Note on the Effectiveness OF Stochastic Optimization Algorithms for Robust Design

Robust design optimization (RDO) uses statistical decision theory and optimization techniques to optimize a design over a range of uncertainty (introduced by the manufacturing process and unintended uses). Since engineering ob jective functions tend to be costly to evaluate and prohibitively expensive to integrate (required within RDO), surrogates are introduced to allow the use of traditional optimization methods to find solutions. This paper explores the suitability of radically different (deterministic and stochastic) optimization methods to solve prototypical robust design problems. The algorithms include a genetic algorithm using a penalty function formulation, the simultaneous perturbation stochastic approximation (SPSA) method, and two gradient-based constrained nonlinear optimizers (method of feasible directions and sequential quadratic programming). The results show that the fully deterministic standard optimization algorithms are consistently more accurate, consistently more likely to terminate at feasible points, and consistently considerably less expensive than the fully nondeterministic algorithms.