Add support for callbacks

[SouthEndMusic]

It would be nice to be able to pass a callback function that is applied after each optimization for an objective (particularly in the case of lexicographic multi-objective optimization). The reason I ask is that I'm having trouble achieving what I want in the constricting context of the lexicographic algorithm. It would look something like

callback!(model::JuMP.model, objective::JuMP.AffExpr, objective_index::Int; my_struct = nothing)

So within the scope of this callback I can access the model to read the values of the decision variables resulting from the latest optimization and modify bounds. Ideally I can also pass a generic object my_struct to store (processed) results. The objective and objective_index can be used to decide what parsing must be done after this particular objective.

[kofgokhan]

I was thinking of something similar. I also think this would be an incredibly nice feature for problems with structure. Not all algorithms should have this, perhaps.

[kofgokhan]

For the time being, maybe you can write your own lexicographic algorithm with the callback embedded somewhere.

[SouthEndMusic]

For the time being, maybe you can write your own lexicographic algorithm

Thanks for the tip, but I just refactored that out of my code ^^

[odow]

Can you provide a minimal example of a model with your callback?

[odow]

Another option is for you to write your own algorithm. You don't need to implement much. Lexicographic is pretty trivial:

https://github.com/jump-dev/MultiObjectiveAlgorithms.jl/blob/master/src/algorithms/Lexicographic.jl

I tend to think that a callback here won't be helpful/is out of scope for this package. Your callback is in the JuMP-level space, but MultiObjectiveAlgorithms is written at the MOI layer. There may not be a one-to-one mapping of your variables and constraints. Also, by default the Lexicographic algorithm iterates over multiple permutations of the objective vectors. And it isn't obvious whether the callback would be a good fit for other algorithms in MultiObjectiveAlgorithms.jl.

[SouthEndMusic]

@odow thanks for looking into this

[odow]

Can you provide a minimal example of what you were trying to achieve?

[SouthEndMusic]

I have a flow network with flow demands of different priorities within the network. I want to know the demand per priority at inlets into the network. I could solve this by making a commodity per priority but I'd like to avoid that if possible.

using JuMP
using HiGHS

model = Model(HiGHS.Optimizer)
set_silent(model)
demand = rand(5) .+ 0.2

@variable(model, inlet_flow ≥ 0)
@variable(model, 0 ≤ other_source_flow ≤ 1.0)
@variable(model, 0 ≤ allocated[i=1:5] ≤ demand[i])

# Flow conservation
@constraint(model, sum(allocated) == inlet_flow + other_source_flow)

objectives = vcat([[demand[i] - allocated[i], inlet_flow] for i in 1:5]...)

set_constraint_condition(model, objective_index) = isodd(objective_index)

function callback!(model, objective_index, inlet_demand)
    isodd(objective_index) && return
    inlet_demand_index = Int(objective_index // 2)

    if inlet_demand_index == 1
        inlet_demand[1] = value(inlet_flow)
    else
        inlet_demand[inlet_demand_index] = value(inlet_flow) - sum(inlet_demand[1:inlet_demand_index-1])
    end
    return nothing
end

inlet_demand = zeros(5)

for (objective_index, objective) in enumerate(objectives)
    @objective(model, Min, objective)
    optimize!(model)
    callback!(model, objective_index, inlet_demand)
    if set_constraint_condition(model, objective_index)
        @constraint(model, objective == objective_value(model))
    end
end

@assert value.(allocated) ≈ demand
@assert value(other_source_flow) ≈ 1.0
@assert all(inlet_demand .<= demand)

[odow]

If I had to summarise your need slightly differently:

You want to be able to access the primal variable values at each iteration of lexicographic and you're not using the callback to modify the problem during the iterations?

Adding an opt-in for extra primal solutions is something we could consider doing.

[SouthEndMusic]

Ah yes you're right, I don't actually have to modify the problem during the iterations, having access to the intermediate solutions would be sufficient. It is important for me though to have the ability not to add a constraint for certain objectives.