Periodical SDDP

[FSchmidtDIW]

Hi Oscar,

I am dealing with an end-of-horizon effect in a capacity expansion problem.
Currently, I have added a soft constraint to the final node that penalises shortfalls from a target storage level decided along with the capacities in node 1. This is rather restrictive. I want to explore other options. Unfortunately, an infinite-horizon reformulation with a unicyclic graph is in all likelihood computationally intractable given my discount rate and the complexity of the subproblems.

Alternatively, I came across the Shapiro and Ding (2020) paper. Unless I am misunderstanding they suggest for periodical problems to solve an additional node at the end of the horizon. So if I normally modeled a year with an investment stage and 12 monthly operational stages from Jan to Dec, I would add another Jan at the end. They then add the cutting plane model of operational node 1 (first Jan) to operational node 13 (second Jan).

How "simple" would it be to add the cutting plane model of one stage to another stage in SDDP.jl? Is that something I could do in a new ForwardPass?

Thanks a lot,

Felix

[odow]

Shapiro's "periodical SDDP" is just SDDP with a policy graph that forms a single cycle (our unicyclic graph).

If you don't care about the global optimal solution, then just train a heuristic policy.

It sounds like your idea is to have a unicyclic graph with 12 nodes, and then train with:

SDDP.train(
    model;
    sampling_scheme = SDDP.InSampleMonteCarlo(;
        max_depth::Int = 13,
    ),
)

Another option would be to just train with a smaller discount factor (higher interest rate), and then simulate the policy with the true factor.

[FSchmidtDIW]

Ah, of course! This makes sense. Thanks a lot!