Is there a way to extract the number of mixed-integer iterations during a particular iteration or solve in the SDDP.jl?

Specific Domains Optimization (Mathematical)
1

I am dealing with a multi-stage mixed-integer stochastic global supply chain optimization problem and want to solve it using the SDDiP algorithm using the SDDP.jl package in Julia.

In this regard, I want to determine the number of mixed-integer iterations during a particular iteration or solve in the SDDiP algorithm to compare various solvers (with their default parameters) used within the SDDiP algorithm.

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This isn’t possible.

Since you’ve asked a few related questions recently, it might be worth stepping back a bit.

  • What are you trying to do and why?

It looks like you’re trying to compare the performance of different solvers on some multistage stochastic problems, and potentially compare to the deterministic equivalent. This is both useful and not useful at the same time, and there are number of things to take into consideration

When comparing against the deterministic equivalent:

  • SDDP.jl cannot (always) find a provably optimal policy. Your state variables must be pure binary, and you must use duality_handler = SDDP.LagragianDuality().
  • Even if you can fairly compare runtimes against the deterministic equivalent, it is trivially possible to make SDDP.jl look arbitrarily better, merely by increasing the size of the sample space at each node.
  • Once trained, SDDP.jl can evaluate out-of-sample realizations of the random variables, which the deterministic equivalent cannot.

I really see SDDP.jl and the deterministic equivalent as solving separate problems. They’re not usefully directly comparable.

When comparing between two solvers:

  • Even if you set the random seed before calling SDDP.train, the algorithm is not guaranteed to follow identical paths because the two solvers may converge to different primal points. This particularly the case with MIP solvers if you solve to some optimality gap. Thus, comparing the total number of branch and bound nodes isn’t a very useful comparison metric.
  • I have noticed that some solvers like CPLEX (and even GLPK) may outperform Gurobi on simple examples, but this is because they are less numerically robust. If you tweak the problem slightly they may error or fail to converge, while Gurobi normally has fewer problems.
1 Like
3

Got it, then I will use the solution objective function values to benchmark SDDiP’s performance with extensive-form linear programming (deterministic). In addition, I have decided to report computational time, memory resource consumption, and the number of SDDiP training iterations.

It is just to benchmark the SDDiP performance, as SDDiP does not provide provably optimal solutions. It is not intended to evenhandedly compare the two algorithms.

As for the comparison between solvers, I have decided to make the problem instances so that the solvers can be effectively compared for the extraction of insights about their abilities for their use in extensive-form linear programming and the SDDiP algorithm.