{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T00:35:03Z","timestamp":1780446903038,"version":"3.54.1"},"reference-count":45,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,14]],"date-time":"2022-02-14T00:00:00Z","timestamp":1644796800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In mechanism design with symmetrical or asymmetrical motions, obtaining high precision of the input path given by working requirements of mechanisms can be a challenge for dimensional optimization. This study proposed a novel hybrid-combined differential evolution (DE) and Jaya algorithm for the dimensional synthesis of four-bar mechanisms with symmetrical motions, called HCDJ. The suggested algorithm uses modified initialization, a hybrid-combined mutation between the classical DE and Jaya algorithm, and the elitist selection. The modified initialization allows generating initial individuals, which are satisfied with Grashof\u2019s condition and consequential constraints. In the hybrid-combined mutation, three differential groups of mutations are combined. DE\/best\/1 and DE\/best\/2, DE\/current to best\/1 and Jaya operator, and DE\/rand\/1, and DE\/rand\/2 belong to the first, second, and third groups, respectively. In the second group, DE\/current to best\/1 is hybrid with the Jaya operator. Additionally, the elitist selection is also applied in HCDJ to find the best solutions for the next generation. To validate the feasibility of HCDJ, the numerical examples of the symmetrical motion of four-bar mechanisms are investigated. From the results, the proposed algorithm can provide accurate optimal solutions that are better than the original DE and Jaya methods, and its solutions are even better than those of many other algorithms that are available in the literature.<\/jats:p>","DOI":"10.3390\/sym14020381","type":"journal-article","created":{"date-parts":[[2022,2,14]],"date-time":"2022-02-14T20:58:03Z","timestamp":1644872283000},"page":"381","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["A New Study on Optimization of Four-Bar Mechanisms Based on a Hybrid-Combined Differential Evolution and Jaya Algorithm"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8234-7013","authenticated-orcid":false,"given":"Sy","family":"Nguyen-Van","sequence":"first","affiliation":[{"name":"Faculty of Mechanical Engineering, Thai Nguyen University of Technology, 3-2 Street, Thai Nguyen City 250000, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9818-9195","authenticated-orcid":false,"given":"Qui X.","family":"Lieu","sequence":"additional","affiliation":[{"name":"Faculty of Civil Engineering, Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet Street, Ward 14, District 10, Ho Chi Minh City 700000, Vietnam"},{"name":"Vietnam National University Ho Chi Minh City (VNU-HCM), Linh Trung Ward, Thu Duc District, Ho Chi Minh City 700000, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5632-9399","authenticated-orcid":false,"given":"Nguyen","family":"Xuan-Mung","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical and Aerospace Engineering, Sejong University, Seoul 05006, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2215-9587","authenticated-orcid":false,"given":"Thi Thanh Nga","family":"Nguyen","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Thai Nguyen University of Technology, 3-2 Street, Thai Nguyen City 250000, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,14]]},"reference":[{"key":"ref_1","first-page":"81","article-title":"Advanced mechanism design: Analysis and synthesis","volume":"20","author":"Freudenstein","year":"1985","journal-title":"Mech. 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