Reliability-based optimization is considered by many authors as the most rigorous approach to structural design, because the search for the optimal solution is performed with consideration of the uncertainties present in the structural and load variables. The practical application of this idea, however, is hindered by the computational difficulties associated to the minimisation of cost functions with probabilistic constraints involving the computation of very small probabilities computed over implicit threshold functions, that is, those given by numerical models such as finite elements. In this chapter, a procedure intended to perform this task with a minimal amount of calls of the finite element code is proposed. It is based on the combination of a computational learning method (the support vector machines) and an artificial life technique (particle swarm optimisation). The former is selected because of its information encoding properties as well as for its elitist procedures that complement hose of the a-life optimisation method. The later has been chosen du to its advantages over classical genetic algorithms. The practical application of the procedure is demonstrated with earthquake engineering examples.
Reliability-Based Design of Thermal Protection Systems with Support Vector Machines