{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T15:39:51Z","timestamp":1772206791824,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T00:00:00Z","timestamp":1753660800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011789","name":"Foundation of the Jilin Provincial Department of Science and Technology","doi-asserted-by":"publisher","award":["YDZJ202201ZYTS565"],"award-info":[{"award-number":["YDZJ202201ZYTS565"]}],"id":[{"id":"10.13039\/501100011789","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The Tree\u2013Seed Algorithm (TSA) is a symmetry-driven metaheuristic algorithm that shows potential for complex optimization problems, but it suffers from local optimum entrapment and slow convergence. To address these limitations, we propose the ADTSA algorithm. First, ADTSA adopts a symmetry-driven dual-layer framework for seed generation, which promotes effective information exchange between subpopulations and accelerates convergence speed. In later iterations, ADTSA enhances the population\u2019s exploitation ability through a population fusion mechanism, further improving the convergence speed. Moreover, we propose a historical optimal solution archiving and replacement mechanism, along with a t-distribution perturbation mechanism, to enhance the algorithm\u2019s ability to escape local optima. ADTSA also strengthens population diversity and avoids local optima through convex lens symmetric reverse generation based on the optimal solution. With these mechanisms, ADTSA converges more effectively to the global optimum during the evolutionary process. Tests on the IEEE CEC 2014 benchmark functions showed that ADTSA outperformed several top-performing algorithms, such as LSHADE, JADE, LSHADE-RSP, and the latest TSA variants, and it also excelled in comparison with other optimization algorithms, including GWO, PSO, BOA, GA, and RSA, underscoring its robust performance across diverse testing scenarios. The proposed ADTSA\u2019s applicability in solving complex constrained problems was also validated, with the results showing that ADTSA achieved the best solutions for these complex problems.<\/jats:p>","DOI":"10.3390\/sym17081200","type":"journal-article","created":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T10:51:14Z","timestamp":1753699874000},"page":"1200","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Symmetry-Driven Adaptive Dual-Subpopulation Tree\u2013Seed Algorithm for Complex Optimization with Local Optima Avoidance and Convergence Acceleration"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-7251-3662","authenticated-orcid":false,"given":"Hao","family":"Li","sequence":"first","affiliation":[{"name":"Center for Artificial Intelligence, Jilin University of Finance and Economics, Changchun 130117, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9149-2922","authenticated-orcid":false,"given":"Jianhua","family":"Jiang","sequence":"additional","affiliation":[{"name":"Center for Artificial Intelligence, Jilin University of Finance and Economics, Changchun 130117, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-1927-7049","authenticated-orcid":false,"given":"Zhixing","family":"Ma","sequence":"additional","affiliation":[{"name":"Center for Artificial Intelligence, Jilin University of Finance and Economics, Changchun 130117, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lingna","family":"Li","sequence":"additional","affiliation":[{"name":"Center for Artificial Intelligence, Jilin University of Finance and Economics, Changchun 130117, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiayi","family":"Liu","sequence":"additional","affiliation":[{"name":"Center for Artificial Intelligence, Jilin University of Finance and Economics, Changchun 130117, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chenxi","family":"Li","sequence":"additional","affiliation":[{"name":"Center for Artificial Intelligence, Jilin University of Finance and Economics, Changchun 130117, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenhao","family":"Yu","sequence":"additional","affiliation":[{"name":"Center for Artificial Intelligence, Jilin University of Finance and Economics, Changchun 130117, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"101865","DOI":"10.1016\/j.swevo.2025.101865","article-title":"Neuro-PSO algorithm for large-scale dynamic optimization","volume":"94","author":"Radwan","year":"2025","journal-title":"Swarm Evol. Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"e70224","DOI":"10.1002\/eng2.70224","article-title":"Multi-Input Multi-Output Modeling of Anthill Clay-Bonded Sand Mold System Using Artificial Neural Networks: Forward and Reverse Predictions","volume":"7","author":"Chate","year":"2025","journal-title":"Eng. Rep."