A new correlated polyhedral uncertainty set for robust optimization

Abstract

Robust optimization approaches are commonly applied in solving a problem with uncertainty. One of the main issues in dealing with uncertainties is the correlations among uncertain parameters. This subject is rarely considered by the researchers and hence the proposed robust approaches normally lead to the solutions which include perturbations with low probability of occurrence. This results in solutions with over conservatism. In this research, an estimation of correlation matrix is applied in order to provide a new uncertainty set that includes probable perturbations. Furthermore in order to trade-off between optimality and level of robustness, a decision making parameter is applied to formulate the corresponding robust counterpart. In order to study the performance of the proposed method, an uncertain optimization problem with correlated uncertain coefficients is solved. Results of the study reveal that the proposed model has superior performance than that of the existing robust approaches.