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The proposed EEO algorithm includes a new performance reinforcement strategy with the L\u00e9vy Flight mechanism. The algorithm addresses the shortcomings of the original Equilibrium Optimizer (EO) and aims to provide better solutions (than those provided by EO) to global optimization problems, especially OPF problems. The proposed EEO efficiency was confirmed by comparing its results on the ten functions of the CEC\u201920 test suite, to those of other algorithms, including high-performance algorithms, i.e., CMA-ES, IMODE, AGSK and LSHADE_cnEpSin. Moreover, the statistical significance of these results was validated by the Wilcoxon\u2019s rank-sum test. After that, the proposed EEO was applied to solve the the OPF problem. The OPF is formulated as a nonlinear optimization problem with conflicting objectives and subjected to both equality and inequality constraints. The performance of this technique is deliberated and evaluated on the standard IEEE 30-bus test system for different objectives. The obtained results of the proposed EEO algorithm is compared to the original EO algorithm and those obtained using other techniques mentioned in the literature. These Simulation results revealed that the proposed algorithm provides better optimized solutions than 20 published methods and results as well as the original EO algorithm. The EEO superiority was demonstrated through six different cases, that involved the minimization of different objectives: fuel cost, fuel cost with valve-point loading effect, emission, total active power losses, voltage deviation, and voltage instability. Also, the comparison results indicate that EEO algorithm can provide a robust, high-quality feasible solutions for different OPF problems.<\/jats:p>","DOI":"10.1007\/s10489-022-03796-7","type":"journal-article","created":{"date-parts":[[2022,7,18]],"date-time":"2022-07-18T08:02:40Z","timestamp":1658131360000},"page":"7232-7253","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":73,"title":["Development and application of equilibrium optimizer for optimal power flow calculation of power system"],"prefix":"10.1007","volume":"53","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8127-7233","authenticated-orcid":false,"given":"Essam H.","family":"Houssein","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohamed H.","family":"Hassan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohamed A.","family":"Mahdy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Salah","family":"Kamel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,7,18]]},"reference":[{"issue":"16","key":"3796_CR1","doi-asserted-by":"publisher","first-page":"4265","DOI":"10.3390\/en13164265","volume":"13","author":"A Khan","year":"2020","unstructured":"Khan A, Hizam H, Abdul-Wahab NI, Othman ML (2020) Solution of optimal power flow using non-dominated sorting multi objective based hybrid firefly and particle swarm optimization algorithm. 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