A new criteria for convergence of multistage deterministic dynamic programming applied to multiobjective functions: A Brazilian hydro-thermal dispatch case

摘要

This paper proposes an alternative approach to analyze the convergence of multistage deterministic dual dynamic programming (DDDP). A new convergence stop criteria is proposed and it is based on a measure of gain produced when a new cut is inserted in cost-to-go function, during the backward phase of the algorithm. To do so, an additional linear programming problem is solved to decide if new cut (hyper plan) will be inserted or not on cost-to-go function. The results presented have shown that this approach is an alternative stop criterion when the interval of convergence is difficult to estimate. In this paper the methodology described was used towards DDDP for learning purposes. However, the same methodology can be easily extended for multi-objective problems and also for stochastic dual dynamic programming (SDDP). To prove the method effectiveness, results of a Brazilian study case will be shown, in which the methodology proposed was applied by using SDDP to minimize operative cost and deficit risks.