{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:14:38Z","timestamp":1760058878841,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:00:00Z","timestamp":1746057600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Major Scientific Research Project (Natural Sciences) of Anhui Higher Education Institutions","award":["2024AH040234","2020M671319","2020Z317","2024AH040234"],"award-info":[{"award-number":["2024AH040234","2020M671319","2020Z317","2024AH040234"]}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2024AH040234","2020M671319","2020Z317","2024AH040234"],"award-info":[{"award-number":["2024AH040234","2020M671319","2020Z317","2024AH040234"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010242","name":"Jiangsu Planned Projects for Postdoctoral Research Funds","doi-asserted-by":"publisher","award":["2024AH040234","2020M671319","2020Z317","2024AH040234"],"award-info":[{"award-number":["2024AH040234","2020M671319","2020Z317","2024AH040234"]}],"id":[{"id":"10.13039\/501100010242","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Major Scientific Research Project (Natural Sciences) of Anhui Higher Education Institutions","award":["2024AH040234","2020M671319","2020Z317","2024AH040234"],"award-info":[{"award-number":["2024AH040234","2020M671319","2020Z317","2024AH040234"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study addresses the optimization of actuator arrangements in adaptive cable\u2013strut tension structures to enhance structural controllability and performance. Two novel optimization criteria are proposed: (1) a weighted sensitivity criterion that integrates nodal displacements and internal force increments, and (2) a system strain energy criterion reflecting overall structural stiffness. Nonlinear optimization models are formulated for these criteria, with actuator positions as design variables, and solved using a robust multi-population genetic algorithm. The weighted sensitivity criterion prioritizes targeted control of specific nodes and members, while the strain energy criterion ensures balanced global response. Numerical validation is conducted on a Geiger cable dome and a four-layer tensegrity structure. Results demonstrate that both criteria yield actuator arrangements satisfying geometric symmetry while achieving high sensitivity in displacement and internal force control. The proposed framework offers practical insights for optimizing adaptive structures under static control requirements, and advances the field by bridging localized and global response optimization, enabling smarter, more resilient tension structures.<\/jats:p>","DOI":"10.3390\/sym17050695","type":"journal-article","created":{"date-parts":[[2025,5,4]],"date-time":"2025-05-04T20:42:37Z","timestamp":1746391357000},"page":"695","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimization of Actuator Arrangement of Cable\u2013Strut Tension Structures Based on Multi-Population Genetic Algorithm"],"prefix":"10.3390","volume":"17","author":[{"given":"Huiting","family":"Xiong","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Wanjiang University of Technology, Ma\u2019anshan 243031, China"}]},{"given":"Tingmei","family":"Zhou","sequence":"additional","affiliation":[{"name":"CISDI Shanghai Engineering Co., Ltd., Shanghai 200940, China"}]},{"given":"Pei","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Civil and Transportation Engineering, Hohai University, Nanjing 210024, China"}]},{"given":"Zhibing","family":"Shang","sequence":"additional","affiliation":[{"name":"College of Civil and Transportation Engineering, Hohai University, Nanjing 210024, China"}]},{"given":"Mithun","family":"Biswas","sequence":"additional","affiliation":[{"name":"College of Civil and Transportation Engineering, Hohai University, Nanjing 210024, China"}]},{"given":"Hao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Wanjiang University of Technology, Ma\u2019anshan 243031, China"}]},{"given":"Huayang","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Wanjiang University of Technology, Ma\u2019anshan 243031, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1016\/j.ijsolstr.2005.03.008","article-title":"The stiffness of prestressed frameworks: A unifying approach","volume":"43","author":"Guest","year":"2006","journal-title":"Int. J. Solids Struct."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Obara, P., and Tomasik, J. (2021). Active control of stiffness of tensegrity plate-like structures built with simplex modules. Materials, 14.","DOI":"10.3390\/ma14247888"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2085","DOI":"10.21595\/jve.2017.18709","article-title":"Deployment accuracy analysis of cable-strut deployable mechanism with joint clearances and forces constrained","volume":"20","author":"Lin","year":"2018","journal-title":"J. Vibroengineering"},{"key":"ref_4","first-page":"302","article-title":"Geometric and Material Nonlinear Analyses of Trusses Subjected to Thermomechanical Loads","volume":"33","author":"Masoodi","year":"2022","journal-title":"Struct. Eng. Int."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3272","DOI":"10.1016\/j.ijsolstr.2009.04.026","article-title":"Investigation of clustered actuation in tensegrity structures","volume":"46","author":"Moored","year":"2009","journal-title":"Int. J. Solids Struct."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1016\/j.ijsolstr.2016.11.030","article-title":"Initial prestress design and optimization of tensegrity systems based on symmetry and stiffness","volume":"106\u2013107","author":"Zhang","year":"2017","journal-title":"Int. J. Solids Struct."