Dynamic programming with the principle of progressive optimality for searching rule curves

Rule curves are monthly reservoir-operation guidelines for meeting the minimum of water shortage over the long run. This paper proposes a dynamic programming (DP) approach for finding the optimal rule curves of single- and multi-reservoir systems. The proposed DP approach uses a traditional DP technique conditionally and applies the principle of progressive optimality (PPO) to search its optimal solutions. The proposed DP-PPO approach is suitable because of the multi-stage, nonlinear, and continuous-type characteristics of the rule curve search. Its dimensionality is relatively small, as compared with that of the traditional one. Results of an illustrative application to a multi-reservoir system under two different initial feasible solutions (i.e., new or existing reservoirs) have demonstrated that the DP- PPO approach is generally fast and robust. Its convergence varies only slightly, according to the initial conditions.