Stochastic Subset Optimization for optimal reliability problems

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An efficient approach to reliability-based topology optimization for continua under material uncertainty (2015, background): “…learning techniques or special sampling methodologies, promising approaches that reduce the computational cost dramatically have recently emerged (Youn and Choi 2004; Agarwal and Renaud 2004; Kim and Choi 2008; Taflanidis and Beck 2008; Basudhar and Missoum 2008; Valdebenito and Schuëller 2011).”
Reliability-based optimization of stochastic systems using line search (2009, methodology): “In these approaches the values of the random functions are used directly as inputs to the optimization algorithm [40,41].”
A survey on approaches for reliability-based optimization (2010, methodology): “According to results in the literature (see, e.g. Ching and Hsieh (2007a); Taflanidis and Beck (2008b); Jensen et al (2009)), the number of function evaluations required for solving a RBO problem may vary between three and five orders of magnitude.”
Aerodynamic shape optimization for minimum robust drag and lift reliability constraint (2016, methodology): “Stochastic approaches for the estimation of the statistical moments are usually based on advanced Monte-Carlo (MC) methods [27,49,19] which are costly due to the very large number of analyses on the sample points required to compute these integrals.”