{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T21:04:39Z","timestamp":1768770279385,"version":"3.49.0"},"reference-count":60,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,4,1]],"date-time":"2021-04-01T00:00:00Z","timestamp":1617235200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,4,1]],"date-time":"2021-04-01T00:00:00Z","timestamp":1617235200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61772295"],"award-info":[{"award-number":["61772295"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61572270"],"award-info":[{"award-number":["61572270"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61773056"],"award-info":[{"award-number":["61773056"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010338","name":"Chongqing Normal University","doi-asserted-by":"publisher","award":["19XLB003"],"award-info":[{"award-number":["19XLB003"]}],"id":[{"id":"10.13039\/100010338","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Supported by the Science and Technology Research Program of Chongqing Municipal Education Commission","award":["No.KJZDM202000501"],"award-info":[{"award-number":["No.KJZDM202000501"]}]},{"name":"Chongqing Technology Innovation and application development special general project","award":["cstc2020jscx-lyjsA0063"],"award-info":[{"award-number":["cstc2020jscx-lyjsA0063"]}]},{"name":"Chongqing Normal University Graduate Scientific Research Innovation Project","award":["YKC20042"],"award-info":[{"award-number":["YKC20042"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2021,4]]},"DOI":"10.1007\/s11128-021-03067-3","type":"journal-article","created":{"date-parts":[[2021,4,3]],"date-time":"2021-04-03T08:02:31Z","timestamp":1617436951000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["An improved hybrid quantum optimization algorithm for solving nonlinear equations"],"prefix":"10.1007","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4857-325X","authenticated-orcid":false,"given":"Yumin","family":"Dong","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5099-8601","authenticated-orcid":false,"given":"Jinlei","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,4,3]]},"reference":[{"issue":"4\u20135","key":"3067_CR1","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1016\/S0375-9601(00)00725-8","volume":"277","author":"E Fan","year":"2000","unstructured":"Fan, E.: Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277(4\u20135), 212\u2013218 (2000)","journal-title":"Phys. Lett. A"},{"issue":"10","key":"3067_CR2","doi-asserted-by":"publisher","first-page":"1768","DOI":"10.1016\/j.nucengdes.2009.05.021","volume":"239","author":"G Derek","year":"2009","unstructured":"Derek, G., Chris, N., Glen, H., Damien, L.G.: Moose: a parallel computational framework for coupled systems of nonlinear equations. Nucl. Eng. Des. 239(10), 1768\u20131778 (2009)","journal-title":"Nucl. Eng. Des."},{"issue":"1\u20135","key":"3067_CR3","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/0375-9601(96)00283-6","volume":"216","author":"M Wang","year":"1996","unstructured":"Wang, M., Zhou, Y., Li, Z.: Application of a ho-mogeneous balance method to exact solutions of nonlinear equations in mathematical physics. Phys. Lett. A 216(1\u20135), 67\u201375 (1996)","journal-title":"Phys. Lett. A"},{"key":"3067_CR4","doi-asserted-by":"crossref","unstructured":"Gen, M., Lin, L.: Genetic algorithms. Wiley Encyclopedia of Computer Science and Engineering, pp. 1\u201315, (2007)","DOI":"10.1002\/9780470050118.ecse169"},{"key":"3067_CR5","unstructured":"Such, F.P., Madhavan, V., Conti, E., Lehman, J., Stanley, K.O., Clune, J.: Deep neuroevolu-tion: genetic algorithms are a competitive alternative for training deep neural networks for reinforcement learning. arXiv preprint arXiv:1712.06567, (2017)"},{"key":"3067_CR6","doi-asserted-by":"crossref","unstructured":"Kelley, C.T.: Solving nonlinear equations with Newton\u2019s method, vol. 1. SIAM, (2003)","DOI":"10.1137\/1.9780898718898"},{"issue":"1\u20133","key":"3067_CR7","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1007\/BF01581275","volume":"58","author":"L Qi","year":"1993","unstructured":"Qi, L., Sun, J.: A nonsmooth version of Newton\u2019s method. Math. Program. 