{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T08:51:16Z","timestamp":1778662276951,"version":"3.51.4"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2018,3,1]],"date-time":"2018-03-01T00:00:00Z","timestamp":1519862400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2019,9]]},"DOI":"10.1007\/s00521-018-3382-8","type":"journal-article","created":{"date-parts":[[2018,3,1]],"date-time":"2018-03-01T05:48:04Z","timestamp":1519883284000},"page":"5609-5627","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["On the efficiency of metaheuristics for solving the optimal power flow"],"prefix":"10.1007","volume":"31","author":[{"given":"Hitarth","family":"Buch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Indrajit N.","family":"Trivedi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,3,1]]},"reference":[{"key":"3382_CR1","doi-asserted-by":"crossref","unstructured":"Carpentier J (1985) Optimal power flows: uses, methods and developments. In: Proceedings of IFAC conference","DOI":"10.1016\/S1474-6670(17)60410-5"},{"issue":"5","key":"3382_CR2","first-page":"450","volume":"4","author":"KS Pandya","year":"2005","unstructured":"Pandya KS, Joshi SK (2005) A survey of optimal power flow methods. J Appl Inf Technol 4(5):450\u2013458","journal-title":"J Appl Inf Technol"},{"issue":"1","key":"3382_CR3","doi-asserted-by":"publisher","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":"3382_CR4","doi-asserted-by":"publisher","first-page":"1055","DOI":"10.1080\/15325000290085343","volume":"30","author":"SR Paranjothi","year":"2002","unstructured":"Paranjothi SR, Anburaja SR (2002) Optimal power flow using refined genetic algorithm. Electr Power Compon Syst 30(10):1055\u20131063","journal-title":"Electr Power Compon Syst"},{"issue":"5","key":"3382_CR5","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/S0142-0615(96)00051-8","volume":"19","author":"LL Lai","year":"1997","unstructured":"Lai LL, Ma JT, Yokoyama R, Zhao M (1997) Improved genetic algorithms for optimal power flow under both normal and contingent operation states. Int J Electr Power Energy Syst 19(5):287\u2013292","journal-title":"Int J Electr Power Energy Syst"},{"issue":"7","key":"3382_CR6","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1016\/S0142-0615(01)00067-9","volume":"24","author":"MMAM Abido","year":"2002","unstructured":"Abido MMAM (2002) Optimal power flow using particle swarm optimization. J Electr Power Energy Syst 24(7):563\u2013571","journal-title":"J Electr Power Energy Syst"},{"key":"3382_CR7","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1080\/15325000252888425","volume":"30","author":"MA Abido","year":"2002","unstructured":"Abido MA (2002) Optimal power flow using tabu search algorithm. Electr Power Compon Syst 30:469\u2013483","journal-title":"Electr Power Compon Syst"},{"issue":"1","key":"3382_CR8","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/S0142-0615(02)00020-0","volume":"25","author":"CA Roa-Sepulveda","year":"2003","unstructured":"Roa-Sepulveda CA, Pavez-Lazo BJ (2003) A solution to the optimal power flow using simulated annealing. Int J Electr Power Energy Syst 25(1):47\u201357","journal-title":"Int J Electr Power Energy Syst"},{"issue":"7","key":"3382_CR9","doi-asserted-by":"publisher","first-page":"878","DOI":"10.1016\/j.epsr.2009.12.018","volume":"80","author":"AAA Abou El Ela","year":"2010","unstructured":"Abou El Ela AAA, Abido MAA, Spea SRR (2010) Optimal power flow using differential evolution algorithm. Electr Power Syst Res 80(7):878\u2013885","journal-title":"Electr Power Syst Res"},{"key":"3382_CR10","unstructured":"Ghanizadeh AJ, Mokhtari G, Abedi M, Gharehpetian GB (2011) Optimal power flow based on imperialist competitive algorithm. Int Rev Electr Eng 6(4):1847\u20131852"},{"issue":"5","key":"3382_CR11","doi-asserted-by":"publisher","first-page":"2364","DOI":"10.1016\/j.asoc.2013.01.024","volume":"13","author":"N Sinsuphan","year":"2013","unstructured":"Sinsuphan N, Leeton U, Kulworawanichpong T (2013) Optimal power flow solution using improved harmony search method. Appl Soft Comput J 13(5):2364\u20132374","journal-title":"Appl Soft Comput J"},{"key":"3382_CR12","doi-asserted-by":"publisher","first-page":"879","DOI":"10.1016\/j.asoc.2014.08.056","volume":"24","author":"HREH Bouchekara","year":"2014","unstructured":"Bouchekara HREH (2014) Optimal power