{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T02:37:57Z","timestamp":1783478277821,"version":"3.55.0"},"reference-count":97,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,13]],"date-time":"2022-06-13T00:00:00Z","timestamp":1655078400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Technology Plan Project of Changzhou","award":["CJ20210155"],"award-info":[{"award-number":["CJ20210155"]}]},{"name":"Technology Plan Project of Changzhou","award":["21KJD520002"],"award-info":[{"award-number":["21KJD520002"]}]},{"name":"Technology Plan Project of Changzhou","award":["BRA2020152"],"award-info":[{"award-number":["BRA2020152"]}]},{"name":"Natural Science Foundation of the Jiangsu Higher Education Institutions of China","award":["CJ20210155"],"award-info":[{"award-number":["CJ20210155"]}]},{"name":"Natural Science Foundation of the Jiangsu Higher Education Institutions of China","award":["21KJD520002"],"award-info":[{"award-number":["21KJD520002"]}]},{"name":"Natural Science Foundation of the Jiangsu Higher Education Institutions of China","award":["BRA2020152"],"award-info":[{"award-number":["BRA2020152"]}]},{"name":"Jiangsu Province \u201c333\u201d","award":["CJ20210155"],"award-info":[{"award-number":["CJ20210155"]}]},{"name":"Jiangsu Province \u201c333\u201d","award":["21KJD520002"],"award-info":[{"award-number":["21KJD520002"]}]},{"name":"Jiangsu Province \u201c333\u201d","award":["BRA2020152"],"award-info":[{"award-number":["BRA2020152"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Big Data is impacting and changing the way we live, and its core lies in the use of machine learning to extract valuable information from huge amounts of data. Optimization problems are a common problem in many steps of machine learning. In the face of complex optimization problems, evolutionary computation has shown advantages over traditional methods. Therefore, many researchers are working on improving the performance of algorithms for solving various optimization problems in machine learning. The equilibrium optimizer (EO) is a member of evolutionary computation and is inspired by the mass balance model in environmental engineering. Using particles and their concentrations as search agents, it simulates the process of finding equilibrium states for optimization. In this paper, we propose an improved equilibrium optimizer (IEO) based on a decreasing equilibrium pool. IEO provides more sources of information for particle updates and maintains a higher population diversity. It can discard some exploration in later stages to enhance exploitation, thus achieving a better search balance. The performance of IEO is verified using 29 benchmark functions from IEEE CEC2017, a dynamic economic dispatch problem, a spacecraft trajectory optimization problem, and an artificial neural network model training problem. In addition, the changes in population diversity and computational complexity brought by the proposed method are analyzed.<\/jats:p>","DOI":"10.3390\/sym14061227","type":"journal-article","created":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T01:43:32Z","timestamp":1655171012000},"page":"1227","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["An Improved Equilibrium Optimizer with a Decreasing Equilibrium Pool"],"prefix":"10.3390","volume":"14","author":[{"given":"Lin","family":"Yang","sequence":"first","affiliation":[{"name":"School of Computer Information and Engineering, Changzhou Institute of Technology, Changzhou 213032, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhe","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Computer Information and Engineering, Changzhou Institute of Technology, Changzhou 213032, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanting","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Software and Big Data, Changzhou College of Information Technology, Changzhou 213164, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guozhong","family":"Tian","sequence":"additional","affiliation":[{"name":"School of Computer Information and Engineering, Changzhou Institute of Technology, Changzhou 213032, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1137\/16M1080173","article-title":"Optimization methods for large-scale machine learning","volume":"60","author":"Bottou","year":"2018","journal-title":"Siam Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3668","DOI":"10.1109\/TCYB.2019.2950779","article-title":"A survey of optimization methods from a machine learning perspective","volume":"50","author":"Sun","year":"2019","journal-title":"IEEE Trans. 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