A new correlated polyhedral uncertainty set for robust optimization

• Published in: Computers & industrial engineering Vol. 157; p. 107346
• Main Authors: Daneshvari, Hamed, Shafaei, Rasoul
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2021
• Subjects: Correlation; Over conservatism; Polyhedral uncertainty set; Robust optimization; Over conservatism; Correlation; Robust optimization; Polyhedral uncertainty set
• ISSN: 0360-8352; 1879-0550
• DOI: 10.1016/j.cie.2021.107346

•The correlation between coefficients should be considered in robust optimization.•Including perturbations with low probability of occurrence leads to over conservatism.•An estimation of correlation matrix is applied to introduce the new uncertainty set.•A decision making parameter is applied to formulate the robust counterpart.•The robustness and the over conservatism level of the proposed approach are improved. 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.