{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T01:47:48Z","timestamp":1782265668749,"version":"3.54.5"},"reference-count":67,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T00:00:00Z","timestamp":1781308800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>The power flow problem is one of the most challenging tasks in power systems, affecting both generation cost and energy quality. Optimal power flow (OPF) further complicates this task by requiring the optimal adjustment of system variables and parameters. This paper adapts the Modified Effective Butterfly Optimizer (MEBO) to solve multi-objective optimal power flow (MOOPF) problems with the contribution of optimized weighting using multiple Pareto archives. MEBO is an advanced optimization algorithm that utilizes population reduction and parameter learning to guide subsequent searches for unconstrained problems. The proposed technique has been tested on IEEE 30 and 57 bus test systems, and the results have been compared with existing methods reported in the literature. In the paper, four single-objective functions, namely generator cost, active power loss, fuel emission, and voltage deviation, are used to construct four multi-objective (MO) problems: cost\u2013loss, cost\u2013voltage, cost-emission, and emission\u2013loss. For the cost-emission case, the proposed MEBO achieved compromised solutions of 791.1951 $\/h fuel cost with 0.10873 ton\/h emission and 801.8172 $\/h fuel cost with 0.10044 ton\/h emission under different Pareto-based optimization metrics. In the emission\u2013loss case, the algorithm obtained 0.20539 ton\/h emission with 3.1403 MW\/h power loss, demonstrating the effectiveness of the proposed approach in balancing conflicting objectives. The Pareto curves of MEBO in achieving MO problems are presented, along with the suggested compromised solutions acquired from the literature. In the literature, this is the first application of MEBO for solving MOOPF problems. The results demonstrate that MEBO performs better than most other alternatives; this shows potential for further improvements with respect to the MOOPF problem.<\/jats:p>","DOI":"10.3390\/biomimetics11060418","type":"journal-article","created":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T05:59:47Z","timestamp":1781503187000},"page":"418","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Implementation of Modified Effective Butterfly Optimizer in Solving Multi-Objective Pareto Optimal Power Flow Problem with Renewable Uncertainties"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6465-8480","authenticated-orcid":false,"given":"Hakan","family":"I\u015f\u0131ker","sequence":"first","affiliation":[{"name":"Electrical & Electronics Engineering Department, Faculty of Engineering, Mersin University, Mersin 33100, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3312-992X","authenticated-orcid":false,"given":"Ali","family":"Akda\u011fl\u0131","sequence":"additional","affiliation":[{"name":"Electrical & Electronics Engineering Department, Faculty of Engineering, Mersin University, Mersin 33100, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0331-8818","authenticated-orcid":false,"given":"Volkan","family":"Yama\u00e7l\u0131","sequence":"additional","affiliation":[{"name":"Computer Engineering Department, Faculty of Engineering, Mersin University, Mersin 33100, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5918-6565","authenticated-orcid":false,"given":"Zeki","family":"Yetgin","sequence":"additional","affiliation":[{"name":"Computer Engineering Department, Faculty of Engineering, Mersin University, Mersin 33100, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6164-2048","authenticated-orcid":false,"given":"\u0130brahim \u00c7a\u011fr\u0131","family":"Barut\u00e7u","sequence":"additional","affiliation":[{"name":"Electricity and Energy Department, Hakkari University, Hakkari 30000, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kadir","family":"Abac\u0131","sequence":"additional","affiliation":[{"name":"Electrical & Electronics Engineering Department, Faculty of Engineering, Mersin University, Mersin 33100, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9379-2163","authenticated-orcid":false,"given":"Furkan","family":"G\u00f6z\u00fckara","sequence":"additional","affiliation":[{"name":"Computer Engineering Department, Faculty of Engineering, Mersin University, Mersin 33100, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,13]]},"reference":[{"key":"ref_1","first-page":"431","article-title":"Contribution a l\u2019etude Du Dispaching Economique","volume":"8","author":"Carpentier","year":"1962","journal-title":"Bull. Soc. Fr. Electr."