{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T17:59:04Z","timestamp":1772301544179,"version":"3.50.1"},"reference-count":81,"publisher":"Springer Science and Business Media LLC","issue":"22","license":[{"start":{"date-parts":[[2023,8,3]],"date-time":"2023-08-03T00:00:00Z","timestamp":1691020800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,8,3]],"date-time":"2023-08-03T00:00:00Z","timestamp":1691020800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2023,11]]},"DOI":"10.1007\/s00500-023-09019-6","type":"journal-article","created":{"date-parts":[[2023,8,3]],"date-time":"2023-08-03T02:02:06Z","timestamp":1691028126000},"page":"16809-16841","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A hybrid capuchin search algorithm with gradient search algorithm for economic dispatch problem"],"prefix":"10.1007","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4180-3734","authenticated-orcid":false,"given":"Malik","family":"Braik","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammed A.","family":"Awadallah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammed Azmi","family":"Al-Betar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdelaziz I.","family":"Hammouri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,8,3]]},"reference":[{"issue":"19","key":"9019_CR1","doi-asserted-by":"crossref","first-page":"14061","DOI":"10.1007\/s00521-023-08400-8","volume":"35","author":"M Abd Elaziz","year":"2023","unstructured":"Abd Elaziz M, Ouadfel S, Ibrahim RA (2023) Boosting capuchin search with stochastic learning strategy for feature selection. Neural Comput Appl 35(19):14061\u201314080","journal-title":"Neural Comput Appl"},{"key":"9019_CR2","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.ins.2020.06.037","volume":"540","author":"I Ahmadianfar","year":"2020","unstructured":"Ahmadianfar I, Bozorg-Haddad O, Chu X (2020) Gradient-based optimizer: a new metaheuristic optimization algorithm. Inf Sci 540:131\u2013159","journal-title":"Inf Sci"},{"key":"9019_CR3","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.epsr.2018.07.026","volume":"164","author":"KO Alawode","year":"2018","unstructured":"Alawode KO, Jubril AM, Kehinde LO, Ogunbona PO (2018) Semidefinite programming solution of economic dispatch problem with non-smooth, non-convex cost functions. Electric Power Syst Res 164:178\u2013187","journal-title":"Electric Power Syst Res"},{"key":"9019_CR4","doi-asserted-by":"crossref","unstructured":"Al-Betar MA, Awadallah MA, Doush IA, Alsukhni E, ALkhraisat H (2018) A non-convex economic dispatch problem with valve loading effect using a new modified $$\\beta $$-hill climbing local search algorithm. Arabian Journal for Sci Eng, 1\u201318","DOI":"10.1007\/s13369-018-3098-1"},{"issue":"4","key":"9019_CR5","doi-asserted-by":"crossref","first-page":"1985","DOI":"10.1007\/s42835-021-00758-w","volume":"16","author":"MA Al-Betar","year":"2021","unstructured":"Al-Betar MA (2021) Island-based harmony search algorithm for non-convex economic load dispatch problems. J Electr Eng Technol 16(4):1985\u20132015","journal-title":"J Electr Eng Technol"},{"key":"9019_CR6","doi-asserted-by":"crossref","first-page":"1985","DOI":"10.1007\/s42835-021-00758-w","volume":"16","author":"MA Al-Betar","year":"2021","unstructured":"Al-Betar MA (2021) Island-based harmony search algorithm for non-convex economic load dispatch problems. J Electr Eng Technol 16:1985\u20132015","journal-title":"J Electr Eng Technol"},{"key":"9019_CR7","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/j.asoc.2016.05.034","volume":"47","author":"MA Al-Betar","year":"2016","unstructured":"Al-Betar MA, Awadallah MA, Khader AT, Bolaji AL (2016) Tournament-based harmony search algorithm for non-convex economic load dispatch problem. Appl Soft Comput 47:449\u2013459","journal-title":"Appl Soft Comput"},{"issue":"10","key":"9019_CR8","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1007\/s00521-016-2611-2","volume":"29","author":"MA Al-Betar","year":"2018","unstructured":"Al-Betar MA, Awadallah MA, Khader AT, Bolaji AL, Almomani A (2018) Economic load dispatch problems with valve-point loading