{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T17:06:51Z","timestamp":1763831211443,"version":"3.37.3"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T00:00:00Z","timestamp":1616544000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T00:00:00Z","timestamp":1616544000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities of China","doi-asserted-by":"crossref","award":["2019YBZZ062"],"award-info":[{"award-number":["2019YBZZ062"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Postgraduate Research & Practice Innovation Program of Jiangsu Province","award":["KYCX20_1144"],"award-info":[{"award-number":["KYCX20_1144"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s11227-021-03713-8","type":"journal-article","created":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T11:03:56Z","timestamp":1616583836000},"page":"11288-11309","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Study of the generalized discrete grey polynomial model based on the quantum genetic algorithm"],"prefix":"10.1007","volume":"77","author":[{"given":"Chong","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wen-Ze","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1045-0024","authenticated-orcid":false,"given":"Wanli","family":"Xie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,3,24]]},"reference":[{"key":"3713_CR1","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/j.asoc.2018.07.022","volume":"72","author":"J Wang","year":"2018","unstructured":"Wang J, Du P, Lu H, Yang W, Niu T (2018) An improved grey model optimized by multi-objective ant lion optimization algorithm for annual electricity consumption forecasting. Appl Soft Comput 72:321\u2013337","journal-title":"Appl Soft Comput"},{"issue":"3","key":"3713_CR2","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1093\/biomet\/66.3.429","volume":"66","author":"J Buckley","year":"1979","unstructured":"Buckley J, James I (1979) Linear regression with censored data. Biometrika 66(3):429\u2013436","journal-title":"Biometrika"},{"issue":"1","key":"3713_CR3","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1287\/opre.49.1.14.11195","volume":"49","author":"SA Gabriel","year":"2001","unstructured":"Gabriel SA, Kydes AS, Whitman P (2001) The national energy modeling system: a large-scale energy-economic equilibrium model. Oper Res 49(1):14\u201325","journal-title":"Oper Res"},{"key":"3713_CR4","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/j.energy.2018.09.157","volume":"165","author":"N Elamin","year":"2018","unstructured":"Elamin N, Fukushige M (2018) Modeling and forecasting hourly electricity demand by SARIMAX with interactions. Energy 165:257\u2013268","journal-title":"Energy"},{"key":"3713_CR5","doi-asserted-by":"publisher","first-page":"734","DOI":"10.1016\/j.energy.2016.09.065","volume":"115","author":"G Cao","year":"2016","unstructured":"Cao G, Wu L (2016) Support vector regression with fruit fly optimization algorithm for seasonal electricity consumption forecasting. Energy 115:734\u2013745","journal-title":"Energy"},{"key":"3713_CR6","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1016\/j.rser.2018.10.018","volume":"100","author":"J Fan","year":"2019","unstructured":"Fan J, Wu L, Zhang F, Cai H, Zeng W, Wang X, Zou H (2019) Empirical and machine learning models for predicting daily global solar radiation from sunshine duration: a review and case study in China. Renew SustEnerg Rev 100:186\u2013212","journal-title":"Renew SustEnerg Rev"},{"key":"3713_CR7","doi-asserted-by":"publisher","first-page":"801","DOI":"10.1016\/j.energy.2018.04.078","volume":"153","author":"L Wang","year":"2018","unstructured":"Wang L, Hu H, Ai XY, Liu H (2018) Effective electricity energy consumption forecasting using echo state network improved by differential evolution algorithm. Energy 153:801\u2013815","journal-title":"Energy"},{"issue":"6","key":"3713_CR8","doi-asserted-by":"publisher","first-page":"4318","DOI":"10.1016\/j.eswa.2009.11.068","volume":"37","author":"LC Hsu","year":"2010","unstructured":"Hsu LC (2010) A genetic algorithm based nonlinear grey Bernoulli model for output forecasting in integrated circuit industry. Expert SystAppl 37(6):4318\u20134323","journal-title":"Expert SystAppl"},{"key":"3713_CR9","first-page":"749","volume":"127","author":"S Ding","year":"2019","unstructured":"Ding S (2019) A novel discrete grey multivariable model and its application in forecasting the output value of China\u2019s high-tech industries. ComputIndEng 