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evolution (DE) is one of the most extensively applied methods. However, it is difficult to choose appropriate control parameters and to avoid falling into local optimum and poor convergence when handling complex numerical optimization problems. To handle these problems, an improved DE (BROMLDE) with the Bernstein operator and refracted oppositional-mutual learning (ROML) is proposed, which can reduce parameter selection, converge faster, and avoid trapping in local optimum. Firstly, a new ROML strategy integrates mutual learning (ML) and refractive oppositional learning (ROL), achieving stochastic switching between ROL and ML during the population initialization and generation jumping period to balance exploration and exploitation. Meanwhile, a dynamic adjustment factor is constructed to improve the ability of the algorithm to jump out of the local optimum. Secondly, a Bernstein operator, which has no parameters setting and intrinsic parameters tuning phase, is introduced to improve convergence performance. Finally, the performance of BROMLDE is evaluated by 10 bound-constrained benchmark functions from CEC 2019 and CEC 2020, respectively. Two engineering optimization problems are utilized simultaneously. The comparative experimental results show that BROMLDE has higher global optimization capability and convergence speed on most functions and engineering problems.<\/jats:p>","DOI":"10.3390\/e24091205","type":"journal-article","created":{"date-parts":[[2022,8,29]],"date-time":"2022-08-29T21:01:31Z","timestamp":1661806891000},"page":"1205","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["An Enhanced Differential Evolution Algorithm with Bernstein Operator and Refracted Oppositional-Mutual Learning Strategy"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6094-8221","authenticated-orcid":false,"given":"Fengbin","family":"Wu","sequence":"first","affiliation":[{"name":"State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 550025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junxing","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4759-6000","authenticated-orcid":false,"given":"Shaobo","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dongchao","family":"Lv","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Guizhou University, Guiyang 550025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4528-0555","authenticated-orcid":false,"given":"Menghan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Guizhou University, Guiyang 550025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s12559-016-9442-4","article-title":"On Global Smooth Path Planning for Mobile Robots Using a Novel Multimodal Delayed PSO Algorithm","volume":"9","author":"Song","year":"2017","journal-title":"Cognit. 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