using natural updated harmony search. Neural Comput Appl 29(10):767\u2013781","journal-title":"Neural Comput Appl"},{"issue":"16","key":"9019_CR9","doi-asserted-by":"crossref","first-page":"12127","DOI":"10.1007\/s00521-019-04284-9","volume":"32","author":"MA Al-Betar","year":"2019","unstructured":"Al-Betar MA, Awadallah MA, Krishan MM (2019) A non-convex economic load dispatch problem with valve loading effect using a hybrid grey wolf optimizer. Neural Comput Appl 32(16):12127\u201312154","journal-title":"Neural Comput Appl"},{"issue":"16","key":"9019_CR10","doi-asserted-by":"crossref","first-page":"12127","DOI":"10.1007\/s00521-019-04284-9","volume":"32","author":"MA Al-Betar","year":"2020","unstructured":"Al-Betar MA, Awadallah MA, Krishan MM (2020) A non-convex economic load dispatch problem with valve loading effect using a hybrid grey wolf optimizer. Neural Comput Appl 32(16):12127\u201312154","journal-title":"Neural Comput Appl"},{"key":"9019_CR11","doi-asserted-by":"crossref","first-page":"8721","DOI":"10.1007\/s13369-021-05646-z","volume":"46","author":"MS Alkoffash","year":"2021","unstructured":"Alkoffash MS, Awadallah MA, Alweshah M, Zitar RA, Assaleh K, Al-Betar MA (2021) A non-convex economic load dispatch using hybrid salp swarm algorithm. Arabian J Sci Eng 46:8721\u20138740","journal-title":"Arabian J Sci Eng"},{"issue":"9","key":"9019_CR12","doi-asserted-by":"crossref","first-page":"102095","DOI":"10.1016\/j.asej.2022.102095","volume":"14","author":"MA Al-qaness","year":"2023","unstructured":"Al-qaness MA, Ewees AA, Fan H, Abualigah L, Elsheikh AH, Abd Elaziz M (2023) Wind power prediction using random vector functional link network with capuchin search algorithm. Ain Shams Eng J 14(9):102095","journal-title":"Ain Shams Eng J"},{"issue":"5","key":"9019_CR13","doi-asserted-by":"crossref","first-page":"1773","DOI":"10.1016\/j.apenergy.2009.10.007","volume":"87","author":"JS Alsumait","year":"2010","unstructured":"Alsumait JS, Sykulski JK, Al-Othman AK (2010) A hybrid GA\u2013PS\u2013SQP method to solve power system valve-point economic dispatch problems. Appl Energy 87(5):1773\u20131781","journal-title":"Appl Energy"},{"issue":"8","key":"9019_CR14","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1016\/j.ijepes.2010.01.023","volume":"32","author":"N Amjady","year":"2010","unstructured":"Amjady N, Sharifzadeh H (2010) Solution of non-convex economic dispatch problem considering valve loading effect by a new modified differential evolution algorithm. Int J Electr Power Energy Syst 32(8):893\u2013903","journal-title":"Int J Electr Power Energy Syst"},{"issue":"15","key":"9019_CR15","doi-asserted-by":"crossref","first-page":"6455","DOI":"10.1007\/s00500-018-3299-2","volume":"23","author":"MA Awadallah","year":"2019","unstructured":"Awadallah MA, Al-Betar MA, Bolaji AL, Alsukhni EM, Al-Zoubi H (2019) Natural selection methods for artificial bee colony with new versions of onlooker bee. Soft Comput 23(15):6455\u20136494","journal-title":"Soft Comput"},{"issue":"1","key":"9019_CR16","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.energy.2011.11.023","volume":"37","author":"R Azizipanah-Abarghooee","year":"2012","unstructured":"Azizipanah-Abarghooee R, Niknam T, Roosta A, Malekpour AR, Zare M (2012) Probabilistic multiobjective wind-thermal economic emission dispatch based on point estimated method. Energy 37(1):322\u2013335","journal-title":"Energy"},{"key":"9019_CR17","first-page":"161","volume":"24","author":"K Balamurugan","year":"2020","unstructured":"Balamurugan K, Umamaheswari K, Prabhu\u00a0Raj M, Nivetha S, Giriprasad K, Ravirahul M, Guhaneeswaran V, Arun RM (2020) Solving economic load dispatch using JAYA optimization algorithm. Res J Chem Environ 24:161\u2013165","journal-title":"Res J Chem Environ"},{"key":"9019_CR18","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/j.ijepes.2016.02.005","volume":"80","author":"M Basu","year":"2016","unstructured":"Basu M (2016) Kinetic gas molecule optimization for nonconvex economic dispatch problem. Int J Electr Power Energy Syst 80:325\u2013332","journal-title":"Int J Electr Power Energy