Robust Granular Optimization: A Structured Approach for Optimization Under Integrated Uncertainty

Solving optimization problems under hybrid uncertainty bears a heavy computational burden. In this study, we propose a unified structured optimization approach, termed robust granular optimization (RGO), to tackle the optimization problems under hybrid manifold uncertainties in a computationally tractable manner. Essentially, the RGO can be regarded as a complementary fusion of granular computing and robust optimization techniques. The paradigm of RGO consists of three core phases: 1) uncertainty identification, 2) information granulation in which basic granular units (BGUs) are formed, and 3) robust optimization realized over the BGUs. Following the proposed paradigm, we develop two classes of RGO models for general single-stage and two-stage optimization problems with separable and higher order hybrid uncertainties, respectively. It is shown that both types RGO models can be equivalently transformed into linear programs or mixed integer linear programs that can be handled efficiently by off-the-shelf solvers. Furthermore, a target-based tradeoff model is developed to enhance the flexibility of the RGO models in balancing the granularity level (or robustness level) and the solution conservativeness. The tradeoff model can also be efficiently solved by a binary search algorithm. Finally, sufficient computational studies are presented, and comparisons with the existing approaches show that the RGO models can bring much higher computational efficiency and scalability without losing much optimality, and the RGO solutions exhibit a stronger resistance to the uncertainty.