flow using black-hole-based optimization approach. Appl Soft Comput 24:879\u2013888","journal-title":"Appl Soft Comput"},{"key":"3382_CR13","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.epsr.2014.03.032","volume":"114","author":"HREH Bouchekara","year":"2014","unstructured":"Bouchekara HREH, Abido MA, Boucherma M (2014) Optimal power flow using teaching\u2013learning-based optimization technique. Electr Power Syst Res 114:49\u201359","journal-title":"Electr Power Syst Res"},{"issue":"6","key":"3382_CR14","doi-asserted-by":"publisher","first-page":"1889","DOI":"10.1007\/s00521-016-2794-6","volume":"30","author":"Indrajit N. Trivedi","year":"2016","unstructured":"Trivedi IN, Jangir P, Parmar SA, Jangir N (2016) Optimal power flow with voltage stability improvement and loss reduction in power system using Moth-Flame Optimizer. Neural Comput Appl 1\u201316. \n                    https:\/\/doi.org\/10.1007\/s00521-016-2794-6","journal-title":"Neural Computing and Applications"},{"key":"3382_CR15","doi-asserted-by":"crossref","unstructured":"Buch H, Trivedi IN, Jangir P (2017) Moth flame optimization to solve optimal power flow with non-parametric statistical evaluation validation. Cogent Eng 4(1):1\u201322","DOI":"10.1080\/23311916.2017.1286731"},{"key":"3382_CR16","doi-asserted-by":"publisher","first-page":"562","DOI":"10.1016\/j.ijepes.2014.07.010","volume":"64","author":"R Roy","year":"2015","unstructured":"Roy R, Jadhav H (2015) Optimal power flow solution of power system incorporating stochastic wind power using Gbest guided artificial bee colony algorithm. J Electr Power Energy Syst 64:562\u2013578","journal-title":"J Electr Power Energy Syst"},{"key":"3382_CR17","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1016\/j.epsr.2016.09.025","volume":"142","author":"A-AA Mohamed","year":"2017","unstructured":"Mohamed A-AA, Mohamed YS, El-Gaafary AAM, Hemeida AM (2017) Optimal power flow using moth swarm algorithm. Electr Power Syst Res 142:190\u2013206","journal-title":"Electr Power Syst Res"},{"key":"3382_CR18","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1016\/j.enconman.2014.06.088","volume":"87","author":"HREH Bouchekara","year":"2014","unstructured":"Bouchekara HREH, Abido MA, Chaib AE, Mehasni R (2014) Optimal power flow using the league championship algorithm: a case study of the Algerian power system. Energy Convers Manag 87:58\u201370","journal-title":"Energy Convers Manag"},{"key":"3382_CR19","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1016\/j.ijepes.2016.02.004","volume":"81","author":"AAEA Chaib","year":"2016","unstructured":"Chaib AAEA, Bouchekara HREH, Mehasni R, Abido MA (2016) Optimal power flow with emission and non-smooth cost functions using backtracking search optimization algorithm. Int J Electr Power Energy Syst 81:64\u201377","journal-title":"Int J Electr Power Energy Syst"},{"key":"3382_CR20","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/j.asoc.2016.01.041","volume":"42","author":"HREH Bouchekara","year":"2016","unstructured":"Bouchekara HREH, Chaib AE, Abido MA, El-Sehiemy RA (2016) Optimal power flow using an Improved Colliding Bodies Optimization algorithm. Appl Soft Comput 42:119\u2013131","journal-title":"Appl Soft Comput"},{"issue":"2","key":"3382_CR21","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/s00202-015-0357-y","volume":"98","author":"M G\u00fc\u00e7yetmez","year":"2016","unstructured":"G\u00fc\u00e7yetmez M, \u00c7am E (2016) A new hybrid algorithm with genetic-teaching learning optimization (G-TLBO) technique for optimizing of power flow in wind-thermal power systems. Electr Eng 98(2):145\u2013157","journal-title":"Electr Eng"},{"key":"3382_CR22","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1016\/j.ijepes.2016.01.036","volume":"80","author":"SS Reddy","year":"2016","unstructured":"Reddy SS, Rathnam CS (2016) Optimal power flow using glowworm swarm optimization. Int J Electr Power Energy Syst 80:128\u2013139","journal-title":"Int J Electr Power Energy Syst"},{"key":"3382_CR23","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.chaos.2015.06.020","volume":"78","author":"A Mukherjee","year":"2015","unstructured":"Mukherjee A, Mukherjee V (2015) Solution of optimal power flow using chaotic krill herd algorithm. Chaos Solitons Fract 78:10\u201321","journal-title":"Chaos Solitons