{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T15:05:13Z","timestamp":1789571113304,"version":"build-2803163510"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T00:00:00Z","timestamp":1789516800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100007847","name":"Jilin Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["YDZJ202501ZYTS367"],"award-info":[{"award-number":["YDZJ202501ZYTS367"]}],"id":[{"id":"10.13039\/100007847","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>Particle swarm optimization (PSO) is a widely used bio-inspired optimization method. However, global guidance can align particle trajectories, reduce population diversity, and lead to premature convergence. To address this issue, we propose GRACE-PSO, a particle swarm optimizer based on group rank assessment and cooperative evolution. The method introduces group-best learning as an intermediate layer between personal-best and global-best learning to improve the balance between exploration and exploitation. GRACE-PSO integrates three coupled mechanisms: (1) a group-learning update that provides the population with multiple group-specific search directions; (2) a rank-based group-utility assessment that evaluates relative search effectiveness through pairwise comparisons of personal-best fitness values; and (3) a utility-driven adaptive strategy that adjusts the strengths of group-best and global-best learning and selectively reinitializes a small number of underperforming particles in stagnant groups. Experiments on 29 CEC 2017 benchmark functions at 30 and 50 dimensions against seven representative PSO methods show that GRACE-PSO achieves average ranks of 1.2414 and 1.3793, respectively. Experiments on two practical flexible intelligent metasurface optimization problems further demonstrate its competitive performance and practical applicability.<\/jats:p>","DOI":"10.3390\/biomimetics11090664","type":"journal-article","created":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T13:50:27Z","timestamp":1789566627000},"page":"664","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["GRACE-PSO: Particle Swarm Optimization with Group Rank Assessment and Cooperative Evolution"],"prefix":"10.3390","volume":"11","author":[{"given":"Honggang","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Changchun University of Science and Technology, Changchun 130022, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]},{"given":"Jinxiao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Changchun University of Science and Technology, Changchun 130022, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"given":"Yufei","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Changchun University, Changchun 130022, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-3180-1931","authenticated-orcid":false,"given":"Lidong","family":"Gu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Changchun University of Science and Technology, Changchun 130022, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"given":"Pengyu","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Instrumentation and Electrical Engineering, Jilin University, Changchun 130061, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,16]]},"reference":[{"key":"ref_1","unstructured":"Kennedy, J., and Eberhart, R. 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