{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T11:28:26Z","timestamp":1782818906289,"version":"3.54.5"},"reference-count":44,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,1]],"date-time":"2024-10-01T00:00:00Z","timestamp":1727740800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper presents a new optimization technique based on the hybridization of two meta-heuristic methods, Jellyfish Search (JS) and Moth Flame Optimizer (MFO), to solve the Optimal Power Flow (OPF) problem. The JS algorithm offers good exploration capacity but lacks performance in its exploitation mechanism. To improve its efficiency, we combined it with the Moth Flame Optimizer, which has proven its ability to exploit good solutions in the search area. This hybrid algorithm combines the advantages of both algorithms. The performance and precision of the hybrid optimization approach (JS-MFO) were investigated by minimizing well-known mathematical benchmark functions and by solving the complex OPF problem. The OPF problem was solved by optimizing non-convex objective functions such as total fuel cost, total active transmission losses, total gas emission, total voltage deviation, and the voltage stability index. Two test systems, the IEEE 30-bus network and the Mauritanian RIM 27-bus transmission network, were considered for implementing the JS-MFO approach. Experimental tests of the JS, MFO, and JS-MFO algorithms on eight well-known benchmark functions, the IEEE 30-bus, and the Mauritanian RIM 27-bus system were conducted. For the IEEE 30-bus test system, the proposed hybrid approach provides a percent cost saving of 11.4028%, a percent gas emission reduction of 14.38%, and a percent loss saving of 50.60% with respect to the base case. For the RIM 27-bus system, JS-MFO achieved a loss percent saving of 50.67% and percent voltage reduction of 62.44% with reference to the base case. The simulation results using JS-MFO and obtained with the MATLAB 2009b software were compared with those of JS, MFO, and other well-known meta-heuristics cited in the literature. The comparison report proves the superiority of the JS-MFO method over JS, MFO, and other competing meta-heuristics in solving difficult OPF problems.<\/jats:p>","DOI":"10.3390\/a17100438","type":"journal-article","created":{"date-parts":[[2024,10,1]],"date-time":"2024-10-01T05:26:33Z","timestamp":1727760393000},"page":"438","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Solving Optimal Power Flow Using New Efficient Hybrid Jellyfish Search and Moth Flame Optimization Algorithms"],"prefix":"10.3390","volume":"17","author":[{"given":"Chiva","family":"Mayouf","sequence":"first","affiliation":[{"name":"Unit\u00e9 de Recherche des Nouvelles Technologies des Energies et Syst\u00e8mes Thermo-Fluides (nTEST), D\u00e9partement de Physique, Facult\u00e9 des Sciences et Technologie, Universit\u00e9 de Nouakchott, Nouakchott BP 888, Mauritania"},{"name":"Electrical Engineering D\u00e9partment, LGEB Laboratory, University of Biskra, BP 145, Biskra 07000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-4888-8365","authenticated-orcid":false,"given":"Ahmed","family":"Salhi","sequence":"additional","affiliation":[{"name":"Electrical Engineering D\u00e9partment, LGEB Laboratory, University of Biskra, BP 145, Biskra 07000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fanta","family":"Haidara","sequence":"additional","affiliation":[{"name":"Unit\u00e9 de Recherche des Nouvelles Technologies des Energies et Syst\u00e8mes Thermo-Fluides (nTEST), D\u00e9partement de Physique, Facult\u00e9 des Sciences et Technologie, Universit\u00e9 de Nouakchott, Nouakchott BP 888, Mauritania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fatima Zahra","family":"Aroua","sequence":"additional","affiliation":[{"name":"Electrical Engineering D\u00e9partment, LGEB Laboratory, University of Biskra, BP 145, Biskra 07000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3340-4031","authenticated-orcid":false,"given":"Ragab A.","family":"El-Sehiemy","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, Kafrelsheikh University, Kafrelsheikh 33516, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Djemai","family":"Naimi","sequence":"additional","affiliation":[{"name":"Electrical Engineering D\u00e9partment, LGEB Laboratory, University of Biskra, BP 145, Biskra 07000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chouaib","family":"Aya","sequence":"additional","affiliation":[{"name":"Unit\u00e9 de Recherche des Nouvelles Technologies des Energies et Syst\u00e8mes Thermo-Fluides (nTEST), D\u00e9partement de Physique, Facult\u00e9 des Sciences et Technologie, Universit\u00e9 de Nouakchott, Nouakchott BP 888, Mauritania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cheikh Sidi Ethmane","family":"Kane","sequence":"additional","affiliation":[{"name":"Unit\u00e9 de Recherche des Nouvelles Technologies des Energies et Syst\u00e8mes Thermo-Fluides (nTEST), D\u00e9partement de Physique, Facult\u00e9 des Sciences et Technologie, Universit\u00e9 de Nouakchott, Nouakchott BP 888, Mauritania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s12667-012-0056-y","article-title":"Optimal power flow: A bibliographic survey I","volume":"3","author":"Frank","year":"2012","journal-title":"Energy Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/j.energy.2012.07.053","article-title":"Reserve constrained dynamic optimal power flow subject to valve-point effects, prohibited zones and multi-fuel constraints","volume":"47","author":"Niknam","year":"2012","journal-title":"Energy"},{"key":"ref_3","unstructured":"El Ela, A.A.A., El-Sehiemy, R.A., Shaheen, A.M., and Shalaby, A.S. (2017, January 19\u201321). Application of the crow search algorithm for economic environmental dispatch. Proceedings of the 2017 IEEE Nineteenth International Middle East Power Systems Conference (MEPCON), Cairo, Egypt."