Fract"},{"key":"3382_CR24","doi-asserted-by":"crossref","unstructured":"Trivedi IN, Jangir P, Jangir N, Parmar SA, Bhoye M, Kumar A (2016) Voltage stability enhancement and voltage deviation minimization using multi-verse optimizer algorithm. In: 2016 International conference on circuit, power and computing technologies (ICCPCT), pp 1\u20135","DOI":"10.1109\/ICCPCT.2016.7530136"},{"key":"3382_CR25","doi-asserted-by":"crossref","unstructured":"Trivedi IN, Bhoye M, Jangir P, Parmar SA, Jangir N, Kumar A (2016) Voltage stability enhancement and voltage deviation minimization using BAT optimization algorithm. In: 2016 3rd international conference on electrical energy systems, ICEES 2016, pp 112\u2013116","DOI":"10.1109\/ICEES.2016.7510626"},{"issue":"4","key":"3382_CR26","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/s40565-014-0089-4","volume":"2","author":"M Niu","year":"2014","unstructured":"Niu M, Wan C, Xu Z (2014) A review on applications of heuristic optimization algorithms for optimal power flow in modern power systems. J Mod Power Syst Clean Energy 2(4):289\u2013297","journal-title":"J Mod Power Syst Clean Energy"},{"issue":"4","key":"3382_CR27","doi-asserted-by":"publisher","first-page":"694","DOI":"10.1016\/j.epsr.2008.10.004","volume":"79","author":"MR AlRashidi","year":"2009","unstructured":"AlRashidi MR, El-Hawary ME (2009) Applications of computational intelligence techniques for solving the revived optimal power flow problem. Electr Power Syst Res 79(4):694\u2013702","journal-title":"Electr Power Syst Res"},{"issue":"3","key":"3382_CR28","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/s12667-012-0057-x","volume":"3","author":"S Frank","year":"2012","unstructured":"Frank S, Steponavice I, Rebennack S (2012) Optimal power flow: a bibliographic survey II. Energy Syst 3(3):259\u2013289","journal-title":"Energy Syst"},{"key":"3382_CR29","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1016\/j.knosys.2015.07.006","volume":"89","author":"S Mirjalili","year":"2015","unstructured":"Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl Based Syst 89:228\u2013249","journal-title":"Knowl Based Syst"},{"key":"3382_CR30","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","volume":"69","author":"S Mirjalili","year":"2014","unstructured":"Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46\u201361","journal-title":"Adv Eng Softw"},{"issue":"4","key":"3382_CR31","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1007\/s00521-015-1920-1","volume":"27","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27(4):1053\u20131073","journal-title":"Neural Comput Appl"},{"key":"3382_CR32","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.knosys.2015.12.022","volume":"96","author":"S Mirjalili","year":"2015","unstructured":"Mirjalili S (2015) SCA: a sine cosine algorithm for solving optimization problems. Knowl Based Syst 96:120\u2013133","journal-title":"Knowl Based Syst"},{"key":"3382_CR33","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.advengsoft.2015.01.010","volume":"83","author":"S Mirjalili","year":"2015","unstructured":"Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80\u201398","journal-title":"Adv Eng Softw"},{"issue":"2","key":"3382_CR34","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1007\/s00521-015-1870-7","volume":"27","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27(2):495\u2013513","journal-title":"Neural Comput Appl"},{"key":"3382_CR35","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.advengsoft.2017.01.004","volume":"105","author":"S Saremi","year":"2017","unstructured":"Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30\u201347","journal-title":"Adv Eng Softw"},{"key":"3382_CR36","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/j.asoc.2015.03.035","volume":"32","author":"B Javidy","year":"2015","unstructured":"Javidy B, Hatamlou A, Mirjalili S (2015) Ions motion algorithm for solving optimization problems. Appl Soft Comput J 32:72\u201379","journal-title":"Appl Soft Comput J"},{"key":"3382_CR37","doi-asserted-by":"publisher","first-page":"680","DOI":"10.1080\/01621459.1979.10481670","volume":"74","author":"D Quade","year":"1979","unstructured":"Quade D (1979) Using weighted rankings in the analysis of complete blocks with additive block effects. J Am Stat Assoc 74:680\u2013683","journal-title":"J Am Stat