A novel nested dynamic programming (nDP) algorithm for multipurpose reservoir optimization

In this article we present a novel nested dynamic programming (nDP) algorithm for multipurpose reservoir optimization with additional decision variables related to different water users. The nDP algorithm is built from two algorithms: (1) dynamic programming (DP) and (2) nested optimization algorithm implemented with Simplex and quadratic Knapsack methods. The novel idea is to include a nested optimization algorithm into the DP transition that reduces the initial problem dimension and alleviates the DP's curse of dimensionality. The nDP can solve multi-objective optimization problems, without significantly increasing the algorithm complexity and the computational expenses. Computationally, the nDP can handle dense and irregular variable discretization; it is coded in Java as a prototype application and has been successfully tested with eight objectives at the Knezevo reservoir in the Republic of Macedonia. The article presents a discussion on comparison of nDP with other DP methods and highlights the advantages of nDP.