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"137502","DOI":"10.1016\/j.energy.2025.137502","article-title":"Energy-efficient optimization method for air conditioning terminal systems in IDC based on genetic algorithm","volume":"333","author":"Huang","year":"2025","journal-title":"Energy"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Basar, G., Der, O., and Guvenc, M.A. (2025). AI-powered hybrid metaheuristic optimization for predicting surface roughness and kerf width in CO2 laser cutting of 3D-printed PLA-CF composites. J. Thermoplast. Compos. Mater., 08927057251344183.","DOI":"10.1177\/08927057251344183"},{"key":"ref_5","first-page":"100749","article-title":"Two non-linear programming models for the multi-stage multi-cycle smart production system with autonomation and remanufacturing in same and different cycles to reduce wastes","volume":"44","author":"Sarkar","year":"2025","journal-title":"J. Ind. Inf. Integr."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"106810","DOI":"10.1016\/j.neunet.2024.106810","article-title":"Fractional-order stochastic gradient descent method with momentum and energy for deep neural networks","volume":"181","author":"Zhou","year":"2025","journal-title":"Neural Netw."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Jiang, J., Huang, J., Wu, J., Luo, J., Yang, X., and Li, W. (2024). DTSA: Dynamic Tree-Seed Algorithm with Velocity-Driven Seed Generation and Count-Based Adaptive Strategies. Symmetry, 16.","DOI":"10.3390\/sym16070795"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1631","DOI":"10.1109\/TITS.2024.3510532","article-title":"Efficient Algorithms for Approximate k-Radius Coverage Query on Large-Scale Road Networks","volume":"26","author":"Li","year":"2024","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/4235.585893","article-title":"No free lunch theorems for optimization","volume":"1","author":"Wolpert","year":"1997","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6686","DOI":"10.1016\/j.eswa.2015.04.055","article-title":"TSA: Tree-seed algorithm for continuous optimization","volume":"42","author":"Kiran","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"112220","DOI":"10.1016\/j.asoc.2024.112220","article-title":"A tree seed algorithm with multi-strategy for parameter estimation of solar photovoltaic models","volume":"167","author":"Kiran","year":"2024","journal-title":"Appl. Soft Comput."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zhou, Q., Dai, R., Zhou, G., Ma, S., and Luo, S. (2024). An Enhanced Tree-Seed Algorithm for Function Optimization and Production Optimization. Biomimetics, 9.","DOI":"10.3390\/biomimetics9060334"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Qiao, Z., Wu, L., Heidari, A.A., Zhao, X., and Chen, H. (2025). An enhanced tree-seed algorithm for global optimization and neural architecture search optimization in medical image segmentation. Biomed. Signal Process. Control, 104.","DOI":"10.1016\/j.bspc.2024.107457"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Aslan, M.F., Sabanci, K., and Ropelewska, E. (2022). A new approach to COVID-19 detection: An ANN proposal optimized through tree-seed algorithm. Symmetry, 14.","DOI":"10.3390\/sym14071310"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"122105","DOI":"10.1016\/j.ins.2025.122105","article-title":"A forward k-means algorithm for regression clustering","volume":"711","author":"Lu","year":"2025","journal-title":"Inf. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Zhu, X., Zhang, J., Jia, C., Liu, Y., and Fu, M. (2025). A Hybrid Black-Winged Kite Algorithm with PSO and Differential Mutation for Superior Global Optimization and Engineering Applications. Biomimetics, 10.","DOI":"10.3390\/biomimetics10040236"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"113951","DOI":"10.1016\/j.chaos.2023.113951","article-title":"Exploring a family of Bernoulli-like shift chaotic maps and its amplitude control","volume":"175","year":"2023","journal-title":"Chaos Soliton. Fract."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"16735","DOI":"10.1109\/JIOT.2025.3532749","article-title":"Military UCAV 3D path planning based on multi-strategy developed human evolutionary optimization algorithm","volume":"12","author":"Wang","year":"2025","journal-title":"IEEE Internet Things J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"71","DOI":"10.4316\/AECE.2017.02010","article-title":"Golden sine algorithm: A novel math-inspired algorithm","volume":"17","author":"Tanyildizi","year":"2017","journal-title":"Adv. Electr. Comput. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"114333","DOI":"10.1016\/j.measurement.2024.114333","article-title":"Research and implementation of fault data recovery method for dry-type transformer temperature control sensor based on ISSA-LSTM algorithm","volume":"228","author":"Wang","year":"2024","journal-title":"Measurement"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"118311","DOI":"10.1016\/j.eswa.2022.118311","article-title":"Enhance tree-seed algorithm using hierarchy mechanism for constrained optimization problems","volume":"209","author":"Jiang","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"121312","DOI":"10.1016\/j.eswa.2023.121312","article-title":"Advanced strategies on update mechanism of tree-seed algorithm for function optimization and engineering design