Uncertain Requirements in the Design Selection Problem

The problem of identifying a specific design or architecture that satisfies all the system requirements is complex. This problem is further complicated in the presence of uncertainty and risk. When a requirement is subject to uncertainty, there are a number of approaches available to systems engineers, each of which has its own pros and cons. Classical robust optimization is an attractive approach in optimization under uncertainty, as it selects a design with the best performance when the worst-case scenario occurs. In this framework, uncertainty is described deterministically through uncertainty sets. The specification of these sets directly impacts characteristics of the robust counterpart problem and quality of the robust solution. In particular, depending on the specifications of the uncertainty sets, there can be a significant chance that the robust formulation becomes infeasible, i.e., no architecture satisfies all the system requirements, while the model is feasible with high probability when the uncertainty in requirements is modeled probabilistically. This paper investigates the effect of uncertainties on the feasibility of the design selection problem and introduces a novel measure of infeasibility.