Near‐Optimality Analysis for Linear Models

Abstract

Linear optimization techniques are often used to find the “best” solution to an engineering design problem. However, it is generally necessary to make certain assumptions, approximations, and idealizations in order to reduce the original problem to a linear format. Therefore, the computed optimal solution may not actually be the best and, in fact, may not even be feasible. In such cases, it is useful to generate other feasible solutions satisfying all the secondary constraints and exhibiting an objective function value close to the computed optimal. An existing algorithm is available to generate alternative solutions in ranked order. This algorithm can be applied to the design problem in order to generate a prespecified number of near‐optimal solutions or all solutions up to a prespecified level of the objective function. An illustrative example utilizes this approach to solve a problem with a nonlinear objective function by a two‐stage linear technique incorporating near‐optimal solutions.