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1016\/j.asoc.2016.06.022","article-title":"A Modified MOEA\/D Approach to the Solution of Multi-Objective Optimal Power Flow Problem","volume":"47","author":"Zhang","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"77837","DOI":"10.1109\/ACCESS.2022.3193371","article-title":"Multiobjective Optimal Power Flow Using Multiobjective Search Group Algorithm","volume":"10","author":"Huy","year":"2022","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1049\/ip-gtd:19981655","article-title":"Optimal Weight Assessment Based on a Range of Objectives in a Multiobjective Optimal Load Flow Study","volume":"145","author":"Nangia","year":"1998","journal-title":"IEE Proc. Gener. Transm. Distrib."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.energy.2011.11.028","article-title":"Optimal Power Flow Solutions through Multi-Objective Programming","volume":"42","author":"Salgado","year":"2012","journal-title":"Energy"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2536","DOI":"10.1080\/15325008.2023.2239237","article-title":"Multi-Objective Optimal Power Flow Using a Modified Weighted Teaching-Learning Based Optimization Algorithm","volume":"51","year":"2023","journal-title":"Electr. Power Compon. Syst."},{"key":"ref_7","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":"Karami","year":"2013","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.1007\/s40998-023-00631-8","article-title":"Multi-Objective Optimal Power Flow Employing a Hybrid Sine Cosine\u2013Grey Wolf Optimizer","volume":"47","author":"Keswani","year":"2023","journal-title":"Iran. J. Sci. Technol.\u2014Trans. Electr. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1080\/23080477.2023.2171696","article-title":"A Chaotic Equilibrium Optimization for Temperature-Dependent Optimal Power Flow","volume":"11","author":"Dao","year":"2023","journal-title":"Smart Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"107796","DOI":"10.1016\/j.epsr.2022.107796","article-title":"A Improved Archimedes Optimization Algorithm for Multi\/Single-Objective Optimal Power Flow","volume":"206","author":"Akdag","year":"2022","journal-title":"Electr. Power Syst. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"e2743","DOI":"10.1002\/etep.2743","article-title":"An Improved Moth-Flame Optimization Algorithm for Solving Optimal Power Flow Problem","volume":"29","author":"Taher","year":"2019","journal-title":"Int. Trans. Electr. Energy Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ijepes.2015.12.021","article-title":"Differential Search Algorithm for Solving Multi-Objective Optimal Power Flow Problem","volume":"79","author":"Abaci","year":"2016","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.asoc.2016.01.041","article-title":"Optimal Power Flow Using an Improved Colliding Bodies Optimization Algorithm","volume":"42","author":"Bouchekara","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"121212","DOI":"10.1016\/j.eswa.2023.121212","article-title":"Optimal Power Flow Using a Hybridization Algorithm of Arithmetic Optimization and Aquila Optimizer","volume":"235","author":"Ahmadipour","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"110230","DOI":"10.1016\/j.compeleceng.2025.110230","article-title":"Optimal Power Flow Solutions for Normal and Critical Loading Scenarios Using Hybrid Rao-2 Sine Cosine Algorithm","volume":"123","author":"Mittal","year":"2025","journal-title":"Comput. Electr. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"110922","DOI":"10.1016\/j.compeleceng.2025.110922","article-title":"Hybrid Brown-Bear and Hippopotamus Optimization with Quasi-Opposition-Based Learning for Optimal Power Flow with Renewable Energy Integration","volume":"131","author":"Lahdeb","year":"2026","journal-title":"Comput. Electr. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"6420","DOI":"10.1016\/j.energy.2011.09.027","article-title":"A Modified Shuffle Frog Leaping Algorithm for Multi-Objective Optimal Power Flow","volume":"36","author":"Niknam","year":"2011","journal-title":"Energy"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.asoc.2017.01.030","article-title":"An Enhanced Self-Adaptive Differential Evolution Based Solution Methodology for Multiobjective Optimal Power Flow","volume":"54","author":"Pulluri","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1016\/j.asoc.2014.04.010","article-title":"Multi-Objective Optimal Power Flow Using Quasi-Oppositional Teaching Learning Based Optimization","volume":"21","author":"Mandal","year":"2014","journal-title":"Appl. Soft Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1016\/j.enconman.2013.09.028","article-title":"A Modified Teaching-Learning Based Optimization for Multi-Objective Optimal Power Flow Problem","volume":"77","author":"Seifi","year":"2014","journal-title":"Energy Convers. Manag."