Assoc"},{"key":"3382_CR38","doi-asserted-by":"publisher","first-page":"675","DOI":"10.1080\/01621459.1937.10503522","volume":"32","author":"M Friedman","year":"1937","unstructured":"Friedman M (1937) The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J Am Stat Assoc 32:675\u2013701","journal-title":"J Am Stat Assoc"},{"issue":"2","key":"3382_CR39","doi-asserted-by":"publisher","first-page":"482","DOI":"10.1214\/aoms\/1177704575","volume":"33","author":"JL Hodges","year":"1962","unstructured":"Hodges JL, Lehmann EL (1962) Rank methods for combination of independent experiments in analysis of variance. Ann Math Stat 33(2):482\u2013497","journal-title":"Ann Math Stat"},{"key":"3382_CR40","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1016\/j.ins.2014.09.051","volume":"294","author":"M Ghasemi","year":"2015","unstructured":"Ghasemi M, Ghavidel S, Ghanbarian MM (2015) Multi-objective optimal electric power planning in the power system using Gaussian bare-bones imperialist competitive algorithm. Inf Sci (NY) 294:286\u2013304","journal-title":"Inf Sci (NY)"},{"key":"3382_CR41","unstructured":"Single Line Diagram of IEEE 57-Bus Test System (online). \n                    http:\/\/al-roomi.org\/power-flow\/57-bus-system\n                    \n                  . Accessed 17 Mar 2017"},{"key":"3382_CR42","unstructured":"2003 Group, IIT Power, \u201cOne-line Diagram of IEEE 118-bus Test System (online). \n                    http:\/\/motor.ece.iit.edu\/data\/IEEE118bus_inf\/IEEE118bus_figure.pdf\n                    \n                  . Accessed 15 Jan 2017"},{"key":"3382_CR43","unstructured":"IEEE 118-Bus Test System Data (online). \n                    http:\/\/motor.ece.iit.edu\/data\/JEAS_IEEE57.doc\n                    \n                  . Accessed 17 Mar 2017"},{"issue":"4","key":"3382_CR44","doi-asserted-by":"publisher","first-page":"2412","DOI":"10.3390\/en8042412","volume":"8","author":"X He","year":"2015","unstructured":"He X, Wang W, Jiang J, Xu L (2015) An improved artificial bee colony algorithm and its application to multi-objective optimal power flow. Energies 8(4):2412\u20132437","journal-title":"Energies"},{"key":"3382_CR45","unstructured":"2014 OPF PROBLEMS (online). \n                    https:\/\/www.uni-due.de\/ieee-wgmho\/competition2014\n                    \n                  . Accessed 09 Jan 2018"},{"issue":"1","key":"3382_CR46","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.swevo.2011.02.002","volume":"1","author":"J Derrac","year":"2011","unstructured":"Derrac J, Garc\u00eda S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3\u201318","journal-title":"Swarm Evol Comput"},{"issue":"6","key":"3382_CR47","doi-asserted-by":"publisher","first-page":"1540","DOI":"10.1016\/j.jestch.2017.12.009","volume":"20","author":"Anulekha Saha","year":"2017","unstructured":"Saha A, Das P, Chakraborty AK (2017) Water evaporation algorithm: a new metaheuristic algorithm towards the solution of optimal power flow. Eng Sci Technol Int J 20(6):1540\u20131552","journal-title":"Engineering Science and Technology, an International Journal"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-018-3382-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-018-3382-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-018-3382-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,30]],"date-time":"2019-09-30T20:37:30Z","timestamp":1569875850000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-018-3382-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,1]]},"references-count":47,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["3382"],"URL":"https:\/\/doi.org\/10.1007\/s00521-018-3382-8","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,1]]},"assertion":[{"value":"25 April 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 February 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 March 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors whose names are listed immediately below certify that they have NO affiliations or entity with any financial interest (such as honoraria; educational grants; participation in speakers\u2019 bureaus; membership, consultancies, stock ownership and expert testimony or patent-licensing arrangements) or non-financial interest in the subject matter or materials discussed in this manuscript.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}