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


Solving optimization issues beneath hybrid uncertainty bears a serious computational burden. In this study, we tend to propose a unified structured optimization approach, termed strong granular optimization (RGO), to tackle the optimization problems underneath hybrid manifold uncertainties in an exceedingly computationally tractable manner. Essentially, the RGO will 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) data granulation in that basic granular units (BGUs) are formed, and 3) sturdy 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 better order hybrid uncertainties, respectively. It is shown that both sorts RGO models can be equivalently remodeled into linear programs or mixed integer linear programs which will be handled efficiently by off-the-shelf solvers. Furthermore, a target-based mostly tradeoff model is developed to boost the pliability 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 present approaches show that the RGO models will bring abundant higher computational efficiency and scalability without losing a lot of optimality, and also the RGO solutions exhibit a stronger resistance to the uncertainty.

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