MPS code is not deterministic

[mlubin]

I haven't tried to create examples, but the use of Dict at

MathOptInterface.jl/src/FileFormats/MPS/MPS.jl

Lines 465 to 473 in 535e7f0

	mutable struct TempMPSModel
	name::String
	obj_name::String
	columns::Dict{String, TempColumn}
	rows::Dict{String, TempRow}
	intorg_flag::Bool # A flag used to parse COLUMNS section.
	TempMPSModel() = new("", "", Dict{String, TempColumn}(),
	Dict{String, TempRow}(), false)
	end

likely makes copy_to not deterministic, e.g.,

MathOptInterface.jl/src/FileFormats/MPS/MPS.jl

Line 538 in 535e7f0

for (name, column) in temp.columns

MathOptInterface.jl/src/FileFormats/MPS/MPS.jl

Line 558 in 535e7f0

for (c_name, row) in temp.rows

Same issue in the ordering of variables when the problem is written out:

MathOptInterface.jl/src/FileFormats/MPS/MPS.jl

Line 169 in 535e7f0

coefficients = Dict{String, Vector{Tuple{String, Float64}}}()

MathOptInterface.jl/src/FileFormats/MPS/MPS.jl

Line 195 in 535e7f0

for (variable, terms) in coefficients

MathOptInterface.jl/src/FileFormats/MPS/MPS.jl

Line 331 in 535e7f0

bounds = Dict{MOI.VariableIndex, Tuple{Float64, Float64}}()

MathOptInterface.jl/src/FileFormats/MPS/MPS.jl

Line 344 in 535e7f0

for (index, (lower, upper)) in bounds

Unless we have a good reason not to, variables should keep their ordering when you round-trip read and write to an MPS file. The ordering of variables makes a huge difference for MIP solvers. Ideally the same would hold for constraints, although that's a bit more complex because of how we represent them in MOI.