Statistical testing of optimality conditions in multiresponse simulation-based optimization

This article studies simulation-based optimization with multiple outputs. It assumes that the simulation model has one random objective function and must satisfy given constraints on the other random outputs. It presents a statistical procedure for testing whether a specific input combination (proposed by some optimization heuristic) satisfies the Karush-Kuhn-Tucker (KKT) first-order optimality conditions. The article focuses on "expensive" simulations, which have small sample sizes. The article applies the classic t test to check whether the specific input combination is feasible, and whether any constraints are binding; next, it applies bootstrapping (resampling) to test the estimated gradients in the KKT conditions. The new methodology is applied to three examples, which gives encouraging empirical results.