Stochastic Unit Commitment

The formulations and dual optimization algorithm mainly draw on the work of Anthony Papavasiliou:

Coupling Renewable Energy Supply with Deferrable Demand

by Papavasiliou, Anthony, Ph.D., University of California, Berkeley, 2011, 99; 3499039

Solve primal problem

$ python main.py <path_to_instance>

Solve linear relaxation

$ python main.py <path_to_instance> --relax

Solve linear relaxation + rounding algorithm

$ python main.py <path_to_instance> --relax --round

Lagrangian decomposition and subgradient optimization

$ python main.py <path_to_instance> --decompose

$ python main.py <path_to_instance> --decompose --nar 6 --epsilon 0.01 --alpha0 2000 --rho 0.96

The parameters for the subgradient algorithm are the following:

1. nar: number of iterations of subgradient algorithm to make before to start applying heuristics to recover primal solutions and upper bounds.
2. epsilon: convergence threshold / duality gap under which the subgradient algorithm is considered to have converged. When $(UB - LB) / UB &lt; \epsilon$, the algorithm stops.
3. alpha0: Initial steplength for updating Lagrange multipliers.
4. rho: discount factor of the steplength (if no feasible primal solution has been found yet).