Reliability Optimization With Mixed Continuous-Discrete Random Variables and Parameters

Abstract

Engineering design problems frequently involve a mix of both continuous and discrete random variables and parameters. However, most methods in the literature deal with only the continuous or the discrete type, but not both. In particular, no method has yet addressed problems for which the random components (variables and∕or parameters) are categorically discrete. This paper develops an efficient optimization method for problems involving mixed continuous-discrete random variables and parameters. The method reduces the number of function evaluations performed by systematically filtering the discrete combinations 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.