{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T14:51:28Z","timestamp":1777387888114,"version":"3.51.4"},"reference-count":41,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2022,7,1]],"date-time":"2022-07-01T00:00:00Z","timestamp":1656633600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"EU Horizon 2020 research and innovation program under project TradeRES","award":["864276"],"award-info":[{"award-number":["864276"]}]},{"name":"EU Horizon 2020 research and innovation program under project TradeRES","award":["UIDB\/00760\/2020"],"award-info":[{"award-number":["UIDB\/00760\/2020"]}]},{"name":"EU Horizon 2020 research and innovation program under project TradeRES","award":["UIDP\/00760\/2020"],"award-info":[{"award-number":["UIDP\/00760\/2020"]}]},{"name":"EU Horizon 2020 research and innovation program under project TradeRES","award":["CEECIND\/02814\/2017"],"award-info":[{"award-number":["CEECIND\/02814\/2017"]}]},{"DOI":"10.13039\/501100001871","name":"GECAD research center","doi-asserted-by":"publisher","award":["864276"],"award-info":[{"award-number":["864276"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"GECAD research center","doi-asserted-by":"publisher","award":["UIDB\/00760\/2020"],"award-info":[{"award-number":["UIDB\/00760\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"GECAD research center","doi-asserted-by":"publisher","award":["UIDP\/00760\/2020"],"award-info":[{"award-number":["UIDP\/00760\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"GECAD research center","doi-asserted-by":"publisher","award":["CEECIND\/02814\/2017"],"award-info":[{"award-number":["CEECIND\/02814\/2017"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>The increased penetration of renewables in power distribution networks has motivated significant interest in local energy systems. One of the main goals of local energy markets is to promote the participation of small consumers in energy transactions. Such transactions in local energy markets can be modeled as a bi-level optimization problem in which players (e.g., consumers, prosumers, or producers) at the upper level try to maximize their profits, whereas a market mechanism at the lower level maximizes the energy transacted. However, the strategic bidding in local energy markets is a complex NP-hard problem, due to its inherently nonlinear and discontinued characteristics. Thus, this article proposes the application of a hybridized Cross Entropy Covariance Matrix Adaptation Evolution Strategy (CE-CMAES) to tackle such a complex bi-level problem. The proposed CE-CMAES uses cross entropy for global exploration of search space and covariance matrix adaptation evolution strategy for local exploitation. The CE-CMAES prevents premature convergence while efficiently exploring the search space, thanks to its adaptive step-size mechanism. The performance of the algorithm is tested through simulation in a practical distribution system with renewable energy penetration. The comparative analysis shows that CE-CMAES achieves superior results concerning overall cost, mean fitness, and Ranking Index (i.e., a metric used in the competition for evaluation) compared with state-of-the-art algorithms. Wilcoxon Signed-Rank Statistical test is also applied, demonstrating that CE-CMAES results are statistically different and superior from the other tested algorithms.<\/jats:p>","DOI":"10.3390\/en15134838","type":"journal-article","created":{"date-parts":[[2022,7,2]],"date-time":"2022-07-02T11:12:35Z","timestamp":1656760355000},"page":"4838","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Cross Entropy Covariance Matrix Adaptation Evolution Strategy for Solving the Bi-Level Bidding Optimization Problem in Local Energy Markets"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8065-9969","authenticated-orcid":false,"given":"Dharmesh","family":"Dabhi","sequence":"first","affiliation":[{"name":"M & V Patel Department of Electrical Engineering, CSPIT, Charusat University, Changa 388421, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0155-000X","authenticated-orcid":false,"given":"Kartik","family":"Pandya","sequence":"additional","affiliation":[{"name":"M & V Patel Department of Electrical Engineering, CSPIT, Charusat University, Changa 388421, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4172-4502","authenticated-orcid":false,"given":"Joao","family":"Soares","sequence":"additional","affiliation":[{"name":"GECAD, School of Engineering, Polytechnic of Porto, 4200-072 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8638-8373","authenticated-orcid":false,"given":"Fernando","family":"Lezama","sequence":"additional","affiliation":[{"name":"GECAD, School of Engineering, Polytechnic of Porto, 4200-072 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4560-9544","authenticated-orcid":false,"given":"Zita","family":"Vale","sequence":"additional","affiliation":[{"name":"GECAD, School of Engineering, Polytechnic of Porto, 4200-072 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2340628","DOI":"10.1155\/2018\/2340628","article-title":"Survey on complex optimization and simulation for the new power system paradigm","volume":"2018","author":"Soares","year":"2018","journal-title":"Complexity"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3898","DOI":"10.1109\/TPWRS.2017.2779540","article-title":"A Local Energy Market for Electricity and Hydrogen","volume":"33","author":"Xiao","year":"2018","journal-title":"IEEE Trans. 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