Syst"},{"issue":"5","key":"9019_CR19","doi-asserted-by":"crossref","first-page":"3605","DOI":"10.1016\/j.eswa.2009.10.031","volume":"37","author":"A Bhattacharya","year":"2010","unstructured":"Bhattacharya A, Chattopadhyay PK (2010) Solving complex economic load dispatch problems using biogeography-based optimization. Expert Syst Appl 37(5):3605\u20133615","journal-title":"Expert Syst Appl"},{"issue":"4","key":"9019_CR20","doi-asserted-by":"crossref","first-page":"1955","DOI":"10.1109\/TPWRS.2010.2043270","volume":"25","author":"A Bhattacharya","year":"2010","unstructured":"Bhattacharya A, Chattopadhyay PK (2010) Hybrid differential evolution with biogeography-based optimization for solution of economic load dispatch. IEEE Trans Power Syst 25(4):1955\u20131964","journal-title":"IEEE Trans Power Syst"},{"key":"9019_CR21","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex optimization","author":"S Boyd","year":"2004","unstructured":"Boyd S, Boyd SP, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge"},{"key":"9019_CR22","doi-asserted-by":"crossref","unstructured":"Braik M (2022) Hybrid enhanced whale optimization algorithm for contrast and detail enhancement of color images. Cluster Comput, 1\u201337","DOI":"10.1007\/s10586-022-03920-9"},{"key":"9019_CR23","doi-asserted-by":"crossref","unstructured":"Braik MS, Awadallah MA, Al-Betar MA, Hammouri AI, Zitar RA (2023) A non-convex economic load dispatch problem using chameleon swarm algorithm with roulette wheel and levy flight methods. Appl Intell 1\u201340","DOI":"10.1007\/s10489-022-04363-w"},{"issue":"4","key":"9019_CR24","doi-asserted-by":"crossref","first-page":"2873","DOI":"10.1007\/s11063-021-10530-w","volume":"53","author":"M Braik","year":"2021","unstructured":"Braik M (2021) A hybrid multi-gene genetic programming with capuchin search algorithm for modeling a nonlinear challenge problem: Modeling industrial winding process, case study. Neural Process Lett 53(4):2873\u20132916","journal-title":"Neural Process Lett"},{"issue":"8","key":"9019_CR25","doi-asserted-by":"crossref","first-page":"6153","DOI":"10.1007\/s00521-022-08015-5","volume":"35","author":"M Braik","year":"2023","unstructured":"Braik M (2023) Enhanced Ali Baba and the forty thieves algorithm for feature selection. Neural Comput Appl 35(8):6153\u20136184","journal-title":"Neural Comput Appl"},{"issue":"7","key":"9019_CR26","doi-asserted-by":"crossref","first-page":"2515","DOI":"10.1007\/s00521-020-05145-6","volume":"33","author":"M Braik","year":"2021","unstructured":"Braik M, Sheta A, Al-Hiary H (2021) A novel meta-heuristic search algorithm for solving optimization problems: capuchin search algorithm. Neural Comput Appl 33(7):2515\u20132547","journal-title":"Neural Comput Appl"},{"issue":"1","key":"9019_CR27","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s10462-022-10164-x","volume":"56","author":"M Braik","year":"2023","unstructured":"Braik M, Al-Zoubi H, Ryalat M, Sheta A, Alzubi O (2023) Memory based hybrid crow search algorithm for solving numerical and constrained global optimization problems. Artif Intell Rev 56(1):27\u201399","journal-title":"Artif Intell Rev"},{"issue":"3","key":"9019_CR28","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/j.asej.2016.02.003","volume":"9","author":"SMA Bulbul","year":"2018","unstructured":"Bulbul SMA, Pradhan M, Roy PK, Pal T (2018) Opposition-based krill herd algorithm applied to economic load dispatch problem. Ain Shams Eng J 9(3):423\u2013440","journal-title":"Ain Shams Eng J"},{"issue":"1","key":"9019_CR29","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1016\/j.energy.2011.11.052","volume":"38","author":"J Cai","year":"2012","unstructured":"Cai J, Li Q, Li L, Peng H, Yang Y (2012) A hybrid FCASO-SQP method for solving the economic dispatch problems with valve-point effects. Energy 38(1):346\u2013353","journal-title":"Energy"},{"issue":"1","key":"9019_CR30","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.enconman.2011.08.023","volume":"53","author":"J Cai","year":"2012","unstructured":"Cai J, Li Q, Li L, Peng H, Yang Y (2012) A hybrid CPSO\u2013SQP method for economic dispatch considering