Nested optimization algorithms
Blagoj Delipetrev · 2020
This chapter presents the idea of nesting an optimization algorithm inside each transition of the multi-stage decision problem of reservoir operation that reduces the starting problem dimension and alleviates the curse of dimensionality. This idea is developed and incorporated in the three algorithms: nested dynamic programming (nDP), nested stochastic dynamic programming (nSDP), and nested reinforcement learning (nRL). These algorithms can solve ORO problem without significant increase in the algorithm complexity. Computationally, the algorithms are efficient and can handle dense and irregular variable discretization. The implementation of the sequence of single-objective optimization searches approach with the nDP, nSDP, and nRL creates multi-objective nDP (MONDP), MOnSDP, and MOnRL algorithms. The only difference between the nSDP and the classical SDP is that in the former there is the nested optimization algorithm that executes at each state transition.