127:749\u2013760","journal-title":"ComputIndEng"},{"key":"3713_CR10","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.cam.2019.03.048","volume":"360","author":"X Liu","year":"2019","unstructured":"Liu X, Xie N (2019) A nonlinear grey forecasting model with double shape parameters and its application. Appl Math Comput 360:203\u2013212","journal-title":"Appl Math Comput"},{"key":"3713_CR11","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1016\/j.energy.2019.04.096","volume":"178","author":"X Ma","year":"2019","unstructured":"Ma X, Mei X, Wu W, Wu X, Zeng B (2019) A novel fractional time delayed grey model with Grey Wolf Optimizer and its applications in forecasting the natural gas and coal consumption in Chongqing China. Energy 178:487\u2013507","journal-title":"Energy"},{"issue":"5","key":"3713_CR12","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1016\/S0167-6911(82)80025-X","volume":"1","author":"JL Deng","year":"1982","unstructured":"Deng JL (1982) Control problems of grey systems. Syst Control Lett 1(5):288\u2013294","journal-title":"Syst Control Lett"},{"key":"3713_CR13","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1016\/j.jclepro.2018.10.010","volume":"207","author":"ZX Wang","year":"2019","unstructured":"Wang ZX, Li Q (2019) Modelling the nonlinear relationship between CO2 emissions and economic growth using a PSO algorithm-based grey Verhulst model. J Clean Prod 207:214\u2013224","journal-title":"J Clean Prod"},{"key":"3713_CR14","doi-asserted-by":"publisher","first-page":"797","DOI":"10.1016\/j.asoc.2019.04.035","volume":"80","author":"P Xiong","year":"2019","unstructured":"Xiong P, Yan W, Wang G, Pei LL (2019) Grey extended prediction model based on IRLS and its application on smog pollution. Appl Soft Comput 80:797\u2013809","journal-title":"Appl Soft Comput"},{"key":"3713_CR15","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1016\/j.wasman.2019.06.023","volume":"95","author":"GM Duman","year":"2019","unstructured":"Duman GM, Kongar E, Gupta SM (2019) Estimation of electronic waste using optimized multivariate grey models. Waste Manage 95:241\u2013249","journal-title":"Waste Manage"},{"key":"3713_CR16","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1016\/j.apm.2018.06.025","volume":"62","author":"LF Wu","year":"2018","unstructured":"Wu LF, Zhang ZY (2018) Grey multivariable convolution model with new information priority accumulation. Appl Math Model 62:595\u2013604","journal-title":"Appl Math Model"},{"key":"3713_CR17","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.cam.2018.07.044","volume":"347","author":"X Ma","year":"2019","unstructured":"Ma X, Liu Z, Wang Y (2019) Application of a novel nonlinear multivariate grey Bernoulli model to predict the tourist income of China. J ComputAppl Math 347:84\u201394","journal-title":"J ComputAppl Math"},{"key":"3713_CR18","doi-asserted-by":"publisher","first-page":"314","DOI":"10.1016\/j.energy.2018.01.169","volume":"149","author":"S Ding","year":"2018","unstructured":"Ding S, Hipel KW, Dang Y (2018) Forecasting China\u2019s electricity consumption using a new grey prediction model. Energy 149:314\u2013328","journal-title":"Energy"},{"issue":"1","key":"3713_CR19","doi-asserted-by":"publisher","first-page":"141","DOI":"10.3233\/JIFS-151249","volume":"32","author":"B Zeng","year":"2017","unstructured":"Zeng B (2017) Forecasting the relation of supply and demand of natural gas in China during 2015\u20132020 using a novel grey model. J Intell Fuzzy Syst 32(1):141\u2013155","journal-title":"J Intell Fuzzy Syst"},{"key":"3713_CR20","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1016\/j.energy.2018.03.045","volume":"151","author":"B Zeng","year":"2018","unstructured":"Zeng B, Duan H, Bai Y, Meng W (2018) Forecasting the output of shale gas in China using an unbiased grey model and weakening buffer operator. Energy 151:238\u2013249","journal-title":"Energy"},{"issue":"4","key":"3713_CR21","first-page":"122","volume":"29","author":"X Ma","year":"2017","unstructured":"Ma X, Liu ZB (2017) The GMC(1, n) model with optimized parameters and its application. J Grey Syst 29(4):122\u2013138","journal-title":"J Grey Syst"},{"issue":"2","key":"3713_CR22","doi-asserted-by":"publisher","first-page":"1173","DOI":"10.1016\/j.apm.2008.01.011","volume":"33","author":"NM Xie","year":"2009","unstructured":"Xie NM, Liu SF (2009) Discrete grey forecasting model and its optimization. Appl Math Model 33(2):1173\u20131186","journal-title":"Appl Math Model"},{"issue":"2","key":"3713_CR23","first-page":"451","volume":"39","author":"D Luo","year":"2019","unstructured":"Luo D, Wei BL (2019) A unified treatment