Julia JUMP Gurobi MIP - query and store best objective and bound at runtime - callback

Question

I am using Gurobi through the JuMP package in Julia to solve a mixed-integer program.
I would like to obtain a graph
like this one, where also a solution based on Python is provided (which was also addressed on
Gurobi community form).
However, I have not found working solutions for Julia calling Gurobi through JuMP.
I understand that callback functions have to be used (such as this suggestion or even the main documentation here), but I do not fully understand how they work and what is essential to achieve my goal.
Any help is much appreciated, as well as a possible description of what the callback function is doing at each step.
If it helps, I am using Gurobi (v.9.0.0), JuMP (v0.20.1), MathOptInterface (v0.9.22) and Julia (v.1.3.0).

Answer 1

You need to use the C API. Here is a translation of Eli's answer on the Gurobi forum:
using JuMP, Gurobi
model = direct_model(Gurobi.Optimizer())
N = 30
#variable(model, x[1:N], Bin)
#constraint(model, rand(N)' * x <= 10)
#objective(model, Max, rand(N)' * x)
data = Any[]
start_time = 0.0
function my_callback_function(cb_data, cb_where::Cint)
#show cb_where
if cb_where == GRB_CB_MIP
objbst = Ref{Cdouble}()
GRBcbget(cb_data, cb_where, GRB_CB_MIP_OBJBST, objbst)
objbnd = Ref{Cdouble}()
GRBcbget(cb_data, cb_where, GRB_CB_MIP_OBJBND, objbnd)
push!(data, (time() - start_time, objbst[], objbnd[]))
end
return
end
MOI.set(model, Gurobi.CallbackFunction(), my_callback_function)
start_time = time()
optimize!(model)
open("data.csv", "w") do io
for x in data
println(io, join(x, ", "))
end
end
p.s. please update to Julia 1.6 and JuMP 0.22. I have not tested whether this works on the older version.