Formulating a customized optimization problem in JuliaOpt

Specific Domains Optimization (Mathematical)
1

Hello everyone,
I have clear modeling requirements, but not sure how to (or is it possible to) implement my problem with Julia optimization packages, like JuMP.
General optimization problem:

Objective function: obj(x, y, z)
Decision variables: (x, y, z)
Constraints: x + y + z = 1 (as an example)

Main requirements for the optimization:

  1. I needed to do a sequential optimization, i.e. repeatedly solve the above optimization problem.
  2. The variables x, y, z are related to actual systems, for example, related to three batteries, x for battery 1, y for battery 2, and z for battery 3.
  3. Thus for the sequential optimization problems, there will be a case at some stage (we do know it in advance, but during the simulation there will be an index value (updated) for each battery to indicate whether a battery is functioning), some batteries may fail due to performance aging.
  4. To adapt to this situation, I need the decision variables to be able to change: for example, if battery 1 fails, I need to "get rid of " decision variable x and continue the optimization with decision variables y, z.

My problem:
Is it possible to implement such varying variables optimization in Julia?
Thank you very much for checking!

2

Sure, you can do all of this in JuMP. However, your question is a little too broad to get a good answer. (It’s easier to provide advice if you have a first attempt at coding that we can offer suggestions to improve, rather than asking generic questions.)

  • Have you formulated this on paper first?
  • Are you trying to find an optimal policy? Or are you okay using a myopic one? For example, do you intend to take into account when the battery will fail in earlier actions?

If you want to formulate this as a multistage stochastic program, check out: https://github.com/odow/SDDP.jl.

Otherwise, you should take a look at some of the examples in the JuMP documentation: Power Systems · JuMP

1 Like
3

Thanks, Odow.
Actually, this is the problem I have already implemented in Python and I didn’t
find a suitable solution. And recently I am learning Julia, so I tried to implement
my problem with Julia.
I will read the materials you provide and then repost a specific problem.

For the two questions you posed,

  1. I will recheck (formulate) my problem and ask with a specific example.
  2. You are right, I was doing something like optimal control and my goal is to find an optimal policy.
    I think I will need to consider various optimization horizons, both short-term and long-term.