Reservoir optimization and Machine Learning methods

Abstract

After showing the efficiency of feedforward networks to estimate control in high dimension in the global optimization of some storages problems, we develop a modification of an algorithm based on some dynamic programming principle. We show that classical feedforward networks are not effective to estimate Bellman values for reservoir problems and we propose some neural networks giving far better results. At last, we develop a new algorithm mixing LP resolution and conditional cuts calculated by neural networks to solve some stochastic linear problems.

A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection

“…For instance X max = 0 corresponds to the much simpler problem without storage nor control of the valuation of a wind power park. See also [22,43]. To represent the almost sure constraint 0 ≤ X t ≤ X max we choose as constrained function…”

“…We give the ŵ function on figure 7. Using Dynamic Programming with the StOpt library [29], we get an optimal value equal to 117.28 while a direct optimization of (31) using some neural networks as in [43], [17] we get a value of 117.11. Encouraged by Remark 6, Figure 3, Figure 6 and the related comments, we empirically estimate the value function by the point where the linear part of the auxiliary function reaches zero when Λ = 1 ε is sufficiently large.…”

“…We discretize the problem in time and use a neural network by time step, since a single network taking time as input is usually not sufficient enough for complex problems, as shown in [43]. In view of the discussion about closed-loop controls in Section 3, the neural network representing the control at each time step takes as inputs the current states X and Z z,α i where z is taken on a discretization of K. The method is described in Algorithm 1 with an example in Section 5.2.…”

A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection

“…For instance X max = 0 corresponds to the much simpler problem without storage nor control of the valuation of a wind power park. See also [22,43]. To represent the almost sure constraint 0 ≤ X t ≤ X max we choose as constrained function…”

“…We give the ŵ function on figure 7. [32], we get an optimal value equal to 117.28 while a direct optimization of (5.5) using some neural networks as in [43], [17] we get a value of 117.11. Encouraged by Remark 5.1, Figure 3, Figure 6 and the related comments, we empirically estimate the value function by the point where the linear part of the auxiliary function reaches zero when Λ = 1 ε is sufficiently large.…”