Reliability-based optimization methods in optimal structural design use mostly the following basic design criteria: I) Minimal weight (volume or costs) and II) high or reliability of the structure. Since, in practice, several parameters of the structure, e.g. elastic moduli, tolerances of structural dimensions, loads, are not given, fixed quantities, but random variables having a certain probability distribution P, a stochastic optimization problem will result from criteria (I), (II), which can be represented
min F(x) with F(x) := Ef(ω, x). (1)
Stochastic approximation methods are considered for solving (1): The gradient estimators are obtained by the response surface methodology (RSM) where especially the improvement of the estimators by using so-called “intermediate” or “intervening” variables is considered.