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"108021","DOI":"10.1016\/j.jcsr.2023.108021","article-title":"Mechanical properties and shape-control abilities of a cable dome under asymmetrical loads","volume":"208","author":"Zhang","year":"2023","journal-title":"J. Constr. Steel Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1177\/1077546313489327","article-title":"Vibration control of tensegrity structures using different active control strategies","volume":"21","author":"Raja","year":"2015","journal-title":"J. Vib. Control"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"116597","DOI":"10.1016\/j.engstruct.2023.116597","article-title":"New actuation planning method for the analysis and design of active tensegrity structures","volume":"293","author":"Hrabaka","year":"2023","journal-title":"Eng. Struct."},{"key":"ref_10","first-page":"119","article-title":"Sensitivity analysis on responses of adaptive cable-struttensile structure with length changeable elements","volume":"42","author":"Li","year":"2014","journal-title":"J. Huazhong Univ. Sci. Technol. (Nat. Sci. Ed.)"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"107913","DOI":"10.1016\/j.ymssp.2021.107913","article-title":"Integrating structure, information architecture and control design: Application to tensegrity systems","volume":"161","author":"Goyal","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"109166","DOI":"10.1016\/j.jcsr.2024.109166","article-title":"Control accuracy and sensitivity of a double rhombic-strut adaptive beam string structure","volume":"224","author":"Zou","year":"2025","journal-title":"J. Constr. Steel Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"112212","DOI":"10.1016\/j.tws.2024.112212","article-title":"Machine learning-based active control for lightweight antenna with force density method and nested genetic algorithm","volume":"203","author":"Lu","year":"2024","journal-title":"Thin-Walled Struct."},{"key":"ref_14","first-page":"223","article-title":"Research on strength control for adaptive structure under multi-loading cases","volume":"34","author":"Sui","year":"2002","journal-title":"Chin. J. Theor. Appl. Mech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.engstruct.2016.01.011","article-title":"Active control for mid-span connection of a deployable tensegrity footbridge","volume":"112","author":"Veuve","year":"2016","journal-title":"Eng. Struct."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2076738","DOI":"10.1155\/2023\/2076738","article-title":"Optimal Active Vibration Control of Tensegrity Structures Using Fast Model Predictive Control Strategy","volume":"2023","author":"Feng","year":"2023","journal-title":"Struct. Control Health Monit."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1016\/j.aei.2009.06.002","article-title":"Configuring and enhancing measurement systems for damage identification","volume":"23","author":"Kripakaran","year":"2009","journal-title":"Adv. Eng. Inform."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2237","DOI":"10.1177\/13694332221092675","article-title":"A combination of genetic algorithm and dynamic relaxation method for practical form-finding of tensegrity structures","volume":"25","author":"Hieu","year":"2022","journal-title":"Adv. Struct. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4294","DOI":"10.1016\/j.ijsolstr.2014.08.014","article-title":"Prismatic tensegrity structures with additional cables: Integral symmetric states of self-stress and cable-controlled reconfiguration procedure","volume":"51","author":"Zhang","year":"2014","journal-title":"Int. J. Solids Struct."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"e2215","DOI":"10.1002\/stc.2215","article-title":"Energy-based comparative analysis of optimal active control schemes for clustered tensegrity structures","volume":"25","author":"Feng","year":"2018","journal-title":"Struct. Control Health Monit."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"114391","DOI":"10.1016\/j.engstruct.2022.114391","article-title":"Dynamics and control of clustered tensegrity systems","volume":"264","author":"Ma","year":"2022","journal-title":"Eng. Struct."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"119878","DOI":"10.1016\/j.engstruct.2025.119878","article-title":"Accurate force evaluation in prestressed cable-strut structures: A robust sparse Bayesian learning method with feedback-driven error optimization","volume":"330","author":"Chen","year":"2025","journal-title":"Eng. Struct."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Zhang, P., Xiong, H.T., and Chen, J.S. (2020). Unified Fundamental Formulas for Static Analysis of Pin-Jointed Bar Assemblies. Symmetry, 12.","DOI":"10.3390\/sym12060994"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"113971","DOI":"10.1016\/j.compstruct.2021.113971","article-title":"Form-finding of complex tensegrity structures using constrained optimization method","volume":"268","author":"Zhang","year":"2021","journal-title":"Compos. Struct."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3025","DOI":"10.1016\/0020-7683(93)90210-X","article-title":"Structural computations with the singular value decomposition of the equilibrium matrix","volume":"30","author":"Pellegrino","year":"1993","journal-title":"Int. J. Solids Struct."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"04020003","DOI":"10.1061\/(ASCE)CP.1943-5487.0000882","article-title":"Feasible prestress modes for cable-strut structures with multiple self-stress states using Particle Swarm Optimization","volume":"34","author":"Chen","year":"2020","journal-title":"J. Comput. Civ. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"114227","DOI":"10.1016\/j.engstruct.2022.114227","article-title":"Structural symmetry recognition in planar structures using Convolutional Neural Networks","volume":"260","author":"Zhang","year":"2022","journal-title":"Eng. 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