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A comparison between robust and risk-based optimization under uncertainty

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Abstract

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 constraints. 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.

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Acknowledgments

Sponsorship of this research project by the São Paulo State Foundation for Research - FAPESP (grant number 2012/21357-1) and by the National Council for Research and Development - CNPq (grant number 303749/2012-1) is greatly acknowledged. Comments by the anonymous reviewers have significantly improved the paper and are also greatly acknowledged.

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Authors and Affiliations

  1. Department of Structural Engineering, São Carlos School of Engineering, University of São Paulo, 13566-590, São Carlos, SP, Brazil

    André T. Beck

  2. Department of Civil Engineering, Federal University of Santa Catarina, Florianópolis, SC, Brazil

    Wellison J. S. Gomes, Rafael H. Lopez & Leandro F. F. Miguel

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  1. André T. Beck
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  2. Wellison J. S. Gomes
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  3. Rafael H. Lopez
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  4. Leandro F. F. Miguel
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Correspondence to André T. Beck.

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Beck, A.T., Gomes, W.J.S., Lopez, R.H. et al. A comparison between robust and risk-based optimization under uncertainty. Struct Multidisc Optim 52, 479–492 (2015). https://doi.org/10.1007/s00158-015-1253-9

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  • DOI: https://doi.org/10.1007/s00158-015-1253-9

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