{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T13:57:08Z","timestamp":1784642228853,"version":"3.55.0"},"reference-count":38,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,9]],"date-time":"2021-06-09T00:00:00Z","timestamp":1623196800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This paper addresses the phase-balancing problem in three-phase power grids with the radial configuration from the perspective of master\u2013slave optimization. The master stage corresponds to an improved version of the Chu and Beasley genetic algorithm, which is based on the multi-point mutation operator and the generation of solutions using a Gaussian normal distribution based on the exploration and exploitation schemes of the vortex search algorithm. The master stage is entrusted with determining the configuration of the phases by using an integer codification. In the slave stage, a power flow for imbalanced distribution grids based on the three-phase version of the successive approximation method was used to determine the costs of daily energy losses. The objective of the optimization model is to minimize the annual operative costs of the network by considering the daily active and reactive power curves. Numerical results from a modified version of the IEEE 37-node test feeder demonstrate that it is possible to reduce the annual operative costs of the network by approximately 20% by using optimal load balancing. In addition, numerical results demonstrated that the improved version of the CBGA is at least three times faster than the classical CBGA, this was obtained in the peak load case for a test feeder composed of 15 nodes; also, the improved version of the CBGA was nineteen times faster than the vortex search algorithm. Other comparisons with the sine\u2013cosine algorithm and the black hole optimizer confirmed the efficiency of the proposed optimization method regarding running time and objective function values.<\/jats:p>","DOI":"10.3390\/computation9060067","type":"journal-article","created":{"date-parts":[[2021,6,9]],"date-time":"2021-06-09T04:22:22Z","timestamp":1623212542000},"page":"67","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Improved Genetic Algorithm for Phase-Balancing in Three-Phase Distribution Networks: A Master-Slave Optimization Approach"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6051-4925","authenticated-orcid":false,"given":"Oscar Danilo","family":"Montoya","sequence":"first","affiliation":[{"name":"Facultad de Ingenier\u00eda, Universidad Distrital Francisco Jos\u00e9 de Caldas, Bogot\u00e1 D.C. 11021, Colombia"},{"name":"Laboratorio Inteligente de Energ\u00eda, Universidad Tecnol\u00f3gica de Bol\u00edvar, Cartagena 131001, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2448-2174","authenticated-orcid":false,"given":"Alexander","family":"Molina-Cabrera","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda, Universidad Tecnol\u00f3gica de Pereira, Pereira 660003, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1409-9756","authenticated-orcid":false,"given":"Luis Fernando","family":"Grisales-Nore\u00f1a","sequence":"additional","affiliation":[{"name":"Grupo GIIEN, Facultad de Ingenier\u00eda, Instituci\u00f3n Universitaria Pascual Bravo, Medell\u00edn 050036, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8282-7826","authenticated-orcid":false,"given":"Ricardo Alberto","family":"Hincapi\u00e9","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda, Universidad Tecnol\u00f3gica de Pereira, Pereira 660003, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2016-6633","authenticated-orcid":false,"given":"Mauricio","family":"Granada","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda, Universidad Tecnol\u00f3gica de Pereira, Pereira 660003, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1016\/j.egypro.2017.11.069","article-title":"Investigation of MV Distribution Networks with High-Penetration Distributed PVs: Study for an Urban Area","volume":"141","author":"Temiz","year":"2017","journal-title":"Energy Procedia"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Cort\u00e9s-Caicedo, B., Avellaneda-G\u00f3mez, L.S., Montoya, O.D., Alvarado-Barrios, L., and Chamorro, H.R. 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