approach for a class of discrete grey forecasting models and its application. SystEng Theory Pract 39(2):451\u2013462","journal-title":"SystEng Theory Pract"},{"key":"3713_CR24","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1016\/j.eswa.2019.06.053","volume":"136","author":"B Wei","year":"2019","unstructured":"Wei B, Xie N, Yang Y (2019) Data-based structure selection for unified discrete grey prediction model. Expert SystAppl 136:264\u2013275","journal-title":"Expert SystAppl"},{"key":"3713_CR25","doi-asserted-by":"publisher","unstructured":"Ding S, Xu N, Ye J, Zhou W, Zhang X (2020) Estimating Chinese energy-related CO2 emissions by employing a novel discrete grey prediction model. J Clean Prod 120793. https:\/\/doi.org\/10.1016\/j.jclepro.2020.120793","DOI":"10.1016\/j.jclepro.2020.120793"},{"issue":"3","key":"3713_CR26","first-page":"243","volume":"9","author":"Z Laboudi","year":"2012","unstructured":"Laboudi Z, Chikhi S (2012) Comparison of genetic algorithm and quantum genetic algorithm. Int Arab J InfTechnol 9(3):243\u2013249","journal-title":"Int Arab J InfTechnol"},{"issue":"7","key":"3713_CR27","doi-asserted-by":"publisher","first-page":"1775","DOI":"10.1016\/j.cnsns.2012.11.017","volume":"18","author":"L Wu","year":"2013","unstructured":"Wu L, Liu S, Yao L, Yan S, Liu D (2013) Grey system model with the fractional order accumulation. Commun Nonlinear Sci 18(7):1775\u20131785","journal-title":"Commun Nonlinear Sci"},{"key":"3713_CR28","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/j.energy.2018.05.147","volume":"157","author":"L Wu","year":"2018","unstructured":"Wu L, Gao X, Xiao Y, Yang Y, Chen X (2018) Using a novel multi-variable grey model to forecast the electricity consumption of Shandong Province in China. Energy 157:327\u2013335","journal-title":"Energy"},{"key":"3713_CR29","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/j.isatra.2019.07.009","volume":"96","author":"X Ma","year":"2020","unstructured":"Ma X, Wu W, Zeng B, Wang Y, Wu X (2020) The conformable fractional grey system model. ISA T 96:255\u2013271","journal-title":"ISA T"},{"key":"3713_CR30","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.renene.2019.03.006","volume":"40","author":"W Wu","year":"2019","unstructured":"Wu W, Ma X, Zeng B, Wang Y, Cai W (2019) Forecasting short-term renewable energy consumption of China using a novel fractional nonlinear grey Bernoulli model. Renew Energ 40:70\u201387","journal-title":"Renew Energ"},{"key":"3713_CR31","doi-asserted-by":"publisher","first-page":"135447","DOI":"10.1016\/j.scitotenv.2019.135447","volume":"707","author":"W Wu","year":"2020","unstructured":"Wu W, Ma X, Zhang Y, Li W, Wang Y (2020) A novel conformable fractional non-homogeneous grey model for forecasting carbon dioxide emissions of BRICS countries. Sci Total Environ 707:135447. https:\/\/doi.org\/10.1016\/j.scitotenv.2019.135447","journal-title":"Sci Total Environ"},{"issue":"7\u20138","key":"3713_CR32","doi-asserted-by":"publisher","first-page":"5063","DOI":"10.1016\/j.apm.2015.12.014","volume":"40","author":"S Mao","year":"2016","unstructured":"Mao S, Gao M, Xiao X, Zhu M (2016) A novel fractional grey system model and its application. Appl Math Model 40(7\u20138):5063\u20135076","journal-title":"Appl Math Model"},{"issue":"10","key":"3713_CR33","first-page":"2247","volume":"32","author":"WY Qian","year":"2012","unstructured":"Qian WY, Dang YG, Liu SF (2012) Grey GM (1, 1, t\u03b1) model with time power and its application. SystEng Theory Pract 32(10):2247\u20132252","journal-title":"SystEng Theory Pract"},{"key":"3713_CR34","doi-asserted-by":"publisher","first-page":"118573","DOI":"10.1016\/j.jclepro.2019.118573","volume":"244","author":"J Xia","year":"2020","unstructured":"Xia J, Ma X, Wu W, Huang B, Li W (2020) Application of a new information priority accumulated grey model with time power to predict short-term wind turbine capacity. J Clean Prod 244:118573. https:\/\/doi.org\/10.1016\/j.jclepro.2019.118573","journal-title":"J Clean Prod"},{"issue":"2","key":"3713_CR35","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1108\/GS-11-2018-0053","volume":"9","author":"W Wu","year":"2019","unstructured":"Wu W, Ma X, Zhang Y, Wang Y, Wu X (2019) Analysis of novel FAGM (1, 1, t\u03b1) model to forecast health expenditure of China. Grey Syst 9(2):232\u2013250","journal-title":"Grey Syst"},{"key":"3713_CR36","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1016\/j.apm.2020.09.045","volume":"91","author":"L Ye","year":"2021","unstructured":"Ye L, Xie N, Hu A (2021) A novel