A Transformation-Proximal Bundle Algorithm for Solving Multistage Adaptive Robust Optimization Problems

Abstract

This paper proposes a novel transformation-proximal bundle algorithmic framework to solve multistage adaptive robust optimization (ARO) problems. Different from existing solution methods, the proposed algorithmic framework partitions recourse decisions into state decisions and local decisions. It applies affine decision rule only to state decision variables and allows local decision variables to be fully adjustable. In this way, the original multistage ARO problem is proved to be transformed into a two-stage ARO problem. The proximal bundle algorithm with the Moreau- Yosida regularization is further developed for the exact solution of the resulting two-stage ARO problem. The transformation-proximal bundle algorithmic framework could generate less conservative solutions compared with the decision rule based approach, while enjoying a high computational efficiency. An application on multiperiod inventory control problem under demand uncertainty is presented to demonstrate the effectiveness and superiority of the proposed algorithm.