Julia - Gurobi Callbacks on array of JuMP variables - optimization

Question

In Gurobi and JuMP 0.21, it is well documented here on how you would access a variable with a callback:
using JuMP, Gurobi, Test
model = direct_model(Gurobi.Optimizer())
#variable(model, 0 <= x <= 2.5, Int)
#variable(model, 0 <= y <= 2.5, Int)
#objective(model, Max, y)
cb_calls = Cint[]
function my_callback_function(cb_data, cb_where::Cint)
# You can reference variables outside the function as normal
push!(cb_calls, cb_where)
# You can select where the callback is run
if cb_where != GRB_CB_MIPSOL && cb_where != GRB_CB_MIPNODE
return
end
# You can query a callback attribute using GRBcbget
if cb_where == GRB_CB_MIPNODE
resultP = Ref{Cint}()
GRBcbget(cb_data, cb_where, GRB_CB_MIPNODE_STATUS, resultP)
if resultP[] != GRB_OPTIMAL
return # Solution is something other than optimal.
end
end
# Before querying `callback_value`, you must call:
Gurobi.load_callback_variable_primal(cb_data, cb_where)
x_val = callback_value(cb_data, x)
y_val = callback_value(cb_data, y)
# You can submit solver-independent MathOptInterface attributes such as
# lazy constraints, user-cuts, and heuristic solutions.
if y_val - x_val > 1 + 1e-6
con = #build_constraint(y - x <= 1)
MOI.submit(model, MOI.LazyConstraint(cb_data), con)
elseif y_val + x_val > 3 + 1e-6
con = #build_constraint(y + x <= 3)
MOI.submit(model, MOI.LazyConstraint(cb_data), con)
end
if rand() < 0.1
# You can terminate the callback as follows:
GRBterminate(backend(model))
end
return
end
# You _must_ set this parameter if using lazy constraints.
MOI.set(model, MOI.RawParameter("LazyConstraints"), 1)
MOI.set(model, Gurobi.CallbackFunction(), my_callback_function)
optimize!(model)
#test termination_status(model) == MOI.OPTIMAL
#test primal_status(model) == MOI.FEASIBLE_POINT
#test value(x) == 1
#test value(y) == 2
i.e., you would use x_val = callback_value(cb_data, x). However, how should you do when you have an array of variables with specific indexes not starting at 1, i.e. my variables are not in a vector but declared thanks to:
#variable(m, x[i=1:n, j=i+1:n], Bin)
Should I access x with double for loops on its two dimensions and call multiple times callback_value? If so, the indexes for j will not be the same, won't they?

Answer 1

Use broadcasting:
x_val = callback_value.(Ref(cb_data), x)
Or just call callback_value(cb_data, x[i, j]) when you need the value.
For example:
using JuMP, Gurobi
model = Model(Gurobi.Optimizer)
#variable(model, 0 <= x[i=1:3, j=i+1:3] <= 2.5, Int)
function my_callback_function(cb_data)
x_val = callback_value.(Ref(cb_data), x)
display(x_val)
for i=1:3, j=i+1:3
con = #build_constraint(x[i, j] <= floor(Int, x_val[i, j]))
MOI.submit(model, MOI.LazyConstraint(cb_data), con)
end
end
MOI.set(model, MOI.LazyConstraintCallback(), my_callback_function)
optimize!(model)
yields
julia> optimize!(model)
Gurobi Optimizer version 9.1.0 build v9.1.0rc0 (mac64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 0 rows, 3 columns and 0 nonzeros
Model fingerprint: 0x5d543c3a
Variable types: 0 continuous, 3 integer (0 binary)
Coefficient statistics:
Matrix range [0e+00, 0e+00]
Objective range [0e+00, 0e+00]
Bounds range [2e+00, 2e+00]
RHS range [0e+00, 0e+00]
JuMP.Containers.SparseAxisArray{Float64,2,Tuple{Int64,Int64}} with 3 entries:
[1, 2] = -0.0
[2, 3] = -0.0
[1, 3] = -0.0
JuMP.Containers.SparseAxisArray{Float64,2,Tuple{Int64,Int64}} with 3 entries:
[1, 2] = 2.0
[2, 3] = 2.0
[1, 3] = 2.0
JuMP.Containers.SparseAxisArray{Float64,2,Tuple{Int64,Int64}} with 3 entries:
[1, 2] = 2.0
[2, 3] = 2.0
[1, 3] = 2.0
JuMP.Containers.SparseAxisArray{Float64,2,Tuple{Int64,Int64}} with 3 entries:
[1, 2] = 2.0
[2, 3] = -0.0
[1, 3] = -0.0
Presolve time: 0.00s
Presolved: 0 rows, 3 columns, 0 nonzeros
Variable types: 0 continuous, 3 integer (0 binary)
JuMP.Containers.SparseAxisArray{Float64,2,Tuple{Int64,Int64}} with 3 entries:
[1, 2] = -0.0
[2, 3] = -0.0
[1, 3] = -0.0
Found heuristic solution: objective 0.0000000
Explored 0 nodes (0 simplex iterations) in 0.14 seconds
Thread count was 8 (of 8 available processors)
Solution count 1: 0
Optimal solution found (tolerance 1.00e-04)
Best objective 0.000000000000e+00, best bound 0.000000000000e+00, gap 0.0000%
User-callback calls 31, time in user-callback 0.14 sec