New Lagrangian multiplier update approach for Lagrangian relaxation based unit commitment

Large scale unit commitment problems are of combinatorial nature and are usually very hard to solve. Among various algorithms, Lagrangian relaxation (LR) based method is one the most promising approaches. LR method typically includes two steps: the dual optimization and feasible solution construction. The dual optimization plays a crucial role in determining the overall computational efficiency and solution quality of the algorithm. The subgradient based method is widely used for dual optimization, but often suffers from slow convergence. This article presents an improved subgradient based method based on the concept of step size scaling factor that may achieve speedy convergence for dual optimization. Case studies have demonstrated the effectiveness of the proposed approach.