58(1\u20133), 353\u2013367 (1993)","journal-title":"Math. Program."},{"key":"3067_CR8","doi-asserted-by":"publisher","first-page":"1449","DOI":"10.1109\/TPAS.1967.291823","volume":"11","author":"WF Tinney","year":"1967","unstructured":"Tinney, W.F., Hart, C.E.: Power flow solution by Newton\u2019s method. IEEE Trans. Power Appar. Syst. 11, 1449\u20131460 (1967)","journal-title":"IEEE Trans. Power Appar. Syst."},{"issue":"6","key":"3067_CR9","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1016\/S0893-9659(04)90104-8","volume":"17","author":"A Yasar \u00d6zban","year":"2004","unstructured":"Yasar \u00d6zban, A.: Some new variants of Newton\u2019s method. Appl. Math. Lett. 17(6), 677\u2013682 (2004)","journal-title":"Appl. Math. Lett."},{"issue":"10\u201312","key":"3067_CR10","doi-asserted-by":"publisher","first-page":"1559","DOI":"10.1016\/j.camwa.2005.08.022","volume":"50","author":"C Chun","year":"2005","unstructured":"Chun, C.: Iterative methods improving Newton\u2019s method by the decomposition method. Comput. Math. Appl. 50(10\u201312), 1559\u20131568 (2005)","journal-title":"Comput. Math. Appl."},{"issue":"5","key":"3067_CR11","doi-asserted-by":"publisher","first-page":"927","DOI":"10.1016\/j.cor.2009.07.002","volume":"37","author":"G Jinwei","year":"2010","unstructured":"Jinwei, G., Manzhan, G., Cao, C., Xingsheng, G.: A novel competitive co-evolutionary quantum genetic algorithm for stochastic job shop scheduling problem. Comput. Oper. Res. 37(5), 927\u2013937 (2010)","journal-title":"Comput. Oper. Res."},{"issue":"2","key":"3067_CR12","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/j.ijepes.2010.08.014","volume":"33","author":"J-C Lee","year":"2011","unstructured":"Lee, J.-C., Lin, W.-M., Liao, G.-C., Tsao, T.-P.: Quantum genetic algorithm for dynamic economic dispatch with valve-point effects and including wind power system. Int. J. Electr. Power Energy Syst. 33(2), 189\u2013197 (2011)","journal-title":"Int. J. Electr. Power Energy Syst."},{"issue":"1","key":"3067_CR13","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.jmaa.2008.12.065","volume":"355","author":"G Jinwei","year":"2009","unstructured":"Jinwei, G., Xingsheng, G., Manzhan, G.: A novel parallel quantum genetic algorithm for stochastic job shop scheduling. J. Math. Anal. Appl. 355(1), 63\u201381 (2009)","journal-title":"J. Math. Anal. Appl."},{"issue":"3","key":"3067_CR14","first-page":"243","volume":"9","author":"Z Laboudi","year":"2012","unstructured":"Laboudi, Z., Chikhi, S.: Comparison of genetic algorithm and quantum genetic algorithm. Int. Arab J. Inf. Technol. 9(3), 243\u2013249 (2012)","journal-title":"Int. Arab J. Inf. Technol."},{"issue":"1","key":"3067_CR15","first-page":"1","volume":"3","author":"F Sabahi","year":"2020","unstructured":"Sabahi, F.: Quantum genetic LMI-based h control with time delay. Int. J. Ind. Electron. Control Optim. 3(1), 1\u201310 (2020)","journal-title":"Int. J. Ind. Electron. Control Optim."},{"key":"3067_CR16","doi-asserted-by":"publisher","first-page":"101408","DOI":"10.1016\/j.scs.2018.12.036","volume":"46","author":"B Li","year":"2019","unstructured":"Li, B., Pingfang, H., Zhu, N., Lei, F., Xing, L.: Performance analysis and optimization of a CCHP-GSHP coupling system based on quantum genetic algorithm. Sustain. Cities Soc. 46, 101408 (2019)","journal-title":"Sustain. Cities Soc."},{"issue":"9","key":"3067_CR17","doi-asserted-by":"publisher","first-page":"10539","DOI":"10.1007\/s11042-017-4592-2","volume":"77","author":"H Lizhen Deng","year":"2018","unstructured":"Lizhen Deng, H., Zhu, Q.Z., Li, Y.: Adaptive top-hat filter based on quantum genetic algorithm for infrared small target detection. Multimed. Tools Appl. 77(9), 10539\u201310551 (2018)","journal-title":"Multimed. Tools Appl."