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2999","DOI":"10.1007\/s00500-019-04077-1","article-title":"Multi-Objective Optimal Power Flow Solutions Using a Constraint Handling Technique of Evolutionary Algorithms","volume":"24","author":"Biswas","year":"2020","journal-title":"Soft Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.1111\/coin.12312","article-title":"Multiobjective Optimal Power Flow Using Interior Search Algorithm: A Case Study on a Real-Time Electrical Network","volume":"36","author":"Chandrasekaran","year":"2020","journal-title":"Comput. Intell."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Khunkitti, S., Siritaratiwat, A., and Premrudeepreechacharn, S. (2021). Multi-Objective Optimal Power Flow Problems Based on Slime Mould Algorithm. Sustainability, 13.","DOI":"10.3390\/su13137448"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Al-Kaabi, M., Dumbrava, V., and Eremia, M. (2022). Single and Multi-Objective Optimal Power Flow Based on Hunger Games Search with Pareto Concept Optimization. Energies, 15.","DOI":"10.3390\/en15228328"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Mallala, B., Papana, V.P., Sangu, R., Palle, K., and Chinthalacheruvu, V.K.R. (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_26","doi-asserted-by":"crossref","unstructured":"Diab, H., Abdelsalam, M., and Abdelbary, A. (2021). A Multi-objective Optimal Power Flow Control of Electrical Transmission Networks Using Intelligent Meta-heuristic Optimization Techniques. Sustainability, 13.","DOI":"10.3390\/su13094979"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Wu, Z., Liu, H., Zhao, J., and Li, Z. (2023). An Improved MOEA\/D Algorithm for the Solution of the Multi-Objective Optimal Power Flow Problem. Processes, 11.","DOI":"10.3390\/pr11020337"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Alsokhiry, F. (2025). Leveraging Harris Hawks Optimization for Enhanced Multi-Objective Optimal Power Flow in Complex Power Systems. Energies, 18.","DOI":"10.3390\/en18010018"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"ElMessmary, M.H., Diab, H.Y., Abdelsalam, M., and Moussa, M.F. (2024). A Novel Optimization Algorithm Inspired by Egyptian Stray Dogs for Solving Multi-Objective Optimal Power Flow Problems. Appl. Syst. Innov., 7.","DOI":"10.3390\/asi7060122"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Hakmi, S.H., Alnami, H., Faiya, B.M.A., and Moustafa, G. (2025). Multidimensional Optimal Power Flow with Voltage Profile Enhancement in Electrical Systems via Honey Badger Algorithm. Biomimetics, 10.","DOI":"10.3390\/biomimetics10120836"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"e32862","DOI":"10.1016\/j.heliyon.2024.e32862","article-title":"Modified Effective Butterfly Optimizer for Solving Optimal Power Flow Problem","volume":"10","author":"Abaci","year":"2024","journal-title":"Heliyon"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"109293","DOI":"10.1109\/ACCESS.2024.3439021","article-title":"Solving Optimal Power Flow Control Problem Using Honey Formation Optimization Algorithm","volume":"12","author":"Abaci","year":"2024","journal-title":"IEEE Access"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Shaheen, M.A.M., Ullah, Z., Qais, M.H., Hasanien, H.M., Chua, K.J., Tostado-V\u00e9liz, M., Turky, R.A., Jurado, F., and Elkadeem, M.R. (2022). Solution of Probabilistic Optimal Power Flow Incorporating Renewable Energy Uncertainty Using a Novel Circle Search Algorithm. Energies, 15.","DOI":"10.3390\/en15218303"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4135","DOI":"10.1038\/s41598-024-54510-1","article-title":"Economical-Environmental-Technical Optimal Power Flow Solutions Using a Novel Self-Adaptive Wild Geese Algorithm with Stochastic Wind and Solar Power","volume":"14","author":"Akbari","year":"2024","journal-title":"Sci. Rep."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"10647","DOI":"10.1038\/s41598-023-37635-7","article-title":"Multi-Objective Pathfinder Algorithm for Multi-Objective Optimal Power Flow Problem with Random Renewable Energy Sources: Wind, Photovoltaic and Tidal","volume":"13","author":"Li","year":"2023","journal-title":"Sci. Rep."