The Cost of Numerical Integration in Statistical Decision-theoretic Methods for Robust Design Optimization

摘要

The Bayes principle from statistical decision theory provides a conceptual frameworkfor quantifying uncertainties that arise in robust design optimization. The difficulty withexploiting this framework is computational, as it leads to objective and constraint functions thatmust be evaluated by numerical integration. Using a prototypical robust design optimizationproblem, this study explores the computational cost of multidimensional integration (computingexpectation) and its interplay with optimization algorithms. It concludes that straightforwardapplication of standard off-the-shelf optimization software to robust design is prohibitivelyexpensive, necessitating adaptive strategies and the use of surrogates.