{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T23:22:39Z","timestamp":1780615359050,"version":"3.54.1"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T00:00:00Z","timestamp":1773100800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006407","name":"Natural Science Foundation of Henan","doi-asserted-by":"crossref","award":["252300421874"],"award-info":[{"award-number":["252300421874"]}],"id":[{"id":"10.13039\/501100006407","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Major Science and Technology Project of Nanyang","award":["25ZDZX007"],"award-info":[{"award-number":["25ZDZX007"]}]},{"name":"Interdisciplinary Sciences Project, Nanyang Institute of Technology"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The Particle swarm optimization (PSO) algorithm has strong universality and fast convergence speed, but when solving complex multimodal optimization problems, it is prone to fall into local optimum due to insufficient population diversity. To address this issue, this paper proposes a dual-population hybrid particle swarm optimization algorithm based on Hooke\u2019s law competition mechanism (HLCM-DHPSO). This algorithm integrates the differential evolution algorithm into the PSO framework, and the two subpopulation sizes dynamically compete for computing resources according to the adaptive mechanism of Hooke\u2019s law. When the algorithm stagnates, HLCM-DHPSO can automatically trace back to historical archives and adjust the inertia weight based on excellent experience data. Meanwhile, HLCM-DHPSO adaptively adjusts the acceleration coefficient through the Sine function to enhance the algorithm\u2019s ability to escape from local optimum. To verify the effectiveness of the HLCM-DHPSO algorithm, it is compared with eight advanced optimization algorithms on the CEC2017 benchmark test set. The experimental results show that HLCM-DHPSO significantly outperforms the comparison algorithms in terms of solution performance, especially in handling high-dimensional and multi-peak complex functions, demonstrating superior global search and optimization capabilities.<\/jats:p>","DOI":"10.3390\/a19030207","type":"journal-article","created":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T09:55:38Z","timestamp":1773136538000},"page":"207","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Dual-Population Hybrid Particle Swarm Optimization Algorithm Based on Hooke\u2019s Law Competition Mechanism"],"prefix":"10.3390","volume":"19","author":[{"given":"Yaopei","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer and Software, Nanyang Institute of Technology, Nanyang 473004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1321-1993","authenticated-orcid":false,"given":"Yufeng","family":"Wang","sequence":"additional","affiliation":[{"name":"Academy for Electronic Information Discipline Studies, Nanyang Institute of Technology, Nanyang 473004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haoxing","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer and Software, Nanyang Institute of Technology, Nanyang 473004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanan","family":"Du","sequence":"additional","affiliation":[{"name":"School of Computer and Software, Nanyang Institute of Technology, Nanyang 473004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pingping","family":"Shan","sequence":"additional","affiliation":[{"name":"School of Computer and Software, Nanyang Institute of Technology, Nanyang 473004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1942","DOI":"10.1109\/ICNN.1995.488968","article-title":"Particle swarm optimization","volume":"Volume 4","author":"Kennedy","year":"1995","journal-title":"Proceedings of ICNN\u201995-International Conference on Neural Networks"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.swevo.2018.04.006","article-title":"A fitness-based multi-role particle swarm optimization","volume":"44","author":"Xia","year":"2019","journal-title":"Swarm Evol. Comput."},{"key":"ref_3","first-page":"931256","article-title":"A comprehensive survey on particle swarm optimization algorithm and its applications","volume":"2015","author":"Zhang","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1162\/EVCO_r_00180","article-title":"Particle swarm optimization for single objective continuous space problems: A review","volume":"25","author":"Bonyadi","year":"2017","journal-title":"Evol. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s10462-013-9400-4","article-title":"A review on particle swarm optimization algorithm and its variants to clustering high-dimensional data","volume":"44","author":"Esmin","year":"2015","journal-title":"Artif. Intell. Rev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"7056","DOI":"10.3934\/mbe.2023305","article-title":"A novel particle swarm optimization based on hybrid-learning model","volume":"20","author":"Wang","year":"2023","journal-title":"Math. Biosci. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s10586-024-04783-y","article-title":"A novel hybrid differential particle swarm optimization based on particle influence","volume":"28","author":"Wang","year":"2025","journal-title":"Clust. Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"101212","DOI":"10.1016\/j.swevo.2022.101212","article-title":"Elite archives-driven particle swarm optimization for large scale numerical optimization and its engineering applications","volume":"76","author":"Zhang","year":"2023","journal-title":"Swarm Evol. Comput."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1118","DOI":"10.1002\/mma.7839","article-title":"Generation of quasi-developable Q-B\u00e9zier strip via PSO-based shape parameters optimization","volume":"45","author":"Cao","year":"2022","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1362","DOI":"10.1109\/TSMCB.2009.2015956","article-title":"Adaptive particle swarm optimization","volume":"39","author":"Zhan","year":"2009","journal-title":"IEEE Trans. Syst. Man Cybern. Part B Cybern."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"114343","DOI":"10.1016\/j.asoc.2025.114343","article-title":"A dual-stage dual-population evolutionary algorithm using new adaptive environmental selection method for complex constrained multi-objective optimization","volume":"187","author":"Deng","year":"2025","journal-title":"Appl. Soft Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2393","DOI":"10.1109\/CEC.2003.1299387","article-title":"Hybrid evolutionary algorithms based on PSO and GA","volume":"Volume 4","author":"Shi","year":"2003","journal-title":"The 2003 Congress on Evolutionary Computation, 2003. CEC\u201903"},{"key":"ref_13","first-page":"3816","article-title":"DEPSO: Hybrid particle swarm with differential evolution operator","volume":"Volume 4","author":"Zhang","year":"2003","journal-title":"SMC\u201903 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme-System Security and Assurance (Cat. No. 03CH37483)"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Shi, Y., and Eberhart, R. (1998). A modified particle swarm optimizer. Proceedings of the 1998 IEEE International Conference on Evolutionary Computation (ICEC 1998), IEEE.","DOI":"10.1109\/ICEC.1998.699146"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1109\/TEVC.2004.826071","article-title":"Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients","volume":"8","author":"Ratnaweera","year":"2004","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2531","DOI":"10.1007\/s11831-021-09694-4","article-title":"Particle swarm optimization algorithm and its applications: A systematic review","volume":"29","author":"Gad","year":"2022","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4862","DOI":"10.1109\/TCYB.2019.2943928","article-title":"Triple archives particle swarm optimization","volume":"50","author":"Xia","year":"2019","journal-title":"IEEE Trans. Cybern."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1016\/j.swevo.2018.07.002","article-title":"Global genetic learning particle swarm optimization with diversity enhancement by ring topology","volume":"44","author":"Lin","year":"2019","journal-title":"Swarm Evol. Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"120432","DOI":"10.1016\/j.ins.2024.120432","article-title":"An adaptive population size based Differential Evolution by mining historical population similarity for path planning of unmanned aerial vehicles","volume":"666","author":"Cao","year":"2024","journal-title":"Inf. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"102808","DOI":"10.1016\/j.parco.2021.102808","article-title":"PEAB: A pool-based distributed evolutionary algorithm model with buffer","volume":"106","author":"Yu","year":"2021","journal-title":"Parallel Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/j.matcom.2022.12.020","article-title":"Multi-sample learning particle swarm optimization with adaptive crossover operation","volume":"208","author":"Yang","year":"2023","journal-title":"Math. Comput. Simul."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1109\/TEVC.2018.2875430","article-title":"Coevolutionary particle swarm optimization with bottleneck objective learning strategy for many-objective optimization","volume":"23","author":"Liu","year":"2018","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1567","DOI":"10.1016\/j.ins.2022.07.131","article-title":"Elite-ordinary synergistic particle swarm optimization","volume":"609","author":"Zhao","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_24","first-page":"26","article-title":"A GA-PSO hybrid algorithm based neural network modeling technique for short-term wind power forecasting","volume":"33","author":"Semero","year":"2018","journal-title":"Distrib. Gener. Altern. Energy J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.1007\/s12065-021-00568-z","article-title":"An adaptive mutation strategy for differential evolution algorithm based on particle swarm optimization","volume":"15","author":"Dixit","year":"2022","journal-title":"Evol. Intell."