},{"key":"3067_CR18","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1016\/j.neucom.2015.12.131","volume":"211","author":"P Chen","year":"2016","unstructured":"Chen, P., Yuan, L., He, Y., Luo, S.: An improved SVM classifier based on double chains quantum genetic algorithm and its application in analogue circuit diagnosis. Neurocomputing 211, 202\u2013211 (2016)","journal-title":"Neurocomputing"},{"issue":"14","key":"3067_CR19","doi-asserted-by":"publisher","first-page":"870","DOI":"10.1049\/el.2018.0609","volume":"54","author":"L Zhang","year":"2018","unstructured":"Zhang, L., Lv, H., Tan, D., Fang, X., Chen, J., Bao, G., Cai, S.: Adaptive quantum genetic algorithm for task sequence planning of complex assembly systems. Electron. Lett. 54(14), 870\u2013872 (2018)","journal-title":"Electron. Lett."},{"issue":"10","key":"3067_CR20","doi-asserted-by":"publisher","first-page":"875","DOI":"10.1016\/j.advengsoft.2011.06.006","volume":"42","author":"PC Li","year":"2011","unstructured":"Li, P.C., Song, K.P., Shang, F.H.: Double chains quantum genetic algorithm with application to neuro-fuzzy controller design. Adv. Eng. Softw. 42(10), 875\u2013886 (2011)","journal-title":"Adv. Eng. Softw."},{"issue":"8","key":"3067_CR21","first-page":"1216","volume":"38","author":"S Li","year":"2006","unstructured":"Li, S., Li, P.: Quantum genetic algorithm based on real encoding and gradient information of object function. J. Harbin Inst. Technol. 38(8), 1216\u20131223 (2006)","journal-title":"J. Harbin Inst. Technol."},{"issue":"2","key":"3067_CR22","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1088\/0034-4885\/61\/2\/002","volume":"61","author":"A Steane","year":"1998","unstructured":"Steane, A.: Quantum computing. Rep. Prog. Phys. 61(2), 117 (1998)","journal-title":"Rep. Prog. Phys."},{"issue":"5856","key":"3067_CR23","doi-asserted-by":"publisher","first-page":"1567","DOI":"10.1126\/science.1142892","volume":"318","author":"JL O\u2019brien","year":"2007","unstructured":"O\u2019brien, J.L.: Optical quantum computing. Science 318(5856), 1567\u20131570 (2007)","journal-title":"Science"},{"issue":"6830","key":"3067_CR24","doi-asserted-by":"publisher","first-page":"789","DOI":"10.1038\/35071024","volume":"410","author":"MN Leuenberger","year":"2001","unstructured":"Leuenberger, M.N., Loss, D.: Quantum computing in molecular magnets. Nature 410(6830), 789\u2013793 (2001)","journal-title":"Nature"},{"issue":"1","key":"3067_CR25","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1109\/72.265966","volume":"5","author":"X Qi","year":"1994","unstructured":"Qi, X., Palmieri, F.: Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space part II: analysis of the diversification role of crossover. IEEE Trans. Neural Netw. 5(1), 120\u2013129 (1994)","journal-title":"IEEE Trans. Neural Netw."},{"issue":"1\u20132","key":"3067_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0304-3975(00)00406-0","volume":"259","author":"LM Schmitt","year":"2001","unstructured":"Schmitt, L.M.: Theory of genetic algorithms. Theor. Comput. Sci. 259(1\u20132), 1\u201361 (2001)","journal-title":"Theor. Comput. Sci."},{"key":"3067_CR27","unstructured":"Abdoun, O., Abouchabaka, J., Tajani C.: Analyzing the performance of mutation operators to solve the travelling salesman problem. arXiv preprint arXiv:1203.3099, (2012)"},{"issue":"5","key":"3067_CR28","first-page":"748","volume":"30","author":"Y Wang","year":"2007","unstructured":"Wang, Y., Li, Y.-H.: A novel quantum genetic algorithm for tsp. Chin. J. Comput. Chin. Ed. 30(5), 748 (2007)","journal-title":"Chin. J. Comput. Chin. Ed."