N.D. Lagaros, Y. Tsompanakis, M. Fragiadakis, V. Plevris and M. Papadrakakis, "Metamodel-based Computational Techniques for Solving Structural Optimization Problems Considering Uncertainties", Chapter 21 in Structural Design Optimization Considering Uncertainties, Y. Tsompanakis, N.D. Lagaros and M. Papadrakakis (Eds.), Taylor and Francis, 2008 (ISBN: 978-0-415-45260-1).

Abstract:
Uncertainties are inherent in engineering problems due to various numerical modeling "imperfections" and due to the inevitable scattering of the design parameters from their nominal values. Under this perspective, there are two main optimal design formulations that account for the probabilistic response of structural systems: Reliability-based Design Optimization (RBDO) and Robust Design Optimization (RDO). In this work both type of problems are briefly addressed and realistic engineering applications are presented. The optimization part of the proposed probabilistic formulations is solved utilizing efficient evolutionary methods. In both types of problems the probabilistic analysis is carried out with the Monte Carlo Simulation (MCS) method incorporating the Latin Hypercube Sampling (LHS) technique for the reduction of the sample size. In order to achieve further improvement of the computational efficiency a Neural Network (NN) is used to replace the time-consuming FE analyses required by the MCS. Moreover, various sources of randomness that arise in structural systems are taken into account in a "holistic" probabilistic perception by implementing a Reliability-based Robust Design Optimization (RRDO) formulation, where additional probabilistic constraints are incorporated into the standard RDO formulation. The proposed RRDO problem is formulated as a multi-criteria optimization problem using the non-dominant Cascade Evolutionary Algorithm (CEA) combined with the weighted Tchebycheff metric.