In robust optimization, an optimum solution of a system is obtained when some uncertainties exist in the system. The uncertainty can be defined by probabilistic characteristics or deterministic intervals (uncertainty ranges or tolerances) that are the main concern in this study. An insensitive objective function is obtained with regard to the uncertainties or the worst case is considered for the objective function within the intervals in robust optimization. A supreme value within the uncertainty interval is minimized. The worst case approach has been extensively utilized in the linear programming (LP) community. However, the method solved only small scale problems of structural optimization where nonlinear programming (NLP) is employed. In this research, a novel worst case approach is proposed to solve large scale problems of structural optimization. An uncertainty interval is defined by a tolerance range of a design variable or problem parameter. A supreme value is obtained by optimization of the objective function subject to the intervals, and this process yields an inner loop. The supremum is minimized in the outer loop. Linearization of the inner loop is proposed to save the computational time for optimization. This technique can be easily extended for constraints with uncertainty intervals because the worst case of a constraint should be satisfied. The optimum sensitivity is utilized for the sensitivity of a supremum in the outer loop. Three examples including a mathematical example and two structural applications are presented to validate the proposed idea.
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Recommended by Associate Editor Gang-Won Jang
Gyung-Jin Park received the B.S. degree from Hanyang University, Korea in 1980, M.S. degree from KAIST, Korea, in 1982, and the Ph.D. from the University of Iowa, USA, in 1986. In 1986–1988, he worked as an Assistant Professor at Purdue University at Indianapolis, USA. His research focuses on Structural Optimization, machine design, design theory and MDO. His work has yielded over 4 books and 360 technical papers. He is currently a Professor in the Department of Mechanical Engineering at Hanyang University, Ansan City, Korea.
Se-Jung Lee received the B.S. degree in mechanical engineering from Soon-ChunHyang University, Korea, in 2003, M.S. degree from Hanyang University, Korea, in 2009, and the Ph.D. from Hanyang University, Korea, in 2014. Her research interests include design methodology and robust design.
Min-Ho Jeong received the B.S. degree in mechanical engineering from Hanyang University, Korea in 2015. He is currently pursuing the Ph.D. degree at Hanyang University. His research interests include design methodology, structural optimization and robust design.
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Lee, SJ., Jeong, MH. & Park, GJ. A novel worst case approach for robust optimization of large scale structures. J Mech Sci Technol 32, 4255–4269 (2018). https://doi.org/10.1007/s12206-018-0824-2
- Robust optimization
- Supremum of a function
- Worst case approach