the valve-point effects. Energy Convers and Manag 53(1):175\u2013181","journal-title":"Energy Convers and Manag"},{"issue":"10","key":"9019_CR31","doi-asserted-by":"crossref","first-page":"1042","DOI":"10.1049\/iet-gtd.2011.0038","volume":"5","author":"S Chakraborty","year":"2011","unstructured":"Chakraborty S, Senjyu T, Yona A, Saber AY, Funabashi T (2011) Solving economic load dispatch problem with valve-point effects using a hybrid quantum mechanics inspired particle swarm optimisation. Gener Transm Distrib IET 5(10):1042\u20131052","journal-title":"Gener Transm Distrib IET"},{"issue":"4","key":"9019_CR32","doi-asserted-by":"crossref","first-page":"1779","DOI":"10.1007\/s00500-022-06757-x","volume":"26","author":"G D\u2019Angelo","year":"2022","unstructured":"D\u2019Angelo G, Palmieri F, Robustelli A (2022) Artificial neural networks for resources optimization in energetic environment. Soft Comput 26(4):1779\u20131792","journal-title":"Soft Comput"},{"issue":"8","key":"9019_CR33","doi-asserted-by":"crossref","first-page":"3029","DOI":"10.1007\/s00521-019-04268-9","volume":"32","author":"D Das","year":"2020","unstructured":"Das D, Bhattacharya A, Ray RN (2020) Dragonfly algorithm for solving probabilistic economic load dispatch problems. Neural Comput Appl 32(8):3029\u20133045","journal-title":"Neural Comput Appl"},{"issue":"12","key":"9019_CR34","doi-asserted-by":"crossref","first-page":"2580","DOI":"10.1016\/j.enconman.2010.05.022","volume":"51","author":"L dos Santos Coelho","year":"2010","unstructured":"dos Santos Coelho L, Cocco MV (2010) An efficient cultural self-organizing migrating strategy for economic dispatch optimization with valve-point effect. Energy Convers Manag 51(12):2580\u20132587","journal-title":"Energy Convers Manag"},{"issue":"10","key":"9019_CR35","doi-asserted-by":"crossref","first-page":"2522","DOI":"10.1016\/j.enconman.2009.05.034","volume":"50","author":"L dos Santos Coelho","year":"2009","unstructured":"dos Santos Coelho L, Mariani VC (2009) An improved harmony search algorithm for power economic load dispatch. Energy Convers Manag 50(10):2522\u20132526","journal-title":"Energy Convers Manag"},{"issue":"12","key":"9019_CR36","doi-asserted-by":"crossref","first-page":"2580","DOI":"10.1016\/j.enconman.2010.05.022","volume":"51","author":"L dos Santos Coelho","year":"2010","unstructured":"dos Santos Coelho L, Mariani VC (2010) An efficient cultural self-organizing migrating strategy for economic dispatch optimization with valve-point effect. Energy Convers Manag 51(12):2580\u20132587","journal-title":"Energy Convers Manag"},{"issue":"7","key":"9019_CR37","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1080\/15325000903489710","volume":"38","author":"S Hemamalini","year":"2010","unstructured":"Hemamalini S, Simon SP (2010) Artificial bee colony algorithm for economic load dispatch problem with non-smooth cost functions. Electric Power Compon Syst 38(7):786\u2013803","journal-title":"Electric Power Compon Syst"},{"key":"9019_CR38","doi-asserted-by":"crossref","first-page":"2779","DOI":"10.1007\/s10489-020-01654-y","volume":"50","author":"Z Huang","year":"2020","unstructured":"Huang Z, Zhao J, Qi L, Gao Z, Duan H (2020) Comprehensive learning cuckoo search with chaos-lambda method for solving economic dispatch problems. Appl Intell 50:2779\u20132799","journal-title":"Appl Intell"},{"key":"9019_CR39","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1016\/j.energy.2016.05.105","volume":"111","author":"T Jayabarathi","year":"2016","unstructured":"Jayabarathi T, Raghunathan T, Adarsh BR, Suganthan PN (2016) Economic dispatch using hybrid grey wolf optimizer. Energy 111:630\u2013641","journal-title":"Energy"},{"issue":"3","key":"9019_CR40","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1080\/01605682.2019.1700184","volume":"72","author":"K Kapelinski","year":"2021","unstructured":"Kapelinski K, Neto JPJ, dos Santos EM (2021) Firefly algorithm with non-homogeneous population: a case study in economic load dispatch problem. J Oper Res Soc 72(3):519\u2013534","journal-title":"J Oper Res