鲁棒线性优化问题研究综述

Survey on robust linear optimization

鲁棒优化(RO)是从计算复杂性的角度研究不确定优化模型鲁棒最优解的数学方法.从单阶段鲁棒优化和多阶段鲁棒优化两个方面对鲁棒线性优化(RLO)理论的研究进展进行综述,前者的研究主要基于不同形式的不确定集合,后者的研究则基于前者的方法.研究多阶段不确定决策中决策变量受不确定参数实现值影响的情况,其核心是影响函数连续时的仿射可调鲁棒对应模型和函数离散时的有限适应性模型.最后对RLO的研究前景作了展望.

Robust optimization is a mathematical method to address optimal solutions for the uncertain optimization models in terms of computational complexity. Main developments of robust linear optimization （RLO） are surveyed from two aspects, single-stage and multi-stage robust optimization. The former is based on various modeling forms of uncertainty set, while the latter investigates that the decision variablesent are depend on the realization of uncertainty parameters on the basis of the former theories, mainly involving affinely adjustable robust counterpart in the case of continuous dependent function and finite adaptability model in the case of discrete dependent function. Finally, the future researches of RLO are prospected.