Data-Driven Adaptive Probabilistic Robust Optimization Using Information Granulation
提出一种数据驱动的自适应概率鲁棒优化方法，通过信息粒化技术从数据中提取知识并构建模型，在最优性与鲁棒性之间取得平衡，可转化为二阶锥规划高效求解，适用于不确定性下的决策问题。
In this paper, we consider a generic class of adaptive optimization problems under uncertainty, and develop a data-driven paradigm of adaptive probabilistic robust optimization (APRO) in a robust and computationally tractable manner. The paradigm comprises two phases: 1) bilayer information granulation (IG), which involves the data-mining techniques and nested decomposition of convex sets that establish and restructure the knowledge from data and 2) robustization and optimization over the restructured knowledge by the IG, which forms the APRO model. The tradeoff between the solution optimality and the robustness of the resulting data-driven APRO model can be achieved by adjusting the number of clusters and the number of nested decomposition units of the IG process. We draw the connections of the APRO model with the stochastic programming and the regular robust optimization models, respectively, and show that the APRO model can be regarded as a generalized version of both models. We show that the APRO model can be transformed into the second-order conic programming which is computationally tractable and can be solved efficiently by the off-the-shelf solvers. Furthermore, the model can be extended by robustizing the probability parameters. Finally, an application on two-stage facility location planning is presented, and the computational results demonstrate the performance and the insights of using the data-driven APRO models.