Sensitivity of Optimum Solutions of Problem Parameters

Abstract

Solution of the optimum sensitivity problem yields the values of derivatives of the optimal objective function and design variables with respect to those physical quantities which were kept constant as problem parameters during optimization. Examples of these sensitivity derivatives might include derivatives of cross-section al area and structural mass with respect to allowable stress and derivatives of fuel consumed and wing aspect ratio with respect to aircraft range. Derivation of the sensitivity equations that yield the sensitivity derivatives directly, which avoids the costly and inaccurate perturb-and-reoptimize approach, is discussed and solvability of the equations is examined. The equations apply to optimum solutions obtained by direct search methods as well as those generated by procedures of the sequential unconstrained minimization technique (SUMT) class. Applications are discussed for the use of the sensitivity derivatives in extrapolation of the optimal objective function and design variable values for incremented parameters, optimization with multiple objectives, and decomposition of large optimization problems. Several aspects of these applications and verification of the sensitivity equations are presented through numerical examples.