To solve multistage adaptive stochastic optimization problems under both endogenous and exogenous uncertainty, a novel solution framework based on robust optimization technique is proposed. The endogenous uncertainty is modeled as scenarios based on an uncertainty set partitioning method. For each scenario, the adaptive binary decision is assumed constant and the continuous variable is approximated by a function linearly dependent on endogenous uncertain parameters. The exogenous uncertainty is modeled using lifting methods. The adaptive decisions are approximated using affine functions of the lifted uncertain parameters. In order to demonstrate the applicability of the proposed framework, a number of numerical examples of different complexity are studied and a case study for infrastructure and production planning of shale gas field development are presented. The results show that the proposed framework can effectively solve multistage adaptive stochastic optimization problems under both types of uncertainty.

中文翻译：

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内生和外生不确定性下的多级自适应随机混合整数优化

为解决内生和外生不确定性下的多级自适应随机优化问题，提出了一种基于鲁棒优化技术的新型求解框架。内生不确定性被建模为基于不确定性集划分方法的情景。对于每个场景，自适应二元决策假定为常数，连续变量由线性依赖于内生不确定参数的函数近似。使用提升方法对外生不确定性进行建模。使用提升的不确定参数的仿射函数来近似自适应决策。为了证明拟议框架的适用性，研究了许多不同复杂性的数值例子，并介绍了页岩气田开发的基础设施和生产规划的案例研究。结果表明，所提出的框架可以有效解决两种不确定性下的多级自适应随机优化问题。