},{"issue":"2","key":"3067_CR29","doi-asserted-by":"publisher","first-page":"742","DOI":"10.1007\/s11227-012-0864-9","volume":"65","author":"S Prakash","year":"2013","unstructured":"Prakash, S., Prakash Vidyarthi, D.: A novel scheduling model for computational grid using quantum genetic algorithm. J. Supercomput. 65(2), 742\u2013770 (2013)","journal-title":"J. Supercomput."},{"issue":"01","key":"3067_CR30","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1142\/S012906571000222X","volume":"20","author":"H Duan","year":"2010","unstructured":"Duan, H., Chun-fang, X., Xing, Z.-H.: A hybrid artificial bee colony optimization and quantum evolutionary algorithm for continuous optimization problems. Int. J. Neural Syst. 20(01), 39\u201350 (2010)","journal-title":"Int. J. Neural Syst."},{"issue":"1\u20133","key":"3067_CR31","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1016\/j.neucom.2007.11.017","volume":"72","author":"P Li","year":"2008","unstructured":"Li, P., Li, S.: Quantum-inspired evolutionary algorithm for continuous space optimization based on Bloch coordinates of qubits. Neurocomputing 72(1\u20133), 581\u2013591 (2008)","journal-title":"Neurocomputing"},{"issue":"6","key":"3067_CR32","first-page":"985","volume":"25","author":"LI Panchi","year":"2008","unstructured":"Panchi, L.I.: Quantum genetic algorithm based on Bloch coordinates of qubits and its application. Control Theory Appl. 25(6), 985\u2013989 (2008)","journal-title":"Control Theory Appl."},{"issue":"4","key":"3067_CR33","doi-asserted-by":"publisher","first-page":"605","DOI":"10.1103\/PhysRevLett.71.605","volume":"71","author":"SV Zaitsev-Zotov","year":"1993","unstructured":"Zaitsev-Zotov, S.V.: Classical to quantum crossover in charge density wave creep at low temperatures. Phys. Rev. Lett. 71(4), 605 (1993)","journal-title":"Phys. Rev. Lett."},{"issue":"3","key":"3067_CR34","doi-asserted-by":"publisher","first-page":"737","DOI":"10.1007\/s11128-013-0686-6","volume":"13","author":"A SaiToh","year":"2014","unstructured":"SaiToh, A., Rahimi, R., Nakahara, M.: A quantum genetic algorithm with quantum crossover and mutation operations. Quantum Inf. Process. 13(3), 737\u2013755 (2014)","journal-title":"Quantum Inf. Process."},{"issue":"1","key":"3067_CR35","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1007\/s11767-003-0089-4","volume":"20","author":"J Yang","year":"2003","unstructured":"Yang, J., Li, B., Zhuang, Z.: Research of quantum genetic algorith and its application in blind source separation. J. Electron. (China) 20(1), 62\u201368 (2003)","journal-title":"J. Electron. (China)"},{"key":"3067_CR36","first-page":"56","volume":"04","author":"ZHANG Xiao-fenga","year":"2013","unstructured":"Xiao-fenga, Z.H.A.N.G., Gui-fanga, S.U.I., Rana, Z.H.E.N.G., Zhi-nongb, L.I., Guo-weia, Y.A.N.G.: An improved quantum genetic algorithm of quantum revolving gate. Comput. Eng. 04, 56 (2013)","journal-title":"Comput. Eng."},{"issue":"2","key":"3067_CR37","doi-asserted-by":"publisher","first-page":"526","DOI":"10.1007\/s10773-014-2245-z","volume":"54","author":"T Hua","year":"2015","unstructured":"Hua, T., Chen, J., Pei, D., Zhang, W., Zhou, N.: Quantum image encryption algorithm based on image correlation decomposition. Int. J. Theor. Phys. 54(2), 526\u2013537 (2015)","journal-title":"Int. J. Theor. Phys."},{"key":"3067_CR38","unstructured":"Xiaohui, Z., Li, C., Peng, Z.: Simulation of quantum cellular automatas based on quantum genetic algorithm [j]. Micronanoelectronic Technology 1, (2011)"},{"key":"3067_CR39","doi-asserted-by":"crossref","unstructured":"Du, T., Hu, Y., Ke, X. : Improved quantum artificial fish algorithm application to distributed network considering distributed generation. Computational intelligence and neuroscience 2015, (2015)","DOI":"10.1155\/2015\/851863"},{"key":"3067_CR40","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00521-018-3890-6","volume":"45","author":"Y Guo","year":"2018","unstructured":"Guo, Y., Wei, L., Xu, X.: A sonar image segmentation algorithm based on quantum-inspired particle swarm optimization and fuzzy clustering. Neural Comput. Appl. 45, 1\u20138 (2018). https:\/\/doi.org\/10.1007\/s00521-018-3890-6","journal-title":"Neural Comput. Appl."