{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T23:51:50Z","timestamp":1776469910821,"version":"3.51.2"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T00:00:00Z","timestamp":1673222400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T00:00:00Z","timestamp":1673222400000},"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":["11971083"],"award-info":[{"award-number":["11971083"]}],"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":["62073344"],"award-info":[{"award-number":["62073344"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2023,4]]},"DOI":"10.1007\/s00521-022-08089-1","type":"journal-article","created":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T08:03:53Z","timestamp":1673251433000},"page":"8109-8123","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Privacy masking distributed saddle-point algorithm for dynamic economic dispatch"],"prefix":"10.1007","volume":"35","author":[{"given":"Kaihui","family":"Xu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jueyou","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5459-4033","authenticated-orcid":false,"given":"Guo","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,1,9]]},"reference":[{"issue":"6","key":"8089_CR1","doi-asserted-by":"publisher","first-page":"2941","DOI":"10.1109\/TSG.2017.2720471","volume":"8","author":"DK Molzahn","year":"2017","unstructured":"Molzahn DK, Dorfler F, Sandberg H, Low SH, Chakrabarti S, Baldick R, Lavaei J (2017) A survey of distributed optimization and control algorithms for electric power systems. IEEE Transact Smart Grid 8(6):2941\u20132962","journal-title":"IEEE Transactions on Smart Grid"},{"issue":"4","key":"8089_CR2","doi-asserted-by":"publisher","first-page":"3630","DOI":"10.1109\/TSG.2018.2833108","volume":"10","author":"R Wang","year":"2018","unstructured":"Wang R, Li Q, Zhang B, Wang L (2018) s based algorithm for economic dispatch in a microgrid. IEEE Transact Smart Grid 10(4):3630\u20133640","journal-title":"IEEE Transactions on Smart Grid"},{"issue":"2","key":"8089_CR3","doi-asserted-by":"publisher","first-page":"12566","DOI":"10.1016\/j.ifacol.2020.12.1816","volume":"53","author":"Z Wang","year":"2020","unstructured":"Wang Z, Xu J, Zhu S, Chen C. (2020) A dual splitting method for distributed economic dispatch in multi-energy systems. IFACPapersOnLine 53(2):12566\u201312571","journal-title":"IFAC-PapersOnLine"},{"issue":"5","key":"8089_CR4","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1080\/0952813X.2019.1673488","volume":"32","author":"Zhi Zheng","year":"2020","unstructured":"Zheng Z, Li J, Han Y (2020) An improved invasive weed optimization algorithm for solving dynamic economic dispatch problems with valve-point effects. J Exp Theor Artif Intell 32(5):805\u2013829","journal-title":"Journal of Experimental &amp; Theoretical Artificial Intelligence"},{"key":"8089_CR5","unstructured":"Tao D, Bie Z (2017) Parallel augmented lagrangian relaxation for dynamic economic dispatch using diagonal quadratic approximation method. IEEE Transact Power Syst 32(2):1115\u20131126"},{"issue":"6","key":"8089_CR6","doi-asserted-by":"publisher","first-page":"638","DOI":"10.1016\/j.conengprac.2011.03.001","volume":"19","author":"Xiaohua Xia","year":"2011","unstructured":"Xia X, Zhang J, Elaiw A (2011) An application of model predictive control to the dynamic economic dispatch of power generation. Control Eng Pract 19(6):638\u2013648","journal-title":"Control Engineering Practice"},{"issue":"6","key":"8089_CR7","doi-asserted-by":"publisher","first-page":"2586","DOI":"10.1109\/TSG.2015.2508779","volume":"7","author":"Hamdi Abdi","year":"2016","unstructured":"Abdi H, Dehnavi E, Mohammadi F (2016) Dynamic economic dispatch problem integrated with demand response (deddr) considering non-linear responsive load models. IEEE Transact Smart Grid 7(6):2586\u20132595","journal-title":"IEEE Transactions on Smart Grid"},{"key":"8089_CR8","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/j.energy.2018.01.029","volume":"147","author":"Dexuan Zou","year":"2018","unstructured":"Zou D, Li S, Kong X, Ouyang H, Li Z (2018) Erential evolution and a repair technique of constraint handling. Energy 147(15):59\u201380","journal-title":"Energy"},{"key":"8089_CR9","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1016\/j.ijepes.2017.11.004","volume":"97","author":"Shanshan Pan","year":"2018","unstructured":"Pan S, Jian J, Yang L (2018) A hybrid milp and ipm approach for dynamic economic dispatch with valve-point effects. Int J Elect Power Energy Syst 97:290\u2013298","journal-title":"International Journal of Electrical Power &amp; Energy Systems"},{"key":"8089_CR10","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1016\/j.energy.2018.05.180","volume":"157","author":"Guojiang Xiong","year":"2018","unstructured":"Xiong G, Shi D (2018) Hybrid biogeography-based optimization with