  In this note, we present a derivative-free trust-region (TR) algorithm for
reliability based optimization (RBO) problems. The proposed algorithm consists
of solving a set of subproblems, in which simple surrogate models of the
reliability constraints are constructed and used in solving the subproblems.
Taking advantage of the special structure of the RBO problems, we employ a
sample reweighting method to evaluate the failure probabilities, which
constructs the surrogate for the reliability constraints by performing only a
single full reliability evaluation in each iteration. With numerical
experiments, we illustrate that the proposed algorithm is competitive against
existing methods.
