Multiple solvers for subproblems

[guimarqu]

We can change the specify! method in BlockDecomposition to allow the user to pass a vector of optimizers :

BD.specify!.(subproblems, lower_multiplicity = 0, solver = [MOI.Gurobi, my_callback_stage2, my_callback_stage3])

and we change the dispatch argument into solver :

stages = [ 
    ClA.ColumnGeneration(pricing_prob_solve_alg = ClA.SolveIpForm(solver = 1)),
    ClA.ColumnGeneration(pricing_prob_solve_alg = ClA.SolveIpForm(solver = 2)),
    ClA.ColumnGeneration(pricing_prob_solve_alg = ClA.SolveIpForm(solver = 3)),
]

So in that case, we do the exact phase with MOI.Gurobi and we use a callback for stages 2 & 3. The user will have to write a callback for each phase.

I don't see any better solution at the moment to handle atoptima/Coluna.jl#525 (comment).

Moreover, if we don't fix this, we'll have a design issue with customized optimizers. I would like to have these optimizers connected to Coluna through MOI. So to avoid buffering changes several times, I suggest to identify the solvers that have the same MOI optimizers and set the parameters just before optimizing the formulation. For instance, if you define solvers of your subproblem like this,

solvers = [
     with_attributes(MOI.RCSP, mode = :exact), 
     with_attributes(MOI.RCSP, mode = :heuristic),
     with_attributes(MOI.RCSP, mode = :speed_heuristic)
]

Coluna will instanciate MOI.RCSP only once for the subproblem, and will set the parameters just before optimizing the subproblem. We'll have to find a way to set parameters only when needed (because changing parameters may need some calculations ?).

What do you think ? (cc @vitornesello )

Originally posted by @guimarqu in atoptima/Coluna.jl#525 (comment)