An outer approximations approach to reliability-based optimal design of structures

We present a new formulation of the problem of minimizing the initial cost of a structure subject to a minimum reliability requirement, expressed in terms of the so-called design points of the first-order reliability theory, i.e., points on limit-state surfaces that are nearest to the origin in a transformed standard normal space, as well as other deterministic constraints. Our formulation makes it possible to use outer approximations algorithms for the solution of such optimal design problems, eliminating some of the major objections associated with treating them as bilevel optimization problems. A numerical example is presented that illustrates the reliability and efficiency of the algorithm.