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.ijepes.2016.02.004","article-title":"Optimal power flow with emission and non-smooth cost functions using backtracking search optimization algorithm","volume":"81","author":"Chaib","year":"2016","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1866","DOI":"10.1109\/TPAS.1968.292150","article-title":"Optimal power flow solutions","volume":"10","author":"Dommel","year":"1968","journal-title":"IEEE Trans. Power Appar. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1109\/59.744495","article-title":"A review of selected optimal power flow literature to 1993. II. Newton, linear programming and interior point methods","volume":"14","author":"Momoh","year":"1999","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_7","first-page":"391","article-title":"A solution to the optimal power flow using genetic algorithm","volume":"155","author":"Osman","year":"2004","journal-title":"Appl. Math. Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1016\/S0142-0615(01)00067-9","article-title":"Optimal power flow using particle swarm optimization","volume":"24","author":"Abido","year":"2002","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_9","first-page":"43","article-title":"Optimal power flow of the Algerian electrical network using an ant colony optimization method","volume":"6","author":"Bouktir","year":"2005","journal-title":"Leonardo J. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.ijepes.2013.04.021","article-title":"Artificial bee colony algorithm for solving multi-objective optimal power flow problem","volume":"53","author":"Adaryani","year":"2013","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.enconman.2012.02.024","article-title":"Optimal power flow using gravitational search algorithm","volume":"59","author":"Duman","year":"2012","journal-title":"Energy Convers. Manag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1548","DOI":"10.1080\/15325008.2015.1041625","article-title":"Single and multi-objective optimal power flow using grey wolf optimizer and differential evolution algorithms","volume":"43","author":"Hasanien","year":"2015","journal-title":"Electr. Power Compon. Syst."},{"key":"ref_13","unstructured":"Ouafa, H., Linda, S., and Tarek, B. (2017, January 22\u201324). Multi-objective optimal power flow considering the fuel cost, emission, voltage deviation and power losses using Multi-Objective Dragonfly algorithm. Proceedings of the International Conference on Recent Advances in Electrical Systems. In Proceedings of the International Conference on Recent Advances in Electrical Systems, Hammamet, Tunusia."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Alanazi, A., Alanazi, M., Memon, Z.A., and Mosavi, A. (2022). Determining Optimal Power Flow Solutions Using New Adaptive Gaussian TLBO Method. Appl. Sci., 12.","DOI":"10.3390\/app12167959"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1786","DOI":"10.17762\/turcomat.v12i2.1515","article-title":"Modern swarm intelligence-based algorithms for solving optimal power flow problem in a regulated power system framework","volume":"12","author":"Ramesh","year":"2021","journal-title":"Turk. J. Comput. Math. Educ. (TURCOMAT)"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Islam, M.Z., Wahab, N.I., Veerasamy, V., Hizam, H., Mailah, N.F., Guerrero, J.M., and Nasir, M.N.M. (2020). A Harris Hawks optimization based single-and multi-objective optimal power flow considering environmental emission. Sustainability, 12.","DOI":"10.3390\/su12135248"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Sarhan, S., El-Sehiemy, R., Abaza, A., and Gafar, M. (2022). Turbulent flow of water-based optimization for solving multi-objective technical and economic aspects of optimal power flow problems. Mathematics, 10.","DOI":"10.3390\/math10122106"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Mirjalili, S. (2023). Handbook of Whale Optimization Algorithm: Variants, Hybrids, Improvements, and Applications, Academic Press Elsevier.","DOI":"10.1201\/9781003205326"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2332","DOI":"10.1109\/ACCESS.2020.3047671","article-title":"An improved sunflower optimization algorithm-based Monte Carlo simulation for efficiency improvement of radial distribution systems considering wind power uncertainty","volume":"9","author":"Shaheen","year":"2020","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"77013","DOI":"10.1109\/ACCESS.2020.2989445","article-title":"Improved whale optimization algorithm based on nonlinear adaptive weight and golden sine operator","volume":"8","author":"Zhang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s40313-017-0362-7","article-title":"Optimal power flow for multi-FACTS power system using hybrid PSO-PS algorithms","volume":"29","author":"Berrouk","year":"2018","journal-title":"J. Control. Autom. Electr. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1007\/s13042-018-0786-9","article-title":"Optimal power flow using hybrid differential evolution and harmony search algorithm","volume":"10","author":"Reddy","year":"2019","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Khunkitti, S., Siritaratiwat, A., Premrudeepreechacharn, S., Chatthaworn, R., and Watson, N.R. (2018). A hybrid DA-PSO optimization algorithm for multi-objective optimal power flow problems. Energies, 11.","DOI":"10.3390\/en11092270"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Khan, A., Hizam, H., Wahab, N.I.B.A., and Othman, M.L. (2020). Optimal power flow using hybrid firefly and particle swarm optimization algorithm. PLoS ONE, 15.","DOI":"10.1371\/journal.pone.0235668"},{"key":"ref_25","first-page":"1825","article-title":"A novel hybrid approach based artificial bee colony and salp swarm algorithms for solving ORPD problem","volume":"23","author":"Salhi","year":"2021","journal-title":"Indones. J. Electr. Eng. Comput. