{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T06:21:47Z","timestamp":1770963707259,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T00:00:00Z","timestamp":1770336000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005269","name":"Anhui Provincial Department of Education","doi-asserted-by":"publisher","award":["2024AH051994"],"award-info":[{"award-number":["2024AH051994"]}],"id":[{"id":"10.13039\/501100005269","id-type":"DOI","asserted-by":"publisher"}]},{"name":"High-level Talent Start-up Project of West Anhui University","award":["WGKQ2024011"],"award-info":[{"award-number":["WGKQ2024011"]}]},{"name":"High-level Talent Start-up Project of West Anhui University","award":["WGKQ2023003"],"award-info":[{"award-number":["WGKQ2023003"]}]},{"name":"Wanxi University's Horizontal Research Project","award":["0045025103"],"award-info":[{"award-number":["0045025103"]}]},{"name":"Wanxi University's Horizontal Research Project","award":["0045025141"],"award-info":[{"award-number":["0045025141"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This paper proposes an Enhanced Projection-Iterative-Methods-based Optimizer (EPIMO) to overcome the limitations of its predecessor, the Projection-Iterative-Methods-based Optimizer (PIMO), including deterministic parameter decay, insufficient diversity maintenance, and static exploration\u2013exploitation balance. The enhancements incorporate three core strategies: (1) an adaptive decay strategy that introduces stochastic perturbations into the step-size evolution; (2) a mirror opposition-based learning strategy to actively inject structured population diversity; and (3) an adaptive adjustment mechanism for the L\u00e9vy flight parameter \u03b2 to enable phase-sensitive optimization behavior. The effectiveness of EPIMO is validated through a multi-stage experimental framework. Systematic evaluations on the CEC 2017 and CEC 2022 benchmark suites, alongside four classical engineering optimization problems (Himmelblau function, step-cone pulley design, hydrostatic thrust bearing design, and three-bar truss design), demonstrate its comprehensive superiority. The Wilcoxon rank-sum test confirms statistically significant performance improvements over its predecessor (PIMO) and a range of state-of-the-art and classical algorithms. EPIMO exhibits exceptional performance in convergence accuracy, stability, robustness, and constraint-handling capability, establishing it as a highly reliable and efficient metaheuristic optimizer. This research contributes a systematic, adaptive enhancement framework for projection-based metaheuristics, which can be generalized to improve other swarm intelligence systems when facing complex, constrained, and high-dimensional engineering optimization tasks.<\/jats:p>","DOI":"10.3390\/computation14020045","type":"journal-article","created":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T16:32:59Z","timestamp":1770395579000},"page":"45","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Enhanced Projection-Iterative-Methods-Based Optimizer for Complex Constrained Engineering Design Problems"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8988-1371","authenticated-orcid":false,"given":"Xuemei","family":"Zhu","sequence":"first","affiliation":[{"name":"Experimental Training Teaching Management Department, West Anhui University, Yu\u2019an District, Lu\u2019an 237012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Han","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Electrical and Optoelectronic Engineering, West Anhui University, Yu\u2019an District, Lu\u2019an 237012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haoyu","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Electrical and Optoelectronic Engineering, West Anhui University, Yu\u2019an District, Lu\u2019an 237012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Artificial Intelligence, West Anhui University, Yu\u2019an District, Lu\u2019an 237012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shirong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Automotive Technology, Anhui Vocational College of Defense Technology, Yu\u2019an District, Lu\u2019an 237011, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Artificial Intelligence, West Anhui University, Yu\u2019an District, Lu\u2019an 237012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,6]]},"reference":[{"key":"ref_1","first-page":"4209","article-title":"Machine learning optimization techniques: A survey, classification, challenges, and future research issues","volume":"31","author":"Bian","year":"2024","journal-title":"Arch. 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