","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/8250480","author":"L Wang","year":"2018","unstructured":"Wang L, Liu X, Sun M, Qu J, Wei Y (2018) A new chaotic starling particle swarm optimization algorithm for clustering problems. Math Probl Eng. https:\/\/doi.org\/10.1155\/2018\/8250480","journal-title":"Math Probl Eng"},{"key":"2746_CR86","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/j.asoc.2015.04.028","volume":"33","author":"W Wei","year":"2015","unstructured":"Wei W, Wang J, Tao M (2015) Constrained differential evolution with multi-objective sorting mutation operators for constrained optimization. Appl Soft Comput 33:207\u2013222","journal-title":"Appl Soft Comput"},{"issue":"2","key":"2746_CR87","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1080\/03052159508941187","volume":"24","author":"SJ Wu","year":"1995","unstructured":"Wu SJ, Chow PT (1995) Genetic algorithms for nonlinear mixed discrete-integer optimization problems via meta-genetic parameter optimization. Eng Optim 24(2):137\u2013159","journal-title":"Eng Optim"},{"key":"2746_CR88","doi-asserted-by":"publisher","DOI":"10.1002\/9780470640425","volume-title":"Engineering optimization: an introduction with metaheuristic applications","author":"XS Yang","year":"2010","unstructured":"Yang XS (2010) Engineering optimization: an introduction with metaheuristic applications. John Wiley and Sons, New Jersey"},{"issue":"4","key":"2746_CR89","doi-asserted-by":"publisher","first-page":"1366","DOI":"10.1016\/j.chaos.2006.04.057","volume":"34","author":"D Yang","year":"2007","unstructured":"Yang D, Li G, Cheng G (2007) On the efficiency of chaos optimization algorithms for global optimization. Chaos Solitons Fractals 34(4):1366\u20131375","journal-title":"Chaos Solitons Fractals"},{"issue":"4","key":"2746_CR90","doi-asserted-by":"publisher","first-page":"1229","DOI":"10.1016\/j.cnsns.2013.08.017","volume":"19","author":"D Yang","year":"2014","unstructured":"Yang D, Liu Z, Zhou J (2014) Chaos optimization algorithms based on chaotic maps with different probability distribution and search speed for global optimization. Commun Nonlinear Sci Numer Simul 19(4):1229\u20131246","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"2746_CR91","doi-asserted-by":"publisher","DOI":"10.1007\/s10845-020-01565-2","author":"W Yi","year":"2020","unstructured":"Yi W, Gao L, Pei Z, Lu J, Chen Y (2020) \u03b5 Constrained differential evolution using halfspace partition for optimization problems. J Intell Manuf. https:\/\/doi.org\/10.1007\/s10845-020-01565-2","journal-title":"J Intell Manuf"},{"issue":"2","key":"2746_CR92","doi-asserted-by":"publisher","first-page":"3880","DOI":"10.1016\/j.eswa.2008.02.039","volume":"36","author":"E Zahara","year":"2010","unstructured":"Zahara E, Kao YT (2010) Hybrid Nelder-Mead simplex search and particle swarm optimization for constrained engineering design problems. Expert Syst Appl 36(2):3880\u20133886","journal-title":"Expert Syst Appl"},{"issue":"15","key":"2746_CR93","doi-asserted-by":"publisher","first-page":"3043","DOI":"10.1016\/j.ins.2008.02.014","volume":"178","author":"M Zhang","year":"2008","unstructured":"Zhang M, Luo W, Wang X (2008) Differential evolution with dynamic stochastic selection for constrained optimization. Inf Sci 178(15):3043\u20133074","journal-title":"Inf Sci"},{"issue":"21","key":"2746_CR94","doi-asserted-by":"publisher","first-page":"7831","DOI":"10.1016\/j.eswa.2015.05.050","volume":"42","author":"C Zhang","year":"2015","unstructured":"Zhang C, Lin Q, Gao L, Li X (2015) Backtracking Search Algorithm with three constraint handling methods for constrained optimization problems. Expert Syst Appl 42(21):7831\u20137845","journal-title":"Expert Syst Appl"}],"container-title":["Journal of Ambient Intelligence and Humanized Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12652-020-02746-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12652-020-02746-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12652-020-02746-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,13]],"date-time":"2022-12-13T03:59:29Z","timestamp":1670903969000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12652-020-02746-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,25]]},"references-count":94,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2021,11]]}},"alternative-id":["2746"],"URL":"https:\/\/doi.org\/10.1007\/s12652-020-02746-w","relation":{},"ISSN":["1868-5137","1868-5145"],"issn-type":[{"value":"1868-5137","type":"print"},{"value":"1868-5145","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,25]]},"assertion":[{"value":"16 April 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 November 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 January 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}