The uncertainty sensitivity index method (USIM) & its extension

This article deals with optimization problems that have some uncertain parameters with unknown probabilities. The article proposes a strategy of transferring the system’s uncertainty associated with these optimization problems into a norm of a set of norms that is added to the original objective function(s) within a multiobjective framework. The uncertainty sensitivity index method (USIM) proposed by Haimes and Hall is extended to several general cases. A robust algorithm is developed to guarantee an ideal solution for cases where the nominal value of the uncertain parameter is itself an uncertain variable. A design problem is also addressed to identify the best-compromise values of the system’s parameters by integrating the USIM with the envelope approach.