一种改进轻鲁棒优化模型及其线性对应式

An Improved Light Robust Optimization Model and Its Linear Counterpart

轻鲁棒优化模型是改善鲁棒优化模型保守性的一种方法,但该模型还存在无法独立求解、计算量较大、不能保证保守性一定改善、约束可能过度违背、不适于对右侧不确定问题进行建模等缺点。针对上述问题,提出一种适用于右侧不确定问题的改进轻鲁棒优化(improved light robust,ILR)模型,并以命题的形式证明了其在保守性改善方面的有效性;然后基于排序截断法,进一步推导出ILR模型在预算不确定集下的线性对应式,并以命题的形式证明线性对应式与原鲁棒约束的等价性;该线性对应式因保持了模型的线性特点,而可直接采用线性方法进行求解,相应提高了求解效率。算例证明了所提方法的有效性。该文研究工作促进了鲁棒优化理论的发展,并为电力系统机组组合等实际优化问题的进一步研究及发展奠定了理论基础。

Light robust（LR） model was originally developed to reduce the conservatism of classic linear robust models. However, some of its limitations impede the application in practice, such as unable being independently solved, significant calculation burden, no guaranteed conservatism improvement, violations of boundless constraints. In this paper, an improved light robust（ILR） model with right hand-side uncertain polynomial is proposed, which could overcome aforementioned shortcomings. The effectiveness of the conservatism improvement through the ILR is justified by a proposition which is strictly proved. Then, its tractable linear counterpart with budgeted uncertain set is further deduced and then its equivalence to the original constraints is justified by a proven proposition. The derived linear counterpart can be efficiently solved by linear programming algorithms because of the preserved linearity characteristics. The results from the examples demonstrate the validity of the proposed model. The research promotes the development of robust optimization theory and meantime it also builds a strong basis for solving other similar optimization problems in power systems such as unit commitment.