problems","volume":"236","author":"Liu","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"104303","DOI":"10.1016\/j.engappai.2021.104303","article-title":"TriTSA: Triple Tree-Seed Algorithm for dimensional continuous optimization and constrained engineering problems","volume":"104","author":"Jiang","year":"2021","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"18627","DOI":"10.1007\/s00500-020-05099-w","article-title":"TSASC: Tree\u2013seed algorithm with sine\u2013cosine enhancement for continuous optimization problems","volume":"24","author":"Jiang","year":"2020","journal-title":"Soft Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"122802","DOI":"10.1016\/j.physa.2019.122802","article-title":"STSA: A sine Tree-Seed Algorithm for complex continuous optimization problems","volume":"537","author":"Jiang","year":"2020","journal-title":"Phys. A"},{"key":"ref_26","unstructured":"Linden, A. (2024, June 01). ITSA: Stata Module to Perform Interrupted Time Series Analysis for Single and Multiple Groups. Available online: https:\/\/ideas.repec.org\/c\/boc\/bocode\/s457793.html."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"122323","DOI":"10.1016\/j.physa.2019.122323","article-title":"EST-TSA: An effective search tendency based to tree seed algorithm","volume":"534","author":"Jiang","year":"2019","journal-title":"Physica A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"106314","DOI":"10.1016\/j.asoc.2020.106314","article-title":"Enhancing tree-seed algorithm via feed-back mechanism for optimizing continuous problems","volume":"92","author":"Jiang","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"125863","DOI":"10.1016\/j.eswa.2024.125863","article-title":"Multi-population dynamic grey wolf optimizer based on dimension learning and Laplace Mutation for global optimization","volume":"265","author":"Wang","year":"2025","journal-title":"Expert Syst. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Tanabe, R., and Fukunaga, A.S. (2014, January 6\u201311). Improving the search performance of SHADE using linear population size reduction. Proceedings of the 2014 IEEE Congress on Evolutionary Computation (CEC), Beijing, China.","DOI":"10.1109\/CEC.2014.6900380"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1109\/TEVC.2009.2014613","article-title":"JADE: Adaptive differential evolution with optional external archive","volume":"13","author":"Zhang","year":"2009","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Stanovov, V., Akhmedova, S., and Semenkin, E. (2018, January 8\u201313). LSHADE algorithm with rank-based selective pressure strategy for solving CEC 2017 benchmark problems. Proceedings of the 2018 IEEE Congress on Evolutionary Computation (CEC), Rio de Janeiro, Brazil.","DOI":"10.1109\/CEC.2018.8477977"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1007\/s00500-018-3102-4","article-title":"Butterfly optimization algorithm: A novel approach for global optimization","volume":"23","author":"Arora","year":"2019","journal-title":"Soft Comput."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"116158","DOI":"10.1016\/j.eswa.2021.116158","article-title":"Reptile Search Algorithm (RSA): A nature-inspired meta-heuristic optimizer","volume":"191","author":"Abualigah","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Zhang, T., Yin, Q., Li, S., Guo, T., and Fan, Z. (2025). An Optimized Genetic Algorithm-Based Wavelet Image Fusion Technique for PCB Detection. Appl. Sci., 15.","DOI":"10.3390\/app15063217"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"105521","DOI":"10.1016\/j.engappai.2022.105521","article-title":"A qualitative systematic review of metaheuristics applied to tension\/compression spring design problem: Current situation, recommendations, and research direction","volume":"118","author":"Tzanetos","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"106933","DOI":"10.1016\/j.asoc.2020.106933","article-title":"Dimension by dimension dynamic sine cosine algorithm for global optimization problems","volume":"98","author":"Li","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Chun, Y., Hua, X., Qi, C., and Yao, Y.X. (2024). Improved marine predators algorithm for engineering design optimization problems. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-63826-x"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1016\/j.ejor.2024.01.049","article-title":"A variable neighborhood search for the green vehicle routing problem with two-dimensional loading constraints and split delivery","volume":"316","author":"Ferreira","year":"2024","journal-title":"Eur. J. Oper. Res."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1200\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:17:15Z","timestamp":1760033835000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1200"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,28]]},"references-count":39,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["sym17081200"],"URL":"https:\/\/doi.org\/10.3390\/sym17081200","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,28]]}}}