Soc"},{"issue":"1","key":"9019_CR41","doi-asserted-by":"crossref","first-page":"4332","DOI":"10.1080\/01430750.2021.1888798","volume":"43","author":"A Kaur","year":"2021","unstructured":"Kaur A, Singh L, Dhillon JS (2021) Modified krill herd algorithm for constrained economic load dispatch problem. Int J Ambient Energy 43(1):4332\u20134342","journal-title":"Int J Ambient Energy"},{"issue":"1","key":"9019_CR42","doi-asserted-by":"crossref","first-page":"4332","DOI":"10.1080\/01430750.2021.1888798","volume":"43","author":"A Kaur","year":"2022","unstructured":"Kaur A, Singh L, Dhillon JS (2022) Modified Krill Herd Algorithm for constrained economic load dispatch problem. Int J Ambient Energy 43(1):4332\u20134342","journal-title":"Int J Ambient Energy"},{"issue":"2","key":"9019_CR43","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.enconman.2009.09.034","volume":"51","author":"S Khamsawang","year":"2010","unstructured":"Khamsawang S, Jiriwibhakorn S (2010) DSPSO\u2013TSA for economic dispatch problem with nonsmooth and noncontinuous cost functions. Energy Convers Manag 51(2):365\u2013375","journal-title":"Energy Convers Manag"},{"key":"9019_CR44","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.asoc.2018.06.035","volume":"71","author":"M Kumar","year":"2018","unstructured":"Kumar M, Dhillon JS (2018) Hybrid artificial algae algorithm for economic load dispatch. Appl Soft Comput 71:89\u2013109","journal-title":"Appl Soft Comput"},{"issue":"1","key":"9019_CR45","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.ijepes.2010.06.021","volume":"33","author":"R Kumar","year":"2011","unstructured":"Kumar R, Sharma D, Sadu A (2011) A hybrid multi-agent based particle swarm optimization algorithm for economic power dispatch. Int J Electr Power Energy Syst 33(1):115\u2013123","journal-title":"Int J Electr Power Energy Syst"},{"key":"9019_CR46","doi-asserted-by":"crossref","first-page":"95585","DOI":"10.1109\/ACCESS.2019.2927574","volume":"7","author":"X Li","year":"2019","unstructured":"Li X, Zhang H, Zhigang L (2019) A differential evolution algorithm based on multi-population for economic dispatch problems with valve-point effects. IEEE Access 7:95585\u201395609","journal-title":"IEEE Access"},{"issue":"1","key":"9019_CR47","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1016\/j.enconman.2010.07.022","volume":"52","author":"W-M Lin","year":"2011","unstructured":"Lin W-M, Gow H-J, Tsai M-T (2011) Combining of direct search and signal-to-noise ratio for economic dispatch optimization. Energy Convers Manag 52(1):487\u2013493","journal-title":"Energy Convers Manag"},{"issue":"5","key":"9019_CR48","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1109\/TSMCC.2012.2190401","volume":"42","author":"MR Lohokare","year":"2012","unstructured":"Lohokare MR, Panigrahi KB, Pattnaik SS, Devi S, Mohapatra A (2012) Neighborhood search-driven accelerated biogeography-based optimization for optimal load dispatch. EEE Trans Syst Man Cybern Part C (Appl Rev) 42(5):641\u2013652","journal-title":"EEE Trans Syst Man Cybern Part C (Appl Rev)"},{"issue":"9","key":"9019_CR49","doi-asserted-by":"crossref","first-page":"921","DOI":"10.1016\/j.ijepes.2010.03.001","volume":"32","author":"H Lu","year":"2010","unstructured":"Lu H, Sriyanyong P, Song YH, Dillon T (2010) Experimental study of a new hybrid PSO with mutation for economic dispatch with non-smooth cost function. Int J Electr Power Energy Syst 32(9):921\u2013935","journal-title":"Int J Electr Power Energy Syst"},{"issue":"1","key":"9019_CR50","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1109\/TPWRS.2009.2030359","volume":"25","author":"K Meng","year":"2010","unstructured":"Meng K, Wang HG, Dong ZY, Wong KP (2010) Quantum-inspired particle swarm optimization for valve-point economic load dispatch. IEEE Trans Power Syst 25(1):215\u2013222","journal-title":"IEEE Trans Power Syst"},{"issue":"1","key":"9019_CR51","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1016\/j.ijepes.2012.04.060","volume":"42","author":"B Mohammadi-Ivatloo","year":"2012","unstructured":"Mohammadi-Ivatloo B, Rabiee A, Soroudi A, Ehsan M (2012) Iteration PSO with time varying acceleration coefficients