},{"key":"ref_26","first-page":"83","article-title":"Research on vehicle routing planning based on adaptive ant colony and particle swarm optimization algorithm","volume":"19","author":"Jiang","year":"2021","journal-title":"Int. J. Intell. Transp. Syst. Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1007\/s11004-020-09864-3","article-title":"A comparison of extremal optimization, differential evolution and particle swarm optimization methods for well placement design in groundwater management","volume":"53","author":"Redoloza","year":"2021","journal-title":"Math. Geosci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s12065-020-00486-6","article-title":"Hybridizing salp swarm algorithm with particle swarm optimization algorithm for recent optimization functions","volume":"15","author":"Singh","year":"2022","journal-title":"Evol. Intell."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4849","DOI":"10.1007\/s00521-018-3878-2","article-title":"An integrated particle swarm optimization approach hybridizing a new self-adaptive particle swarm optimization with a modified differential evolution","volume":"32","author":"Tang","year":"2020","journal-title":"Neural Comput. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Chernyak, Y., Mohammad, I.A., Masnicak, N., Pivoluska, M., and Plesch, M. (2024). Harmonic Oscillator based Particle Swarm Optimization. PLoS ONE, 20.","DOI":"10.1371\/journal.pone.0326173"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"5129","DOI":"10.1109\/ACCESS.2025.3525850","article-title":"Convergence-Driven Adaptive Many-Objective Particle Swarm Optimization","volume":"13","author":"Yi","year":"2025","journal-title":"IEEE Access"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Chen, J., Wang, Y., Shao, Z., Zeng, H., and Zhao, S. (2025). Dual-Population Cooperative Correlation Evolutionary Algorithm for Constrained Multi-Objective Optimization. Mathematics, 13.","DOI":"10.3390\/math13091441"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4518","DOI":"10.1038\/s41598-024-82648-5","article-title":"A hybrid differential evolution particle swarm optimization algorithm based on dynamic strategies","volume":"15","author":"Xu","year":"2026","journal-title":"Sci. Rep."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"108780","DOI":"10.1016\/j.compbiomed.2024.108780","article-title":"DRPSO: A multi-strategy fusion particle swarm optimization algorithm with a replacement mechanisms for colon cancer pathology image segmentation","volume":"178","author":"Hu","year":"2024","journal-title":"Comput. Biol. Med."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"101222","DOI":"10.1016\/j.swevo.2022.101222","article-title":"Incorporating surprisingly popular algorithm and euclidean distance-based adaptive topology into PSO","volume":"76","author":"Wu","year":"2023","journal-title":"Swarm Evol. Comput."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1109\/TEVC.2004.826069","article-title":"A cooperative approach to particle swarm optimization","volume":"8","author":"Engelbrecht","year":"2004","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"120104","DOI":"10.1016\/j.ins.2024.120104","article-title":"Collaborative resource allocation-based differential evolution for solving numerical optimization problems","volume":"660","author":"Li","year":"2024","journal-title":"Inf. Sci."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"13733","DOI":"10.1007\/s00521-022-07193-6","article-title":"Enhancing firefly algorithm with sliding window for continuous optimization problems","volume":"34","author":"Peng","year":"2022","journal-title":"Neural Comput. Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1016\/j.future.2019.02.028","article-title":"Harris hawks optimization: Algorithm and applications","volume":"97","author":"Heidari","year":"2019","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.advengsoft.2016.01.008","article-title":"The whale optimization algorithm","volume":"95","author":"Mirjalili","year":"2016","journal-title":"Adv. Eng. Softw."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/3\/207\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T05:37:29Z","timestamp":1773293849000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/3\/207"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,10]]},"references-count":40,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["a19030207"],"URL":"https:\/\/doi.org\/10.3390\/a19030207","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,10]]}}}