Combining Lagrangian relaxation, benders decomposition, and the level bundle method in the stochastic hydrothermal unit-commitment problem

In recent years, stochastic programming has gained increasing attention as a tool to support the scheduling of generating units in the face of uncertain information. One approach that has a long-standing history in stochastic programming is the Benders decomposition (BD). However, BD is known to suffer from a series of shortcomings, for example, oscillation and tailing-off effect. To reduce these drawbacks, regularization techniques are appealing options. However, even if regularized, BD may still struggle to converge due to the growing computational burden of its master problem (MP) over the iterations - this is especially noticeable in mixed-integer programming models. Thus, to tackle this growing MP, we propose decomposing it using dual decomposition. We test our methodology on a testbed comprised of 108 cases from a system with 46 buses. Our results show that our methodology is effective both in terms of running times as well as the optimality gap.