{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T14:13:37Z","timestamp":1760710417366,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,18]],"date-time":"2020-11-18T00:00:00Z","timestamp":1605657600000},"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":["21876187"],"award-info":[{"award-number":["21876187"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>As a novel meta-heuristic algorithm, the Whale Optimization Algorithm (WOA) has well performance in solving optimization problems. However, WOA usually tends to trap in local optimal and it suffers slow convergence speed for large-scale and high-dimension optimization problems. A modified whale optimization algorithm with single-dimensional swimming (abbreviated as SWWOA) is proposed in order to overcome the shortcoming. First, tent map is applied to generate the initialize population for maximize search ability. Second, quasi-opposition learning is adopted after every iteration for further improving the search ability. Third, a novel nonlinearly control parameter factor that is based on logarithm function is presented in order to balance exploration and exploitation. Additionally, the last, single-dimensional swimming is proposed in order to replace the prey behaviour in standard WOA for tuning. The simulation experiments were conducted on 20 well-known benchmark functions. The results show that the proposed SWWOA has better performance in solution precision and higher convergence speed than the comparison methods.<\/jats:p>","DOI":"10.3390\/sym12111892","type":"journal-article","created":{"date-parts":[[2020,11,18]],"date-time":"2020-11-18T07:41:00Z","timestamp":1605685260000},"page":"1892","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Modified Whale Optimization Algorithm with Single-Dimensional Swimming for Global Optimization Problems"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2089-5617","authenticated-orcid":false,"given":"Pengzhen","family":"Du","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiming","family":"Cheng","sequence":"additional","affiliation":[{"name":"Nanjing Research Institute of Electronic Engineering, Nanjing 210007, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ning","family":"Liu","sequence":"additional","affiliation":[{"name":"Nanjing Customs, Nanjing 210001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haofeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianfeng","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/j.ins.2018.10.046","article-title":"Large scale continuous global optimization based on micro differential evolution with local directional search","volume":"477","author":"Yildiz","year":"2019","journal-title":"Inf. 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