Robust optimization considering tolerances of design variables

Optimization techniques have been applied to versatile engineering problems for reducing manufacturing cost and for automatic design. The deterministic approaches of optimization neglect the effects from uncertainties of design variables. The uncertainties include variation or perturbation such as tolerance band. At optimum, the constraints must be satisfied within the tolerance ranges of the design variables. The variation of design variables can also give rise to drastic change of performances. The two issues are related to constraint feasibility and insensitive performance. Robust design suggested in the present study has been developed to obtain an optimum value insensitive to variations on design variables within a feasible region. This is performed by using a mathematical programming algorithm. A multiobjective function is defined to have the mean and the standard deviation of the original objective function, while the constraints are supplemented by adding a penalty term to the original constraints. This method has an advantage in that the second derivatives of the constraints are not required. Several standard problems for structural optimization are solved to check the usefulness of the suggested method.