for solving non-convex economic dispatch problems. Int J Electr Power Energy Syst 42(1):508\u2013516","journal-title":"Int J Electr Power Energy Syst"},{"key":"9019_CR52","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.epsr.2012.07.009","volume":"93","author":"M Moradi-Dalvand","year":"2012","unstructured":"Moradi-Dalvand M, Mohammadi-Ivatloo B, Najafi A, Rabiee A (2012) Continuous quick group search optimizer for solving non-convex economic dispatch problems. Electric Power Syst Res 93:93\u2013105","journal-title":"Electric Power Syst Res"},{"issue":"2","key":"9019_CR53","doi-asserted-by":"crossref","first-page":"896","DOI":"10.1016\/j.energy.2010.12.021","volume":"36","author":"T Niknam","year":"2011","unstructured":"Niknam T, Mojarrad HD, Meymand HZ, Firouzi BB (2011) A new honey bee mating optimization algorithm for non-smooth economic dispatch. Energy 36(2):896\u2013908","journal-title":"Energy"},{"issue":"6","key":"9019_CR54","doi-asserted-by":"crossref","first-page":"1840","DOI":"10.1002\/ese3.957","volume":"10","author":"J-S Pan","year":"2021","unstructured":"Pan J-S, Shan J, Chu S-C, Jiang S-J, Zheng S-G, Liao L (2021) A multigroup marine predator algorithm and its application for the power system economic load dispatch. Energy Sci Eng 10(6):1840\u20131854","journal-title":"Energy Sci Eng"},{"issue":"1","key":"9019_CR55","first-page":"122","volume":"6","author":"VR Pandi","year":"2011","unstructured":"Pandi VR, Panigrahi BK, Mohapatra A, Mallick MK (2011) Economic load dispatch solution by improved harmony search with wavelet mutation. Int J Comput Sci Eng 6(1):122\u2013131","journal-title":"Int J Comput Sci Eng"},{"issue":"1","key":"9019_CR56","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1109\/TPWRS.2009.2030293","volume":"25","author":"J-B Park","year":"2009","unstructured":"Park J-B, Jeong Y-W, Shin J-R, Lee KY (2009) An improved particle swarm optimization for nonconvex economic dispatch problems. IEEE Trans Power Syst 25(1):156\u2013166","journal-title":"IEEE Trans Power Syst"},{"issue":"5","key":"9019_CR57","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1016\/j.ijepes.2009.09.016","volume":"32","author":"S Pothiya","year":"2010","unstructured":"Pothiya S, Ngamroo I, Kongprawechnon W (2010) Ant colony optimisation for economic dispatch problem with non-smooth cost functions. Int J Electr Power Energy Syst 32(5):478\u2013487","journal-title":"Int J Electr Power Energy Syst"},{"key":"9019_CR58","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/j.ijepes.2016.04.034","volume":"83","author":"M Pradhan","year":"2016","unstructured":"Pradhan M, Roy PK, Pal T (2016) Grey wolf optimization applied to economic load dispatch problems. Int J Electr Power Energy Syst 83:325\u2013334","journal-title":"Int J Electr Power Energy Syst"},{"key":"9019_CR59","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.asoc.2017.05.034","volume":"59","author":"Q Qin","year":"2017","unstructured":"Qin Q, Cheng S, Chu X, Lei X, Shi Y (2017) Solving non-convex\/non-smooth economic load dispatch problems via an enhanced particle swarm optimization. Appl Soft Comput 59:229\u2013242","journal-title":"Appl Soft Comput"},{"issue":"1 1.1 Special I","key":"9019_CR60","first-page":"158","volume":"8","author":"NF Ramli","year":"2020","unstructured":"Ramli NF, Kamari NAM, Halim SA, Musirin I (2020) Solving non-smooth economic load dispatch problem via flower pollination algorithm. Int J Emerg Trends Eng Res 8(1 1.1 Special Issue):158\u2013165","journal-title":"Int J Emerg Trends Eng Res"},{"key":"9019_CR61","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1016\/j.ijepes.2012.10.012","volume":"46","author":"AS Reddy","year":"2013","unstructured":"Reddy AS, Vaisakh K (2013) Shuffled differential evolution for economic dispatch with valve point loading effects. Int J Electr Power Energy Syst 46:342\u2013352","journal-title":"Int J Electr Power Energy Syst"},{"key":"9019_CR62","doi-asserted-by":"crossref","first-page":"2015","DOI":"10.1109\/TPAS.1973.293582","volume":"6","author":"GF Reid","year":"1973","unstructured":"Reid GF, Hasdorff L (1973) Economic dispatch