brain storm optimization for non-convex dynamic economic dispatch with valve-point effects. Energy 157:424\u2013435","journal-title":"Energy"},{"key":"8089_CR11","doi-asserted-by":"crossref","unstructured":"Li C, Yu X, Huang T, He X (2017) Distributed optimal consensus over resource allocation network and its application to dynamical economic dispatch. IEEE Transact Neural Netw Learn Syst 29(6):2407\u20132418","DOI":"10.1109\/TNNLS.2017.2691760"},{"issue":"16","key":"8089_CR12","doi-asserted-by":"publisher","first-page":"3955","DOI":"10.1049\/iet-gtd.2016.1945","volume":"11","author":"Tong Xu","year":"2017","unstructured":"Xu T, Wu W, Sun H, Wang L (2017) Fully distributed multi-area dynamic economic dispatch method with second-order convergence for active distribution networks. IET Gener Transm Distrib 11(16):3955\u20133965","journal-title":"IET Generation, Transmission &amp; Distribution"},{"issue":"4","key":"8089_CR13","doi-asserted-by":"publisher","first-page":"4253","DOI":"10.1109\/TPWRS.2017.2771950","volume":"33","author":"Tong Xu","year":"2018","unstructured":"Tong X, Wu W, Zheng W, Sun H, Wang L (2018) Fully distributed quasi-newton multi-area dynamic economic dispatch method for active distribution networks. IEEE Transact Power Syst 33(4):4253\u20134263","journal-title":"IEEE Transactions on Power Systems"},{"key":"8089_CR14","doi-asserted-by":"crossref","unstructured":"Dai P, Yu W, Wen G, Baldi S (2019) Distributed reinforcement learning algorithm for dynamic economic dispatch with unknown generation cost functions. IEEE Transact Indus Inform 16(4):2258\u20132267","DOI":"10.1109\/TII.2019.2933443"},{"issue":"10","key":"8089_CR15","doi-asserted-by":"publisher","first-page":"2594","DOI":"10.1109\/TPDS.2021.3072373","volume":"32","author":"Huaqing Li","year":"2021","unstructured":"Li H, Hu J, Ran L, Wang Z, L\u00fc Q, Du Z, Huang T (2021) Decentralized dual proximal gradient algorithms for non-smooth constrained composite optimization problems. IEEE Transact Parallel Distrib Syst 32(10):2594\u20132605","journal-title":"IEEE Transactions on Parallel and Distributed Systems"},{"key":"8089_CR16","doi-asserted-by":"publisher","first-page":"649","DOI":"10.1613\/jair.3983","volume":"47","author":"T. Leaute","year":"2013","unstructured":"L\u00e9aut\u00e9 T, Faltings B (2013) Protecting privacy through distributed computation in multi-agent decision making. J Artif Intell Res 47:649\u2013695","journal-title":"Journal of Artificial Intelligence Research"},{"key":"8089_CR17","doi-asserted-by":"crossref","unstructured":"Mandal A (2016) Privacy preserving consensus-based economic dispatch in smart grid systems. Springer, Cham","DOI":"10.1007\/978-3-319-48021-3_7"},{"issue":"23","key":"8089_CR18","doi-asserted-by":"publisher","first-page":"6162","DOI":"10.1109\/TSP.2018.2872817","volume":"66","author":"Chengcheng Zhao","year":"2018","unstructured":"Zhao C, Chen J, He J, Cheng P (2018) Privacy-preserving consensus-based energy management in smart grids. IEEE Transact Signal Process 66(23):6162\u20136176","journal-title":"IEEE Transactions on Signal Processing"},{"key":"8089_CR19","doi-asserted-by":"crossref","unstructured":"Garcia F, Jacobs B (2010) Privacy-friendly energy-metering via homomorphic encryption. In international workshop on security and trust management, Springer, pp. 226\u2013238","DOI":"10.1007\/978-3-642-22444-7_15"},{"key":"8089_CR20","doi-asserted-by":"crossref","unstructured":"Rottondi C, Verticale G, Capone A (2012) A security framework for smart metering with multiple data consumers. In 2012 Proceedings IEEE INFOCOM Workshops, IEEE, pp. 103\u2013108","DOI":"10.1109\/INFCOMW.2012.6193469"},{"key":"8089_CR21","doi-asserted-by":"crossref","unstructured":"Jo H, Kim I, Lee D (2015) Efficient and privacy-preserving metering protocols for smart grid systems. IEEE Transact Smart Grid 7(3):1732\u20131742","DOI":"10.1109\/TSG.2015.2449278"},{"key":"8089_CR22","doi-asserted-by":"crossref","unstructured":"Liu Y, Guo W, Fan C, Chang L, Cheng C (2018) A practical privacy-preserving data aggregation (3pda) scheme for smart grid. IEEE Transact Indus Inform 15(3):1767\u20131774","DOI":"10.1109\/TII.2018.2809672"},{"key":"8089_CR23","doi-asserted-by":"crossref","unstructured":"Dwork C (2008) Differential privacy: a survey of results. In international conference on theory and applications of models of computation, Springer, pp. 1\u201319","DOI":"10.1007\/978-3-540-79228-4_1"},{"key":"8089_CR24","doi-asserted-by":"crossref","unstructured":"Sarwate AD, Chaudhuri K (2013) Signal processing and machine learning with differential privacy: algorithms and challenges for continuous data. IEEE Signal Process Mag 30(5):86\u201394","DOI":"10.1109\/MSP.2013.2259911"},{"key":"8089_CR25","doi-asserted-by":"crossref","unstructured":"Nozari E, Tallapragada P, Cort\u00e9s J (2016) Differentially private distributed convex optimization