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Mallala, B., Papana, V.P., Sangu, R., Palle, K., and Chinthalacheruvu, V.K. (2022). multi-objective optimal power flow solution using a non-dominated sorting hybrid fruit fly-based artificial bee colony. Energies, 15.","DOI":"10.3390\/en15114063"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Alghamdi, A.S. (2022). A Hybrid Firefly\u2013JAYA Algorithm for the Optimal Power Flow Problem Considering Wind and Solar Power Generations. Appl. Sci., 12.","DOI":"10.3390\/app12147193"},{"key":"ref_28","first-page":"125535","article-title":"A novel metaheuristic optimizer inspired by behavior of jellyfish in ocean","volume":"389","author":"Chou","year":"2021","journal-title":"Appl. Math. Comput."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Rai, H., and Verma, H.K. (2021, January 18\u201319). Economic load dispatch using jellyfish search optimizer. Proceedings of the 2021 10th IEEE International Conference on Communication Systems and Network Technologies (CSNT), Bhopal, India.","DOI":"10.1109\/CSNT51715.2021.9509624"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.knosys.2015.07.006","article-title":"Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm","volume":"89","author":"Mirjalili","year":"2015","journal-title":"Knowl.-Based Syst."},{"key":"ref_31","first-page":"42","article-title":"Multi-item EOQ model with nonlinear unit holding cost and partial backordering: Moth-flame optimization algorithm","volume":"34","author":"Khalilpourazari","year":"2016","journal-title":"J. Ind. Prod. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1109\/TPWRD.1986.4308013","article-title":"Estimating the voltage stability of power systems","volume":"1","author":"Kessel","year":"1986","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1016\/j.ijepes.2015.12.004","article-title":"A novel adequate bi-level reactive power planning strategy","volume":"78","author":"Shaheen","year":"2016","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_34","first-page":"19","article-title":"Object-Oriented Economic Power Dispatch of Electrical Power System with minimum pollution using a Genetic Algorithm","volume":"1","author":"Bouktir","year":"2005","journal-title":"J. Electr. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"54465","DOI":"10.1109\/ACCESS.2020.2981406","article-title":"A Hybrid Local Search-Genetic Algorithm for Simultaneous Placement of DG Units and Shunt Capacitors in Radial Distribution Systems","volume":"8","author":"Almabsout","year":"2020","journal-title":"IEEE Access"},{"key":"ref_36","first-page":"34","article-title":"Optimal Power Flow Solution using Efficient Sine Cosine Optimization Algorithm","volume":"2","author":"Messaoudi","year":"2020","journal-title":"J. Intell. Syst. Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"116817","DOI":"10.1016\/j.energy.2019.116817","article-title":"A novel multi-objective hybrid particle swarm and salp optimization algorithm for technical-economical-environmental operation in power systems","volume":"193","author":"Selim","year":"2020","journal-title":"Energy"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"4027","DOI":"10.1007\/s00500-020-05431-4","article-title":"An improved version of salp swarm algorithm for solving optimal power flow problem","volume":"25","author":"Kamel","year":"2021","journal-title":"Soft Comput."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"6287","DOI":"10.1007\/s00500-018-3284-9","article-title":"A modified artificial bee colony algorithm for load balancing in network-coding-based multicast","volume":"23","author":"Xing","year":"2019","journal-title":"Soft Comput."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1016\/j.ijepes.2014.07.010","article-title":"Optimal power flow solution of power system incorporating stochastic wind power using Gbest guided artificial bee colony algorithm","volume":"64","author":"Roy","year":"2015","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_41","first-page":"734","article-title":"Optimal power flow resolution using artificial bee colony algorithm-based grenade explosion method","volume":"12","author":"Salhi","year":"2016","journal-title":"J. Electr. Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"106252","DOI":"10.1016\/j.asoc.2020.106252","article-title":"Optimal power flow using the AMTPG-Jaya algorithm","volume":"91","author":"Warid","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_43","first-page":"716","article-title":"A solution to the optimal power flow using multi-verse optimizer","volume":"12","author":"Bentouati","year":"2016","journal-title":"Electr. Syst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.engappai.2017.10.019","article-title":"Optimal power flow solutions using differential evolution algorithm integrated with effective constraint handling techniques","volume":"68","author":"Biswas","year":"2018","journal-title":"Eng. Appl. Artif. Intell."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/10\/438\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:08:39Z","timestamp":1760112519000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/10\/438"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,1]]},"references-count":44,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["a17100438"],"URL":"https:\/\/doi.org\/10.3390\/a17100438","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,1]]}}}