using quadratic programming. IEEE Trans Power Appar Syst 6:2015\u20132023","journal-title":"IEEE Trans Power Appar Syst"},{"issue":"4","key":"9019_CR63","doi-asserted-by":"crossref","first-page":"1608","DOI":"10.1016\/j.asoc.2012.12.014","volume":"13","author":"S Sayah","year":"2013","unstructured":"Sayah S, Hamouda A (2013) A hybrid differential evolution algorithm based on particle swarm optimization for nonconvex economic dispatch problems. Appl Soft Comput 13(4):1608\u20131619","journal-title":"Appl Soft Comput"},{"issue":"1","key":"9019_CR64","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.epsr.2008.05.001","volume":"79","author":"AI Selvakumar","year":"2009","unstructured":"Selvakumar AI, Thanushkodi K (2009) Optimization using civilized swarm: solution to economic dispatch with multiple minima. Electric Power Syst Res 79(1):8\u201316","journal-title":"Electric Power Syst Res"},{"key":"9019_CR65","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1016\/j.energy.2018.11.034","volume":"169","author":"D Singh","year":"2019","unstructured":"Singh D, Dhillon JS (2019) Ameliorated grey wolf optimization for economic load dispatch problem. Energy 169:398\u2013419","journal-title":"Energy"},{"issue":"1","key":"9019_CR66","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1109\/TEVC.2002.806788","volume":"7","author":"N Sinha","year":"2003","unstructured":"Sinha N, Chakrabarti R, Chattopadhyay PK (2003) Evolutionary programming techniques for economic load dispatch. IEEE Trans Evol Comput 7(1):83\u201394","journal-title":"IEEE Trans Evol Comput"},{"issue":"4","key":"9019_CR67","first-page":"3431","volume":"10","author":"SR Spea","year":"2020","unstructured":"Spea SR (2020) Solving practical economic load dispatch problem using crow search algorithm. Int J Electr Comput Eng 10(4):3431\u20133440","journal-title":"Int J Electr Comput Eng"},{"issue":"3","key":"9019_CR68","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1109\/JSYST.2013.2297471","volume":"9","author":"MSP Subathra","year":"2015","unstructured":"Subathra MSP, Selvan SE, Victoire TAA, Christinal AH, Amato U (2015) A hybrid with cross-entropy method and sequential quadratic programming to solve economic load dispatch problem. IEEE Syst J 9(3):1031\u20131044","journal-title":"IEEE Syst J"},{"issue":"9","key":"9019_CR69","doi-asserted-by":"crossref","first-page":"1014","DOI":"10.1016\/j.ijepes.2010.02.003","volume":"32","author":"P Subbaraj","year":"2010","unstructured":"Subbaraj P, Rengaraj R, Salivahanan S, Senthilkumar TR (2010) Parallel particle swarm optimization with modified stochastic acceleration factors for solving large scale economic dispatch problem. Int J Electr Power Energy Syst 32(9):1014\u20131023","journal-title":"Int J Electr Power Energy Syst"},{"issue":"1","key":"9019_CR70","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.asoc.2009.10.019","volume":"11","author":"P Subbaraj","year":"2011","unstructured":"Subbaraj P, Rengaraj R, Salivahanan S (2011) Enhancement of self-adaptive real-coded genetic algorithm using Taguchi method for economic dispatch problem. Appl Soft Comput 11(1):83\u201392","journal-title":"Appl Soft Comput"},{"key":"9019_CR71","first-page":"1619","volume":"10","author":"MH Suleiman","year":"2015","unstructured":"Suleiman MH, Mustafa Z, Mohmed MR (2015) Grey wolf optimizer for solving economic dispatch problem with valve-loading effects. APRN J Eng Appl Sci 10:1619\u20131628","journal-title":"APRN J Eng Appl Sci"},{"issue":"1","key":"9019_CR72","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1109\/59.651616","volume":"13","author":"DL Travers","year":"1998","unstructured":"Travers DL, Kaye RJ (1998) Dynamic dispatch by constructive dynamic programming. IEEE Trans Power Syst 13(1):72\u201378","journal-title":"IEEE Trans Power Syst"},{"issue":"4","key":"9019_CR73","doi-asserted-by":"crossref","first-page":"1070","DOI":"10.1016\/j.ijepes.2011.01.026","volume":"33","author":"M-T Tsai","year":"2011","unstructured":"Tsai M-T, Gow H-J, Lin W-M (2011) A novel stochastic search method for the solution of economic dispatch problems with non-convex fuel cost functions. Int