Enhanced Lagrangian relaxation solution to the generation scheduling problem

This paper proposes an enhanced Lagrangian relaxation (LR) solution to the generation scheduling problem of thermal units, known as unit commitment (UCP). The proposed solution method is characterized by a new Matlab function created to determine the optimal path of the dual problem, in addition, the initialization of Lagrangian multipliers in our method is based on both unit and time interval classification. The proposed algorithm is distinguished by a flexible adjustment of Lagrangian multipliers, and dynamic search for uncertain stage scheduling, using a Lagrangian relaxation–dynamic programming method (LR–DP). After the LR best feasible solution is reached, a unit decommitment is used to enhance the solution when identical or similar units exist in the same system. The proposed algorithm is tested and compared to conventional Lagrangian relaxation (LR), genetic algorithm (GA), evolutionary programming (EP), Lagrangian relaxation and genetic algorithm (LRGA), and genetic algorithm based on unit characteristic classification (GAUC) on systems with the number of generating units in the range of 10–100. The total system production cost of the proposed algorithm is less than the others especially for the larger number of generating units. Computational time was found to increase almost increases linearly with system size, which is favorable for large-scale implementation.