Binary variables with bounds are incorrect

[odow]

See https://discourse.julialang.org/t/xpress-julia-api-has-bug-with-fixing-variables/82895/4

julia> model = Model(Xpress.Optimizer)
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: EMPTY_OPTIMIZER
Solver name: Xpress

julia> @variable(model, x, Bin)
x

julia> @objective(model, Max, x)
x

julia> fix(x, 0; force = true)

julia> optimize!(model)
FICO Xpress v8.13.3, Hyper, solve started 0:09:54, Jun 17, 2022
Heap usage: 74KB (peak 74KB, 360KB system)
Maximizing MILP  using up to 8 threads, with these control settings:
OUTPUTLOG = 1
MPSNAMELENGTH = 64
CALLBACKFROMMASTERTHREAD = 1
Original problem has:
         0 rows            1 cols            0 elements         1 globals
Presolved problem has:
         0 rows            1 cols            0 elements         1 globals
Presolve finished in 0 seconds
Heap usage: 75KB (peak 89KB, 362KB system)

Coefficient range                    original                 solved
  Coefficients   [min,max] : [      0.0,       0.0] / [      0.0,       0.0]
  RHS and bounds [min,max] : [ 1.00e+00,  1.00e+00] / [ 1.00e+00,  1.00e+00]
  Objective      [min,max] : [ 1.00e+00,  1.00e+00] / [ 1.00e+00,  1.00e+00]
Autoscaling applied standard scaling

Will try to keep branch and bound tree memory usage below 10.7GB
 *** Solution found:      .000000   Time:   0    Heuristic: T ***
 *** Solution found:     1.000000   Time:   0    Heuristic: T ***
STOPPING - MIPRELSTOP target reached (MIPRELSTOP=0.0001  gap=-0).
 *** Search completed ***
Uncrunching matrix
Final MIP objective                   : 1.000000000000000e+00
Final MIP bound                       : 1.000000000000000e+00
  Solution time / primaldual integral :         0s/ 92.741939%
  Number of solutions found / nodes   :         2 /         0
  Max primal violation      (abs/rel) :       0.0 /       0.0
  Max integer violation     (abs    ) :       0.0

julia> value(x)
1.0

There are tests for this in MOI.
https://github.com/jump-dev/MathOptInterface.jl/blob/b7600485d29d6cc72e5904d03a4fd47b50cac783/src/Test/test_variable.jl#L395-L419
Is it not being run for some reason?

[rafabench]

So, these MOI tests are being run with the full_bridge_optimizer.
If you run

optimizer = Xpress.Optimizer(OUTPUTLOG = 0)
cached = MOI.Bridges.full_bridge_optimizer(optimizer, Float64)
model = direct_model(cached)
@variable(model, x, Bin)
@objective(model, Max, x)
fix(x, 0; force = true)
optimize!(model)
@show value(x)

It gives the right value. It's still a bug though.
Also, this is not the first time a bug has happened on fixing the binary variables (#118), I thought this PR fixed it (#119).

[odow]

Does it error without the bridge? And yeah, this is quite annoying API design by Xpress. It looks like we need some more tests.

[rafabench]

But wait, this MOI test (https://github.com/jump-dev/MathOptInterface.jl/blob/b7600485d29d6cc72e5904d03a4fd47b50cac783/src/Test/test_variable.jl#L395-L419) does not catch this bug.

T = Float64
config = MOI.Test.Config(atol = 1e-3, rtol = 1e-3)
model = Xpress.Optimizer()
x = MOI.add_variable(model)
MOI.add_constraint(model, x, MOI.LessThan(T(0)))
f = MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(T(1), x)], T(0))
MOI.add_constraint(model, x, MOI.ZeroOne())
MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
MOI.Test._test_model_solution(
        model,
        config;
        objective_value = T(0),
        variable_primal = [(x, T(0))],
    )
Xpress.writeprob(model.inner,"bin_prob_fix","l")

It gives the right answer, although the optimization problem is wrong

\Problem name:                                                                  
\FICO Xpress v8.13.0, Hyper, written 14:19:45, Jun 19, 2022

Minimize
 C1

Subject To

Bounds

Binaries
C1 

End

I think we should add one test like this one, the same as the issue.

T = Float64
config = MOI.Test.Config(atol = 1e-3, rtol = 1e-3)
model = Xpress.Optimizer()
x = MOI.add_variable(model)
MOI.add_constraint(model, x, MOI.EqualTo(T(1)))
f = MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(T(1), x)], T(0))
MOI.add_constraint(model, x, MOI.ZeroOne())
MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
MOI.Test._test_model_solution(
        model,
        config;
        objective_value = T(1),
        variable_primal = [(x, T(1))],
    )

This second test fails.

[odow]

MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)

Ahhhh. The problem is that we're minimizing! I can fix this in MOI.