J Electr Power Energy Syst 33(4):1070\u20131076","journal-title":"Int J Electr Power Energy Syst"},{"issue":"3","key":"9019_CR74","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1016\/j.ejor.2012.01.047","volume":"221","author":"ASSMB Ullah","year":"2012","unstructured":"Ullah ASSMB, Sarker R, Lokan C (2012) Handling equality constraints in evolutionary optimization. Eur J Oper Res 221(3):480\u2013490","journal-title":"Eur J Oper Res"},{"issue":"3","key":"9019_CR75","doi-asserted-by":"crossref","first-page":"1325","DOI":"10.1109\/59.260861","volume":"8","author":"DC Walters","year":"1993","unstructured":"Walters DC, Sheble GB (1993) Genetic algorithm solution of economic dispatch with valve point loading. IEEE Trans Power Syst 8(3):1325\u20131332","journal-title":"IEEE Trans Power Syst"},{"issue":"1","key":"9019_CR76","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1016\/j.ijepes.2012.08.021","volume":"44","author":"L Wang","year":"2013","unstructured":"Wang L, Li L-P (2013) An effective differential harmony search algorithm for the solving non-convex economic load dispatch problems. Int J Electr Power Energy Syst 44(1):832\u2013843","journal-title":"Int J Electr Power Energy Syst"},{"issue":"5","key":"9019_CR77","doi-asserted-by":"crossref","first-page":"2097","DOI":"10.1109\/TPWRS.2014.2306933","volume":"29","author":"MQ Wang","year":"2014","unstructured":"Wang MQ, Gooi HB, Chen SX, Lu S (2014) A mixed integer quadratic programming for dynamic economic dispatch with valve point effect. IEEE Trans Power Syst 29(5):2097\u20132106","journal-title":"IEEE Trans Power Syst"},{"issue":"1","key":"9019_CR78","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/4235.585893","volume":"1","author":"DH Wolpert","year":"1997","unstructured":"Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67\u201382","journal-title":"IEEE Trans Evol Comput"},{"issue":"10","key":"9019_CR79","doi-asserted-by":"crossref","first-page":"7369","DOI":"10.1007\/s00521-022-07980-1","volume":"35","author":"H Yi\u011fit","year":"2023","unstructured":"Yi\u011fit H, \u00dcrg\u00fcn S, Mirjalili S (2023) Comparison of recent metaheuristic optimization algorithms to solve the she optimization problem in mli. Neural Comput Appl 35(10):7369\u20137388","journal-title":"Neural Comput Appl"},{"issue":"22","key":"9019_CR80","doi-asserted-by":"crossref","first-page":"16951","DOI":"10.1007\/s00521-020-05036-w","volume":"32","author":"J Yu","year":"2020","unstructured":"Yu J, Kim C-H, Rhee S-B (2020) Clustering cuckoo search optimization for economic load dispatch problem. Neural Comput Appl 32(22):16951\u201316969","journal-title":"Neural Comput Appl"},{"key":"9019_CR81","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/8869477","author":"J Zhang","year":"2021","unstructured":"Zhang J, Zhang J, Zhang F, Chi M, Wan L (2021) An improved symbiosis particle swarm optimization for solving economic load dispatch problem. J Electr Comput Eng. https:\/\/doi.org\/10.1155\/2021\/8869477","journal-title":"J Electr Comput Eng"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-023-09019-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-023-09019-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-023-09019-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,26]],"date-time":"2023-09-26T09:10:44Z","timestamp":1695719444000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-023-09019-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,3]]},"references-count":81,"journal-issue":{"issue":"22","published-print":{"date-parts":[[2023,11]]}},"alternative-id":["9019"],"URL":"https:\/\/doi.org\/10.1007\/s00500-023-09019-6","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-1761466\/v1","asserted-by":"object"}]},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,3]]},"assertion":[{"value":"7 July 2023","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 August 2023","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"The authors declare that there has no conflict of interest.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"None.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}}]}}