},{"issue":"1\u20133","key":"3067_CR41","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/BF01588777","volume":"49","author":"KA Ariyawansa","year":"1990","unstructured":"Ariyawansa, K.A.: Deriving collinear scaling algorithms as extensions of quasi-newton methods and the local convergence of DFP and BFGS related collinear scaling algorithms. Math. Program. 49(1\u20133), 23\u201348 (1990)","journal-title":"Math. Program."},{"issue":"1","key":"3067_CR42","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1080\/10556780802367205","volume":"24","author":"O G\u00fcler","year":"2009","unstructured":"G\u00fcler, O., G\u00fcrtuna, F., Shevchenko, O.: Duality in quasi-Newton methods and new variational characterizations of the DFP and BFGS updates. Optim. Methods Softw. 24(1), 45\u201362 (2009)","journal-title":"Optim. Methods Softw."},{"issue":"1","key":"3067_CR43","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1007\/BF01582161","volume":"34","author":"MJD Powell","year":"1986","unstructured":"Powell, M.J.D.: How bad are the BFGS and DFP methods when the objective function is quadratic? Math. Program. 34(1), 34\u201347 (1986)","journal-title":"Math. Program."},{"issue":"1","key":"3067_CR44","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/BF00940702","volume":"78","author":"M Contreras","year":"1993","unstructured":"Contreras, M., Tapia, R.A.: Sizing the BFGS and DFP updates: numerical study. J. Optim. Theory Appl. 78(1), 93\u2013108 (1993)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"3067_CR45","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/BF00962795","volume":"61","author":"JE Dennis","year":"1989","unstructured":"Dennis, J.E., Martinez, H.J., Tapia, R.A.: Convergence theory for the structured BFGS secant method with an application to nonlinear least squares. J. Optim. Theory Appl. 61(2), 161\u2013178 (1989)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"3067_CR46","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/BF02591850","volume":"38","author":"MJD Powell","year":"1987","unstructured":"Powell, M.J.D.: Updating conjugate directions by the BFGS formula. Math. Program. 38(1), 29 (1987)","journal-title":"Math. Program."},{"key":"3067_CR47","first-page":"56","volume":"4","author":"Z Xiao-fenga","year":"2013","unstructured":"Xiao-fenga, Z., Gui-fanga, S.U.I., Rana, Z., et al.: An improved quantum genetic algorithm of quantum revolving gate [J]. Comput. Eng. 4, 56 (2013)","journal-title":"Comput. Eng."},{"issue":"4","key":"3067_CR48","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1109\/4235.797972","volume":"3","author":"A Rogers","year":"1999","unstructured":"Rogers, A., Prugel-Bennett, A.: Genetic drift in genetic algorithm selection schemes. IEEE Trans Evolut. Comput. 3(4), 298\u2013303 (1999)","journal-title":"IEEE Trans Evolut. Comput."},{"issue":"4","key":"3067_CR49","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1016\/j.compchemeng.2010.06.014","volume":"35","author":"K-Z Tang","year":"2011","unstructured":"Tang, K.-Z., Sun, T.-K., Yang, J.-Y.: An improved genetic algorithm based on a novel selection strategy for nonlinear programming problems. Comput. Chem. Eng. 35(4), 615\u2013621 (2011)","journal-title":"Comput. Chem. Eng."},{"issue":"3","key":"3067_CR50","doi-asserted-by":"publisher","first-page":"576","DOI":"10.1109\/TSMCB.2006.887946","volume":"37","author":"BB Li","year":"2007","unstructured":"Li, B.B., Wang, L.: A hybrid quantum-inspired genetic algorithm for multiobjective flow shop scheduling. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 37(3), 576\u2013591 (2007)","journal-title":"IEEE Trans. Syst. Man Cybern. Part B (Cybern.)"