Order of columns during copy_to

[odow]

@mlubin and I have been discussing the following example:

julia> using JuMP

julia> function main()
           model = Model()
           @variable(model, x)
           @variable(model, y >= 0)
           @objective(model, Min, x + y)
           write_to_file(model, "file.mps")
           print(read("file.mps", String))
       end
main (generic function with 1 method)

julia> main()
NAME
ROWS
 N  OBJ
COLUMNS
    y         OBJ       1
    x         OBJ       1
RHS
RANGES
BOUNDS
 LO bounds    y         0
 PL bounds    y
 FR bounds    x
ENDATA

In JuMP, the columns are ordered x, y, but the MPS file, they are ordered as y, x.

Since the behavior of MIP solvers can depend on the column (and row) ordering, this can be undesirable.

The problem is:

MathOptInterface.jl/src/Utilities/copy.jl

Lines 199 to 234 in bca8a31

	"""
	_try_constrain_variables_on_creation(
	dest::MOI.ModelLike,
	src::MOI.ModelLike,
	index_map::IndexMap,
	::Type{S},
	) where {S<:MOI.AbstractScalarSet}
	Copy the constraints of type `MOI.VariableIndex`-in-`S` from the model `src` to
	the model `dest` and fill `index_map` accordingly. The copy is only done when the
	variables to be copied are not already keys of `index_map`.
	It returns a list of the constraints that were not added.
	"""
	function _try_constrain_variables_on_creation(
	dest::MOI.ModelLike,
	src::MOI.ModelLike,
	index_map::IndexMap,
	::Type{S},
	) where {S<:MOI.AbstractScalarSet}
	not_added = MOI.ConstraintIndex{MOI.VariableIndex,S}[]
	for ci_src in
	MOI.get(src, MOI.ListOfConstraintIndices{MOI.VariableIndex,S}())
	f_src = MOI.get(src, MOI.ConstraintFunction(), ci_src)
	if haskey(index_map, f_src)
	# Can't add it because it contains a variable previously added
	push!(not_added, ci_src)
	else
	set = MOI.get(src, MOI.ConstraintSet(), ci_src)::S
	vi_dest, ci_dest = MOI.add_constrained_variable(dest, set)
	index_map[ci_src] = ci_dest
	index_map[f_src] = vi_dest
	end
	end
	return not_added
	end

MathOptInterface.jl/src/Utilities/copy.jl

Lines 493 to 497 in bca8a31

	else
	Any[
	_try_constrain_variables_on_creation(dest, src, index_map, S)
	for S in sorted_variable_sets_by_cost(dest, src)
	]

which eagerly tries to constrain variables on creation based on their set type.

I wonder if we should:

1. not do this for scalar variables; or
2. use a better heuristic, that adds variables in the correct order, but puts them in a set iff they are consecutive in the VectorOfVariables function.

The original motivation for doing this is so that variable bridges can be preferentially used.

I don't really have an answer yet. I'll explore some stuff and report here.

[odow]

Okay. It's a bit more effort, but I think we can make this work out-of-the-box, just like we do for writing variable cones in the CBF writer.

See: #2478

x-ref #2494