A comparison between robust and risk-based optimization under uncertainty

• Published in: Structural and multidisciplinary optimization Vol. 52; no. 3; pp. 479 - 492
• Main Authors: Beck, André T., Gomes, Wellison J. S., Lopez, Rafael H., Miguel, Leandro F. F.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2015; Springer Nature B.V
• Subjects: Computational Mathematics and Numerical Analysis; Constants; Engineering; Engineering Design; Failure; Formulations; Normalizing; Optimization; Research Paper; Risk; Robustness; Theoretical and Applied Mechanics; Uncertainty; Reliability analysis; Optimum design; Robust optimization; Structural optimization; Risk optimization
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-015-1253-9

Robust optimization aims at producing designs which are less sensitive to uncertainties. Risk optimization looks for designs with optimal balance between performance and safety. In spite of the different objectives, robust and risk-based formulations have strong similitude, which has not been thoroughly explored before. This paper explores the similarities and differences between these formulations. It is shown that the alpha factors, which are employed in compromise solutions in robust optimization, are equivalent to the costs of failure in risk-based optimization. Moreover, it is shown that the robust objective function is often non-convex, with results being given by (often arbitrary) design constraint s . In some sense, the robust objective function lacks objectiveness, with results largely dependent on arbitrary normalizing constants. On the other hand, when there is a critical limit to performance, which characterizes system failure, and when costs of failure can be defined, the risk-based optimization yields consistent results, and no normalizing constants are needed.