ON OPTIMUM DESIGN OF FRAME STRUCTURES
Optimization of frame structures is formulated as a non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii) optimality criteria method, (iii) non-linear semidefinite p...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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CTU Central Library
2020-03-01
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| Series: | Acta Polytechnica CTU Proceedings |
| Subjects: | |
| Online Access: | https://ojs.cvut.cz/ojs/index.php/APP/article/view/6401 |
| _version_ | 1818524133782192128 |
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| author | Marek Tyburec Jan Zeman Martin Kružík Didier Henrion |
| author_facet | Marek Tyburec Jan Zeman Martin Kružík Didier Henrion |
| author_sort | Marek Tyburec |
| collection | DOAJ |
| description | Optimization of frame structures is formulated as a non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii) optimality criteria method, (iii) non-linear semidefinite programming, and (iv) polynomial optimization. We show that polynomial optimization solves the frame structure optimization to global optimality by building the (moment-sums-of-squares) hierarchy of convex linear semidefinite programming problems, and it also provides guaranteed lower and upper bounds on optimal design. Finally, we solve three sample optimization problems and conclude that the local optimization approaches may indeed converge to local optima, without any solution quality measure, or even to infeasible points. These issues are readily overcome by using polynomial optimization, which exhibits a finite convergence, at the prize of higher computational demands. |
| first_indexed | 2024-12-11T05:53:23Z |
| format | Article |
| id | doaj.art-126c170a28934fe39467b789810ff574 |
| institution | Directory Open Access Journal |
| issn | 2336-5382 |
| language | English |
| last_indexed | 2024-12-11T05:53:23Z |
| publishDate | 2020-03-01 |
| publisher | CTU Central Library |
| record_format | Article |
| series | Acta Polytechnica CTU Proceedings |
| spelling | doaj.art-126c170a28934fe39467b789810ff5742022-12-22T01:18:45ZengCTU Central LibraryActa Polytechnica CTU Proceedings2336-53822020-03-0126011712510.14311/APP.2020.26.01175019ON OPTIMUM DESIGN OF FRAME STRUCTURESMarek Tyburec0Jan Zeman1Martin Kružík2Didier Henrion3Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Prague 6, Czech RepublicCzech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Prague 6, Czech Republic Czech Academy of Sciences, Institute of Information Theory and Automation, Department of Decision-Making Theory, Pod vodárenskou veží 4, 182 08 Prague 8, Czech RepublicCzech Technical University in Prague, Faculty of Civil Engineering, Departement of Physics, Thákurova 7, 166 29 Prague 6, Czech Republic Czech Academy of Sciences, Institute of Information Theory and Automation, Department of Decision-Making Theory, Pod vodárenskou veží 4, 182 08 Prague 8, Czech RepublicUniversity of Toulouse, LAAS-CNRS, 7 Avenue du Colonel Roche, 31400 Toulouse, France Czech Technical University in Prague, Faculty of Electrical Engineering, Department of Control Engineering, Karlovo námestí 13, 121 35 Prague 2, Czech RepublicOptimization of frame structures is formulated as a non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii) optimality criteria method, (iii) non-linear semidefinite programming, and (iv) polynomial optimization. We show that polynomial optimization solves the frame structure optimization to global optimality by building the (moment-sums-of-squares) hierarchy of convex linear semidefinite programming problems, and it also provides guaranteed lower and upper bounds on optimal design. Finally, we solve three sample optimization problems and conclude that the local optimization approaches may indeed converge to local optima, without any solution quality measure, or even to infeasible points. These issues are readily overcome by using polynomial optimization, which exhibits a finite convergence, at the prize of higher computational demands.https://ojs.cvut.cz/ojs/index.php/APP/article/view/6401frame structures, global optimum, polynomial optimization, semidefinite programming, topology optimization. |
| spellingShingle | Marek Tyburec Jan Zeman Martin Kružík Didier Henrion ON OPTIMUM DESIGN OF FRAME STRUCTURES Acta Polytechnica CTU Proceedings frame structures, global optimum, polynomial optimization, semidefinite programming, topology optimization. |
| title | ON OPTIMUM DESIGN OF FRAME STRUCTURES |
| title_full | ON OPTIMUM DESIGN OF FRAME STRUCTURES |
| title_fullStr | ON OPTIMUM DESIGN OF FRAME STRUCTURES |
| title_full_unstemmed | ON OPTIMUM DESIGN OF FRAME STRUCTURES |
| title_short | ON OPTIMUM DESIGN OF FRAME STRUCTURES |
| title_sort | on optimum design of frame structures |
| topic | frame structures, global optimum, polynomial optimization, semidefinite programming, topology optimization. |
| url | https://ojs.cvut.cz/ojs/index.php/APP/article/view/6401 |
| work_keys_str_mv | AT marektyburec onoptimumdesignofframestructures AT janzeman onoptimumdesignofframestructures AT martinkruzik onoptimumdesignofframestructures AT didierhenrion onoptimumdesignofframestructures |