{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T18:23:32Z","timestamp":1783535012143,"version":"3.55.0"},"reference-count":31,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T00:00:00Z","timestamp":1759881600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12502146"],"award-info":[{"award-number":["12502146"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12202214"],"award-info":[{"award-number":["12202214"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["ZKLIVCS-202406"],"award-info":[{"award-number":["ZKLIVCS-202406"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["ZR2024QF188"],"award-info":[{"award-number":["ZR2024QF188"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Zhejiang Key Laboratory of Intelligent Vehicle Comprehensive Safety","award":["12502146"],"award-info":[{"award-number":["12502146"]}]},{"name":"Zhejiang Key Laboratory of Intelligent Vehicle Comprehensive Safety","award":["12202214"],"award-info":[{"award-number":["12202214"]}]},{"name":"Zhejiang Key Laboratory of Intelligent Vehicle Comprehensive Safety","award":["ZKLIVCS-202406"],"award-info":[{"award-number":["ZKLIVCS-202406"]}]},{"name":"Zhejiang Key Laboratory of Intelligent Vehicle Comprehensive Safety","award":["ZR2024QF188"],"award-info":[{"award-number":["ZR2024QF188"]}]},{"DOI":"10.13039\/501100007129","name":"Shandong Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["12502146"],"award-info":[{"award-number":["12502146"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Shandong Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["12202214"],"award-info":[{"award-number":["12202214"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Shandong Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["ZKLIVCS-202406"],"award-info":[{"award-number":["ZKLIVCS-202406"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Shandong Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["ZR2024QF188"],"award-info":[{"award-number":["ZR2024QF188"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, a pattern synthesis method of uniform linear and concentric elliptical antenna arrays using the Kepler optimization algorithm (KOA) is proposed. The KOA, which utilizes Kepler\u2019s laws to predict the position and velocity of planets at arbitrary times, is first applied to deal with the optimization problems of linear and elliptical antenna arrays. Radiation patterns with high gain and low sidelobe levels (SLLs) are synthesized by optimizing the critical parameters (amplitude, phase, and rotation) of the linear arrays. Moreover, a concentric elliptical array is designed to demonstrate the capability of the KOA framework to solve complex problems and achieve the desired performance. In order to accurately consider mutual coupling between the elements, the full-wave method of moments (MoM) is used to calculate the radiation characteristics of the arrays in the optimization method. The effectiveness of the proposed method is proved by four typical examples. The results show that, compared with the butterfly optimization algorithm (BOA), Harris hawks optimization (HHO), and crayfish optimization algorithm (COA), the proposed method possesses high gain and SLL suppression capabilities, which makes it suitable for various array types.<\/jats:p>","DOI":"10.3390\/sym17101680","type":"journal-article","created":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T08:22:08Z","timestamp":1759911728000},"page":"1680","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Pattern Synthesis for Uniform Linear and Concentric Elliptical Antenna Arrays Using Kepler Optimization Algorithm"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8128-7610","authenticated-orcid":false,"given":"Yi","family":"Tang","sequence":"first","affiliation":[{"name":"School of Electromechanical and Automotive Engineering, Yantai University, Yantai 264005, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-3847-368X","authenticated-orcid":false,"given":"Jiaxin","family":"Wan","sequence":"additional","affiliation":[{"name":"School of Electromechanical and Automotive Engineering, Yantai University, Yantai 264005, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yixin","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Electromechanical and Automotive Engineering, Yantai University, Yantai 264005, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electromechanical and Automotive Engineering, Yantai University, Yantai 264005, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guoqing","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Electromechanical and Automotive Engineering, Yantai University, Yantai 264005, China"},{"name":"Zhejiang Key Laboratory of Intelligent Vehicle Comprehensive Safety, Geely Automobile Research Institute (Ningbo) Co., Ltd., Ningbo 315336, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chuan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Ningbo University, Ningbo 315211, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1109\/TAP.2022.3226147","article-title":"Optimal pattern synthesis for polarimetric phased array antenna using representative array patterns","volume":"71","author":"Zhou","year":"2023","journal-title":"IEEE Trans. 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