Robust linear optimization under new distance measure

Abstract

Several robust counterparts of linear optimization problems with uncertain data were proposed since 1970 and have been extensively studied and extended. In these approaches, the uncertainty set plays an important role since it determines the level of protection of the solution; the solution might be too conservative in order to ensure that the solution remains feasible if the disturbance of data is relatively large. In this paper, we propose a new robust counterpart under a new distance measure. The new approach can ensure that all uncertain data can be mapped to a bounded neighborhood of nominal value regardless of the data from the nominal value either near or far. So the new approach succeeds in reducing the price of robustness; on the other hand, the new robust formulation is also a linear optimization problem. Numerical results for the problems of AFIRO and ADLITTLE from the Net Lib library shown that the effectiveness of the new formulation. Key words: Linear programming, data uncertainty, robust linear optimization.