To demonstrate the approach, consider the design of a stiff beam (Figure ). A typical function for a beam is to support a load without sagging. Rather than minimize the beam's mass or cost, the design objective for persistence is to minimize the beam's environmental lifetime at end-of-use. The design constraints on the beam define the loading conditions, amount of tolerable deflection, and geometry. The free, unconstrained variables are the choice of material and some geometric features. To derive an MI for persistence, we first defined the objective equation by solving a degradation rate equation, establishing a mathematical relationship between environmental lifetime and the geometry of the beam.