Reliability-based Optimization is a most appropriate and advantageous methodology for structural design. Its main feature is that it allows determining the best design solution (with respect to prescribed criteria) while explicitly considering the unavoidable effects of uncertainty. In general, the application of this methodology is numerically involved, as it implies the simultaneous solution of an optimization problem and also the use of specialized algorithms for quantifying the effects of uncertainties. In view of this fact, several approaches have been developed in the literature for applying this methodology in problems of practical interest. This contribution provides a survey on approaches for performing Reliability-based Optimization, with emphasis on the theoretical foundations and the main assumptions involved. Early approaches as well as the most recently developed methods are covered. In addition, a qualitative comparison is performed in order to provide some general guidelines on the range of applicability on the different approaches discussed in this contribution.

A survey on approaches for reliability-based optimization

Life-cycle reliability-based optimization of civil and aerospace structures

Matrix formulation of reliability analysis and reliability-based design

A reliability‐based optimization sensitivity analysis technique based on the feasible directions concept is presented for plastic design of redundant structures. This technique is specialized to a formulation of the problem of plastic optimization for minimum weight based on a rational reliability constraint for sizing members. The technique is demonstrated with a structural design example where emphasis is placed on the sensitivity of the reliability‐based optimum solution to both the correlation among strengths and the method for evaluating the overall probability of plastic collapse.

Sensitivity of Reliability‐Based Optimum Design

Reliability-based optimization of maintenance scheduling of mechanical components under fatigue.

Optimum structural design with failure probability constraints.

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Optimum structural design with failure probability constraints.