Statistical testing of optimality conditions in multiresponse simulation-based optimization

B.W.M. Bettonvil, E. Del Castillo, J.P.C. Kleijnen

Research output: Contribution to journalArticleScientificpeer-review

28 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)448-458
JournalEuropean Journal of Operational Research
Issue number2
Publication statusPublished - 2009


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