Chance constrained stochastic programming in design of a frame structure
DOI:
https://doi.org/10.14311/CEJ.2025.01.0001Keywords:
Optimal engineering design, Stochastic programming, Chance constrained optimization, Ordinary differential equationsAbstract
A civil engineering problem concerning an optimal design of a loaded frame structure with random Young's modulus is discussed. The developed multi-criteria optimization model involves ODE-type constraints and also one chance constraint related to the structure’s reliability. A computational scheme for this type of problems is proposed using the finite difference method for the approximation of the ODE constraint and the scenario-based approach for a random variable approximation. The chance constraint is handled by two approaches – analytical approach and penalty reformulation. An a posteriori check of satisfying the chance constraint is made and the upper bounds of the obtainable reliability are computed.
Downloads
References
Plšek J., Štěpánek P., Popela P., 2007. Deterministic and reliability based structural optimization of concrete cross-section. Jornal of Advanced Concrete Technology, vol. 5: 63–74. DOI:10.3151/jact.5.63
Laníková I., Štěpánek P., Šimůnek P., 2014. Optimized design of concrete structures considering environmental aspects. Advances in Structural Engineering, vol. 17, no. 4: 495-511.
DOI:10.1260/1369-4332.17.4.495
Venclovský J., Štěpánek P., Laníková I., 2018. Stochastic optimization of reinforces concrete elements using heuristic algorithm. In: Proceedings of the 24th Concrete Days 2017. Solid State Phenomena, vol. 272: 262-269. DOI:10.4028/www.scientific.net/SSP.272.262
Žampachová E., Popela P., Mrázek M., 2010. Optimum beam design via stochastic programming. Kybernetika, vol. 46, no. 3: 571–582
Žampachová E., Popela P., 2012. Two approaches to multi-criteria stochastic programming in beam design problem. In: Proceedings of the 18th International Conference of Soft Computing MENDEL 2012. Mendel Journal series: 393-397
Žampachová E., Mrázek M., 2010. Stochastic optimization in beam design and its reliability check. In: Proceedings of the 16th International Conference of Soft Computing MENDEL 2010. Mendel Journal series: 405-410
Kůdela J., Popela P., 2018. Chance constrained optimal beam design: Convex reformulation and probabilistic robust design. Kybernetika, vol. 54, no. 6: 1201-1217. DOI:10.14736/kyb-2018-6-1201
Steuer R.E., 1986. Multiple Criteria Optimization: Theory, Computation and Application (New York: John Wiley) 546 pp. DOI:10.1002/oca.4660100109
Oberg E., Jones F.D., Horton H., Ryffel H., McCauley C., 2020. Machinery’s Handbook (Industrial Press). 2996 pp.
Ruszczynski A., Shapiro, A. (eds.), 2003. Handbooks in Operations Research and Management Science, vol.10: Stochastic Programming (Amsterdam: Elsevier) 682 pp.
Birge J., Louveaux F., 1997. Introduction to Stochastic Programming (New York: Springer) 485 pp.
DOI:10.1007/978-1-4614-0237-4
Mathews J.H., Fink K.D., 2004. Numerical Methods using Matlab (New Jersey: Pearson Prentice Hall) 696 pp.
Branda M., Dupačová J., 2012. Approximations and contamination bounds for probabilistic programs. Annals of Operations Research, vol. 193, no.1: 3-19. DOI: 10.1007/s10479-010-0811-1
Bazaraa M.S., Sherali H.D., Shetty C.M., 2005. Nonlinear programming: Theory and Algorithms. (New York: Wiley and Sons) 853 pp. DOI:10.1002/0471787779
Luedtke J., Ahmed S., 2008. A sample approximation approach for optimization with probabilistic constraints. SIAM Journal on Optimization, vol. 19, no. 2: 674-699. DOI:10.1137/070702928
Pagnoncelli B.K., Ahmed S., Shapiro A., 2009. Sample average approximation method for chance constrained programming: Theory and applications. Journal of Optimization Theory and Applications, vol. 142: 399-416. DOI:10.1007/s10957-009-9523-6
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Stavební obzor - Civil Engineering Journal
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