via functional perturbation. IEEE Transact Control Netw Syst 5(1):395\u2013408","DOI":"10.1109\/TCNS.2016.2614100"},{"key":"8089_CR26","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1016\/j.engappai.2020.104151","volume":"99","author":"Jinhui Hu","year":"2021","unstructured":"Hu J, Chen X, Zheng L, Zhang L, Li H (2021) The barzilai-borwein method for distributed optimization over unbalanced directed networks. Eng Appl Artif Intell 99:104\u2013151","journal-title":"Engineering Applications of Artificial Intelligence"},{"key":"8089_CR27","doi-asserted-by":"crossref","unstructured":"Nozari E, Tallapragada P, Cortes J (2016) Differentially private distributed convex optimization via objective perturbation. In 2016 American control conference (ACC)","DOI":"10.1109\/ACC.2016.7525222"},{"issue":"1","key":"8089_CR28","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1109\/TSIPN.2018.2797806","volume":"4","author":"Junlong Zhu","year":"2018","unstructured":"Zhu J, Xu C, Guan J, Wu DO (2018) Differentially private distributed online algorithms over time-varying directed networks. IEEE Transact Signal Inform Process Netw 4(1):4\u201317","journal-title":"IEEE Transactions on Signal and Information Processing over Networks"},{"key":"8089_CR29","doi-asserted-by":"crossref","unstructured":"Chen F, Chen X, Xiang L, Ren W (2021) Distributed economic dispatchvia a predictive scheme: heterogeneous delays and privacy preservation.Automatica, 123:109\u2013356","DOI":"10.1016\/j.automatica.2020.109356"},{"key":"8089_CR30","doi-asserted-by":"crossref","unstructured":"Ding T, Zhu S, Chen C, Xu J, Guan X (2021) Differentially privatedistributed resource allocation via deviation tracking. IEEE Transacti Signal Inform Process Netw, 7:222\u2013235","DOI":"10.1109\/TSIPN.2021.3062985"},{"key":"8089_CR31","doi-asserted-by":"crossref","unstructured":"Ding T, Zhu S, He J, Chen C, Guan X (2021) Differentially privatedistributed optimization via state and direction perturbation in multiagentsystems. IEEE Transact Automa Control, 67(2):722\u2013737","DOI":"10.1109\/TAC.2021.3059427"},{"key":"8089_CR32","doi-asserted-by":"crossref","unstructured":"Saw J, Yang M, Mo T (1984) Chebyshev inequality with estimated mean and variance. Am Stat 38(2):130\u2013132","DOI":"10.1080\/00031305.1984.10483182"},{"key":"8089_CR33","doi-asserted-by":"crossref","unstructured":"Branicky MS (1998) Multiple lyapunov functions and other analysis tools forswitched and hybrid systems. IEEE Transact Automa Control,43(4):475\u2013482","DOI":"10.1109\/9.664150"},{"issue":"12","key":"8089_CR34","doi-asserted-by":"publisher","first-page":"1974","DOI":"10.1016\/j.automatica.2010.08.011","volume":"46","author":"Diego Feijer","year":"2010","unstructured":"Feijer D, Paganini F (2010) Stability of primal-dual gradient dynamics and applications to network optimization. Automatica 46(12):1974\u20131981","journal-title":"Automatica"},{"key":"8089_CR35","doi-asserted-by":"crossref","unstructured":"Li C, Yu X, Yu W (2014) Optimal economic dispatch by fast distributed gradient. In international conference on control automation robotics & vision","DOI":"10.1109\/ICARCV.2014.7064367"},{"key":"8089_CR36","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/j.automatica.2017.03.016","volume":"81","author":"Erfan Nozari","year":"2017","unstructured":"Nozari E, Tallapragada P, Cortes J (2017) Differentially private average consensus: Obstructions, trade-offs, and optimal algorithm design. Automatica 81:221\u2013231","journal-title":"Automatica"},{"issue":"4","key":"8089_CR37","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1007\/BF00940418","volume":"12","author":"R. T. Rockafellar","year":"1973","unstructured":"Rockafellar R (1973) Saddle points of hamiltonian systems in convex problems of lagrange. J Optim Theory Appl 12(4):367\u2013390","journal-title":"Journal of Optimization Theory and Applications"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-022-08089-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-022-08089-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-022-08089-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,21]],"date-time":"2023-03-21T12:32:02Z","timestamp":1679401922000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-022-08089-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,9]]},"references-count":37,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["8089"],"URL":"https:\/\/doi.org\/10.1007\/s00521-022-08089-1","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,9]]},"assertion":[{"value":"5 February 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 November 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 January 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declared that they have no conflicts of interest in this article","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interest"}}]}}