Reliability Optimization Involving Mixed Continuous-Discrete Uncertainties

Abstract

Engineering design problems frequently involve a mix of both continuous and discrete uncertainties. However, most methods in the literature deal with either continuous or discrete uncertainties, but not both. In particular, no method has yet addressed uncertainty for categorically discrete variables or parameters. This article develops an efficient optimization method for problems involving mixed continuous-discrete uncertainties. The method reduces the number of function evaluations performed by systematically filtering the discrete factorials used for estimating reliability based on their importance. This importance is assessed using the spatial distance from the feasible boundary and the probability of the discrete components. The method is demonstrated in examples and is shown to be very efficient with only small errors.