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Al-Kaabi, M., Dumbrava, V., and Eremia, M. (2024). Multi Criteria Frameworks Using New Meta-Heuristic Optimization Techniques for Solving Multi-Objective Optimal Power Flow Problems. Energies, 17.","DOI":"10.3390\/en17092209"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Nazari, A., and Abdi, H. (2023). Solving the Combined Heat and Power Economic Dispatch Problem in Different Scale Systems Using the Imperialist Competitive Harris Hawks Optimization Algorithm. Biomimetics, 8.","DOI":"10.3390\/biomimetics8080587"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"ALBaaj, B., and Kaplan, O. (2025). Enhanced COVID-19 Optimization Algorithm for Solving Multi-Objective Optimal Power Flow Problems with Uncertain Renewable Energy Sources: A Case Study of the Iraqi High-Voltage Grid. Energies, 18.","DOI":"10.3390\/en18030478"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1186\/s43067-025-00291-0","article-title":"An Intelligent Hybrid Metaheuristic for Assessing Techno-Economic and Environmental Performance in Renewable-Integrated Multi-Objective Power Flow Framework","volume":"13","author":"Katkar","year":"2026","journal-title":"J. Electr. Syst. Inf. Technol."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Alghamdi, A.S. (2023). Optimal Power Flow of Hybrid Wind\/Solar\/Thermal Energy Integrated Power Systems Considering Costs and Emissions via a Novel and Efficient Search Optimization Algorithm. Appl. Sci., 13.","DOI":"10.3390\/app13084760"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Abid, M., Belazzoug, M., Mouassa, S., Chanane, A., and Jurado, F. (2024). Multi-Objective Optimal Power Flow Analysis Incorporating Renewable Energy Sources and FACTS Devices Using Non-Dominated Sorting Kepler Optimization Algorithm. Sustainability, 16.","DOI":"10.3390\/su16219599"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"24275","DOI":"10.1038\/s41598-025-09164-y","article-title":"A Golden Jackal Based Optimal Operation and Optimization of a Virtual Power Plant Involving Renewable Resources","volume":"15","author":"Pandey","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Jiang, S., Yue, Y., Chen, C., Chen, Y., and Cao, L. (2024). A Multi-Objective Optimization Problem Solving Method Based on Improved Golden Jackal Optimization Algorithm and Its Application. Biomimetics, 9.","DOI":"10.3390\/biomimetics9050270"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Khamees, A.K., Abdelaziz, A.Y., Eskaros, M.R., Attia, M.A., and Sameh, M.A. (2023). Optimal Power Flow with Stochastic Renewable Energy Using Three Mixture Component Distribution Functions. Sustainability, 15.","DOI":"10.3390\/su15010334"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"e26427","DOI":"10.1016\/j.heliyon.2024.e26427","article-title":"Optimal Stochastic Power Flow Using Enhanced Multi-Objective Mayfly Algorithm","volume":"10","author":"Zhu","year":"2024","journal-title":"Heliyon"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Alanazi, M., Alanazi, A., Abdelaziz, A.Y., and Siano, P. (2023). Power Flow Optimization by Integrating Novel Metaheuristic Algorithms and Adopting Renewables to Improve Power System Operation. Appl. Sci., 13.","DOI":"10.3390\/app13010527"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Lu, K.H., Qian, W., Jiang, Y., and Zhong, Y.S. (2024). The Calibrated Safety Constraints Optimal Power Flow for the Operation of Wind-Integrated Power Systems. Processes, 12.","DOI":"10.3390\/pr12102272"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Riaz, M., Hanif, A., Hussain, S.J., Memon, M.I., Ali, M.U., and Zafar, A. (2021). An Optimization-Based Strategy for Solving Optimal Power Flow Problems in a Power System Integrated with Stochastic Solar and Wind Power Energy. Appl. Sci., 11.","DOI":"10.3390\/app11156883"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Shaheen, M.A.M., Hasanien, H.M., Mekhamer, S.F., Qais, M.H., Alghuwainem, S., Ullah, Z., Tostado-V\u00e9liz, M., Turky, R.A., Jurado, F., and Elkadeem, M.R. (2022). Probabilistic Optimal Power Flow Solution Using a Novel Hybrid Metaheuristic and Machine Learning Algorithm. Mathematics, 10.","DOI":"10.3390\/math10173036"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Yamaguti, L.d.C., Home-Ortiz, J.M., Pourakbari-Kasmaei, M., and Mantovani, J.R.S. (2023). Economic\/Environmental Optimal Power Flow Using a Multiobjective Convex Formulation. Energies, 16.","DOI":"10.3390\/en16124651"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Kumar, A., Misra, R.K., and Singh, D. (2017, January 5\u20138). Improving the Local Search Capability of Effective Butterfly Optimizer Using Covariance Matrix Adapted Retreat Phase. Proceedings of the 2017 IEEE Congress on Evolutionary Computation, CEC 2017\u2014Proceedings, Donostia, Spain.","DOI":"10.1109\/CEC.2017.7969524"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"95","DOI":"10.14257\/ijca.2014.7.6.10","article-title":"Minimization of Power Loss and Voltage Deviation by SVC Placement Using GA","volume":"7","author":"Dixit","year":"2014","journal-title":"Int. J. Control Autom."