DOE based robust optimization considering tolerance bands of design parameters

The paper describes a robust optimization method to account for the tolerance of design variable and the variation in problem parameter. The proposed post-optimization effort is initiated from the deterministic optimum as a baseline. The successive process to find search directions and step sizes toward the robust optimum is conducted by determining the worst design that has the highest level in constraint violation. During the selection of the worst design, an orthogonal array table in the context of design of experiemtns (DOE) is used to reduce the constraint function evaluations especially for higher dimensionality problem. The analysis of means (ANOM) is adopted in a case where the variation in problem parameter is considered. The measurement criterion to select the worst design is based on the degree of cumulative constraint violation. A mathematical function problem is first conducted to examine the tolerance of design variable. A cantilever beam problem described by four design variables and a bracket problem with seven design variables are subsequently explored by considering both tolerance of design variable and variation in problem parameter.