time-delay multivariate grey model for impact analysis of CO2 emissions from China\u2019s transportation sectors. Appl Math Model 91:493\u2013507","journal-title":"Appl Math Model"},{"key":"3713_CR37","doi-asserted-by":"publisher","first-page":"113644","DOI":"10.1016\/j.enconman.2020.113644","volume":"227","author":"S Ding","year":"2021","unstructured":"Ding S, Li R, Tao Z (2021) A novel adaptive discrete grey model with time-varying parameters for long-term photovoltaic power generation forecasting. Energ Convers Manage 227:113644. https:\/\/doi.org\/10.1016\/j.enconman.2020.113644","journal-title":"Energ Convers Manage"},{"issue":"4","key":"3713_CR38","first-page":"1","volume":"39","author":"Y Hu","year":"2020","unstructured":"Hu Y, Ma X, Li W, Wu W, Tu D (2020) Forecasting manufacturing industrial natural gas consumption of China using a novel time-delayed fractional grey model with multiple fractional order. ComputAppl Math 39(4):1\u201330","journal-title":"ComputAppl Math"},{"key":"3713_CR39","doi-asserted-by":"publisher","first-page":"110429","DOI":"10.1016\/j.chaos.2020.110429","volume":"141","author":"C Liu","year":"2020","unstructured":"Liu C, Wu WZ, Xie W, Zhang J (2020) Application of a novel fractional grey prediction model with time power term to predict the electricity consumption of India and China. Chaos Soliton Fract 141:110429. https:\/\/doi.org\/10.1016\/j.chaos.2020.110429","journal-title":"Chaos Soliton Fract"},{"key":"3713_CR40","first-page":"1903","volume":"31","author":"W Meng","year":"2016","unstructured":"Meng W, Zeng B (2016) Discrete grey model with inverse fractional operators and optimized order. Control Decis 31:1903\u20131907","journal-title":"Control Decis"},{"issue":"7","key":"3713_CR41","doi-asserted-by":"publisher","first-page":"5059","DOI":"10.1016\/j.apm.2012.10.037","volume":"37","author":"NM Xie","year":"2013","unstructured":"Xie NM, Liu SF, Yang YJ, Yuan CQ (2013) On novel grey forecasting model based on non-homogeneous index sequence. Appl Math Model 37(7):5059\u20135068","journal-title":"Appl Math Model"},{"issue":"7","key":"3713_CR42","first-page":"1822","volume":"34","author":"LF Wu","year":"2014","unstructured":"Wu LF, Liu SF, Yao LG (2014) Discrete grey model based on fractional order accumulate. SystEng Theory Pract 34(7):1822\u20131827","journal-title":"SystEng Theory Pract"},{"issue":"5","key":"3713_CR43","doi-asserted-by":"publisher","first-page":"1215","DOI":"10.1007\/s00521-014-1605-1","volume":"25","author":"LF Wu","year":"2014","unstructured":"Wu LF, Liu SF, Cui W, Liu DL, Yao TX (2014) Non-homogenous discrete grey model with fractional-order accumulation. Neural ComputAppl 25(5):1215\u20131221","journal-title":"Neural ComputAppl"},{"issue":"18","key":"3713_CR44","doi-asserted-by":"publisher","first-page":"7843","DOI":"10.1002\/mma.4565","volume":"40","author":"B Zeng","year":"2017","unstructured":"Zeng B, Liu S (2017) A self-adaptive intelligence gray prediction model with the optimal fractional order accumulating operator and its application. Math Method ApplSci 40(18):7843\u20137857","journal-title":"Math Method ApplSci"},{"key":"3713_CR45","unstructured":"Lewis CD (1982) Industrial and business forecasting methods: a practical guide to exponential smoothing and curve fitting. Butterworth-Heinemann."},{"key":"3713_CR46","first-page":"46","volume":"69","author":"S Mirjalili","year":"2014","unstructured":"Mirjalili S, Mirjalili S, Lewis A (2014) Grey wolf Optimizer. AdvEngSoftw 69:46\u201361","journal-title":"AdvEngSoftw"},{"key":"3713_CR47","first-page":"51","volume":"95","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili S, Lewis A (2016) The whale optimization algorithm. AdvEngSoftw 95:51\u201367","journal-title":"AdvEngSoftw"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-021-03713-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-021-03713-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-021-03713-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T10:12:09Z","timestamp":1631095929000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-021-03713-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,24]]},"references-count":47,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["3713"],"URL":"https:\/\/doi.org\/10.1007\/s11227-021-03713-8","relation":{},"ISSN":["0920-8542","1573-0484"],"issn-type":[{"type":"print","value":"0920-8542"},{"type":"electronic","value":"1573-0484"}],"subject":[],"published":{"date-parts":[[2021,3,24]]},"assertion":[{"value":"25 February 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}