Structural and Multidisciplinary Optimization

, Volume 60, Issue 5, pp 2157–2176 | Cite as

Surrogate-assisted reliability-based design optimization: a survey and a unified modular framework

  • Maliki MoustaphaEmail author
  • Bruno Sudret
Review Article


Reliability-based design optimization (RBDO) is an active field of research with an ever increasing number of contributions. Numerous methods have been proposed for the solution of RBDO, a complex problem that combines optimization and reliability analysis. Classical approaches are based on approximation methods and have been classified in review papers. In this paper, we first review classical approaches based on approximation methods such as FORM, and also more recent methods that rely upon surrogate modelling and Monte Carlo simulation. We then propose a generalization of the existing surrogate-assisted and simulation-based RBDO techniques using a unified framework that includes three independent blocks, namely adaptive surrogate modelling, reliability analysis, and optimization. These blocks are non-intrusive with respect to each other and can be plugged independently in the framework. After a discussion on numerical considerations that require attention for the framework to yield robust solutions to various types of problems, the latter is applied to three examples (using two analytical functions and a finite element model). Kriging and support vector machines regression together with their own active learning schemes are considered in the surrogate model block. In terms of reliability analysis, the proposed framework is illustrated using both crude Monte Carlo and subset simulation. Finally, the covariance matrix adaptation-evolution scheme (CMA-ES), a global search algorithm, or sequential quadratic programming (SQP), a local gradient-based method, is used in the optimization block. The comparison of the results to benchmark studies shows the effectiveness and efficiency of the proposed framework.


Reliability-based design optimization RBDO Surrogate modelling Simulation methods Active learning 


Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Chair of Risk, Safety and Uncertainty QuantificationETH ZurichZurichSwitzerland

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