},{"key":"3067_CR51","unstructured":"CAI, B.B., ZHANG, X.H.: Hybrid quantum genetic algorithm and its application in VRP [j]. Computer Simulation 7, (2010)"},{"issue":"24","key":"3067_CR52","first-page":"50","volume":"41","author":"F Yang","year":"2013","unstructured":"Yang, F., Yi-liu, J.I.A.N.G., Zhen-kun, L.I.: Optimal allocation of distributed generation for microgrid based on hybrid quantum genetic algorithm. Power Syst. Prot. Control 41(24), 50\u201357 (2013)","journal-title":"Power Syst. Prot. Control"},{"issue":"7","key":"3067_CR53","first-page":"1","volume":"29","author":"D Juan","year":"2008","unstructured":"Juan, D., Liu, Z.G.: A new hybrid quantum genetic algorithm for solving nonlinear equations. Microcomput. Appl. 29(7), 1\u20135 (2008)","journal-title":"Microcomput. Appl."},{"issue":"8","key":"3067_CR54","first-page":"2898","volume":"26","author":"ZG Liu","year":"2009","unstructured":"Liu, Z.G., Xu, S.H.: Training method of process neural networks based on hybrid quantum genetic algorithm. Appl. Res. Comput. 26(8), 2898\u20132901 (2009)","journal-title":"Appl. Res. Comput."},{"issue":"3","key":"3067_CR55","first-page":"53","volume":"29","author":"G Xianlong","year":"2011","unstructured":"Xianlong, G., Xu, W., Ying, D.: The vehicle routing problem in the case of stochastic demand based on hybrid quantum genetic algorithm. Syst. Eng. 29(3), 53\u201359 (2011)","journal-title":"Syst. Eng."},{"issue":"2","key":"3067_CR56","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1016\/j.amc.2005.01.115","volume":"171","author":"L Wang","year":"2005","unstructured":"Wang, L., Tang, F., Hao, W.: Hybrid genetic algorithm based on quantum computing for numerical optimization and parameter estimation. Appl. Math. Comput. 171(2), 1141\u20131156 (2005)","journal-title":"Appl. Math. Comput."},{"key":"3067_CR57","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1016\/j.asoc.2016.12.051","volume":"53","author":"D Konar","year":"2017","unstructured":"Konar, D., Bhattacharyya, S., Sharma, K., Sharma, S., Pradhan, S.R.: An improved hybrid quantum-inspired genetic algorithm (HQIGA) for scheduling of real time task in multiprocessor system. Appl. Soft Comput. 53, 296\u2013307 (2017)","journal-title":"Appl. Soft Comput."},{"issue":"11","key":"3067_CR58","first-page":"1855","volume":"32","author":"Y Xiong","year":"2004","unstructured":"Xiong, Y., Chen, H., Miao, F., Wang, X.: A quantum genetic algorithm to solve combinatorial optimization problem. Acta Electron. Sin. 32(11), 1855\u20131858 (2004)","journal-title":"Acta Electron. Sin."},{"key":"3067_CR59","unstructured":"Chen, Y.: Research on Quantum Genetic Algorithm Based on Optimization Problems. University of Electronic Science and Technology of China, (2019)"},{"issue":"3","key":"3067_CR60","first-page":"476","volume":"32","author":"G Zhang","year":"2004","unstructured":"Zhang, G., Li, N., Jin, W., Hu, L.: A novel quantum genetic algorithm and its application and its application. Acta Electron. Sin. 32(3), 476\u2013479 (2004)","journal-title":"Acta Electron. Sin."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03067-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-021-03067-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03067-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,1]],"date-time":"2023-11-01T16:24:00Z","timestamp":1698855840000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-021-03067-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4]]},"references-count":60,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["3067"],"URL":"https:\/\/doi.org\/10.1007\/s11128-021-03067-3","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4]]},"assertion":[{"value":"29 May 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 March 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 April 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"134"}}