},{"key":"ref_53","first-page":"7","article-title":"Analysis of Distance Measures in Content Based Image Retrieval","volume":"14","author":"Sharma","year":"2014","journal-title":"Glob. J. Comput. Sci. Technol."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Tanabe, R., and Fukunaga, A.S. (2014, January 6\u201311). Improving the Search Performance of SHADE Using Linear Population Size Reduction. Proceedings of the 2014 IEEE Congress on Evolutionary Computation, CEC 2014, Beijing, China.","DOI":"10.1109\/CEC.2014.6900380"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Tanabe, R., and Fukunaga, A. (2013, January 20\u201323). Success-History Based Parameter Adaptation for Differential Evolution. Proceedings of the 2013 IEEE Congress on Evolutionary Computation, CEC 2013, Cancun, Mexico.","DOI":"10.1109\/CEC.2013.6557555"},{"key":"ref_56","unstructured":"Saadat, H. (2011). Power System Analysis, PSA Publishing LLC. [3rd ed.]."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1109\/TPAS.1974.293972","article-title":"Optimal Load Flow with Steady-State Security","volume":"PAS-93","author":"Alsac","year":"1974","journal-title":"IEEE Trans. Power Appar. Syst."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1016\/j.energy.2014.10.007","article-title":"Multi-Objective Optimal Power Flow Considering the Cost, Emission, Voltage Deviation and Power Losses Using Multi-Objective Modified Imperialist Competitive Algorithm","volume":"78","author":"Ghasemi","year":"2014","journal-title":"Energy"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"108334","DOI":"10.1016\/j.asoc.2021.108334","article-title":"Optimization of Optimal Power Flow Problem Using Multi-Objective Manta Ray Foraging Optimizer","volume":"116","author":"Kahraman","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"101850","DOI":"10.1016\/j.swevo.2025.101850","article-title":"Multi-Objective Optimal Power Flow Problem Using Constrained Dynamic Multitasking Multi-Objective Optimization Algorithm","volume":"93","author":"Zhu","year":"2025","journal-title":"Swarm Evol. Comput."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"106321","DOI":"10.1016\/j.asoc.2020.106321","article-title":"Application of Modified Pigeon-Inspired Optimization Algorithm and Constraint-Objective Sorting Rule on Multi-Objective Optimal Power Flow Problem","volume":"92","author":"Chen","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.asoc.2018.04.006","article-title":"Applications of Multi-Objective Dimension-Based Firefly Algorithm to Optimize the Power Losses, Emission, and Cost in Power Systems","volume":"68","author":"Chen","year":"2018","journal-title":"Appl. Soft Comput."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"e08631","DOI":"10.1016\/j.heliyon.2021.e08631","article-title":"Multiobjective Optimal Power Flow for Static Voltage Stability Margin Improvement","volume":"7","author":"Kyomugisha","year":"2021","journal-title":"Heliyon"},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Chen, G., Yi, X., Zhang, Z., and Lei, H. (2018). Solving the Multi-Objective Optimal Power Flow Problem Using the Multi-Objective Firefly Algorithm with a Constraints-Prior Pareto-Domination Approach. Energies, 11.","DOI":"10.3390\/en11123438"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.engappai.2014.01.016","article-title":"Decomposition-Based Modern Metaheuristic Algorithms for Multi-Objective Optimal Power Flow\u2014A Comparative Study","volume":"32","author":"Medina","year":"2014","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1109\/JSYST.2011.2162896","article-title":"Optimal Power Flow Solution Incorporating Wind Power","volume":"6","author":"Shi","year":"2012","journal-title":"IEEE Syst. J."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1007\/s10462-020-09906-6","article-title":"Performance Assessment of the Metaheuristic Optimization Algorithms: An Exhaustive Review","volume":"54","author":"Halim","year":"2021","journal-title":"Artif. Intell. Rev."}],"container-title":["Biomimetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/6\/418\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T01:40:01Z","timestamp":1782265201000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/6\/418"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,13]]},"references-count":67,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["biomimetics11060418"],"URL":"https:\/\/doi.org\/10.3390\/biomimetics11060418","relation":{},"ISSN":["2313-7673"],"issn-type":[{"value":"2313-7673","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,13]]}}}