[Bridge] implement special case for x != y in CountDistinctToMILPBrid…

…ge (#2416)

src/Bridges/Constraint/bridges/count_distinct.jl

@@ -41,6 +41,24 @@ non-zero:
 n - \\sum\\limits_{j \\in \\bigcup_{i=1,\\ldots,d} S_i} y_{j} = 0
 ```
 
+## Formulation (special case)
+
+In the special case that the constraint is `[2, x, y] in CountDistinct(3)`, then
+the constraint is equivalent to `[x, y] in AllDifferent(2)`, which is equivalent
+to `x != y`.
+
+```math
+(x - y <= -1) \\vee (y - x <= -1)
+```
+which is equivalent to (for suitable `M`):
+```math
+\\begin{aligned}
+z \\in \\{0, 1\\} \\\\
+x - y - M * z <= -1 \\\\
+y - x - M * (1 - z) <= -1
+\\end{aligned}
+```
+
 ## Source node
 
 `CountDistinctToMILPBridge` supports:
@@ -232,9 +250,105 @@ function MOI.Bridges.final_touch(
  bridge::CountDistinctToMILPBridge{T,F},
  model::MOI.ModelLike,
 ) where {T,F}
- S = Dict{T,Vector{MOI.VariableIndex}}()
  scalars = collect(MOI.Utilities.eachscalar(bridge.f))
  bounds = Dict{MOI.VariableIndex,NTuple{2,T}}()
+ ret = MOI.Utilities.get_bounds(model, bounds, scalars[1])
+ if MOI.output_dimension(bridge.f) == 3 && ret == (2.0, 2.0)
+ # The special case of
+ # [x, y] in AllDifferent()
+ # bridged to
+ # [2, x, y] in CountDistinct()
+ # This is equivalent to the NotEqualTo set.
+ _final_touch_not_equal_case(bridge, model, scalars)
+ else
+ _final_touch_general_case(bridge, model, scalars)
+ end
+ return
+end
+
+function _final_touch_not_equal_case(
+ bridge::CountDistinctToMILPBridge{T,F},
+ model::MOI.ModelLike,
+ scalars,
+) where {T,F}
+ bounds = Dict{MOI.VariableIndex,NTuple{2,T}}()
+ new_bounds = false
+ for i in 2:length(scalars)
+ x = scalars[i]
+ ret = MOI.Utilities.get_bounds(model, bounds, x)
+ if ret === nothing
+ error(
+ "Unable to use CountDistinctToMILPBridge because element $i " *
+ "in the function has a non-finite domain: $x",
+ )
+ end
+ if length(bridge.bounds) < i - 1
+ # This is the first time calling final_touch
+ push!(bridge.bounds, ret)
+ new_bounds = true
+ elseif bridge.bounds[i-1] == ret
+ # We've called final_touch before, and the bounds match. No need to
+ # reformulate a second time.
+ continue
+ elseif bridge.bounds[i-1] != ret
+ # There is a stored bound, and the current bounds do not match. This
+ # means the model has been modified since the previous call to
+ # final_touch. We need to delete the bridge and start again.
+ MOI.delete(model, bridge)
+ MOI.Bridges.final_touch(bridge, model)
+ return
+ end
+ end
+ if !new_bounds
+ return
+ end
+ # [2, x, y] in CountDistinct()
+ # <-->
+ # x != y
+ # <-->
+ # {x - y >= 1} \/ {y - x >= 1}
+ # <-->
+ # {x - y <= -1} \/ {y - x <= -1}
+ # <-->
+ # {x - y - M * z <= -1} /\ {y - x - M * (1 - z) <= -1}, z in {0, 1}
+ z, _ = MOI.add_constrained_variable(model, MOI.ZeroOne())
+ push!(bridge.variables, z)
+ x, y = scalars[2], scalars[3]
+ bx, by = bridge.bounds[1], bridge.bounds[2]
+ # {x - y - M * z <= -1}, M = u_x - l_y + 1
+ M = bx[2] - by[1] + 1
+ f = MOI.Utilities.operate(-, T, x, y)
+ push!(
+ bridge.less_than,
+ MOI.Utilities.normalize_and_add_constraint(
+ model,
+ MOI.Utilities.operate!(-, T, f, M * z),
+ MOI.LessThan(T(-1));
+ allow_modify_function = true,
+ ),
+ )
+ # {y - x - M * (1 - z) <= -1}, M = u_x - l_y + 1
+ M = by[2] - bx[1] + 1
+ g = MOI.Utilities.operate(-, T, y, x)
+ push!(
+ bridge.less_than,
+ MOI.Utilities.normalize_and_add_constraint(
+ model,
+ MOI.Utilities.operate!(+, T, g, M * z),
+ MOI.LessThan(T(-1 + M));
+ allow_modify_function = true,
+ ),
+ )
+ return
+end
+
+function _final_touch_general_case(
+ bridge::CountDistinctToMILPBridge{T,F},
+ model::MOI.ModelLike,
+ scalars,
+) where {T,F}
+ S = Dict{T,Vector{MOI.VariableIndex}}()
+ bounds = Dict{MOI.VariableIndex,NTuple{2,T}}()
  for i in 2:length(scalars)
  x = scalars[i]
  ret = MOI.Utilities.get_bounds(model, bounds, x)

test/Bridges/Constraint/count_distinct.jl

@@ -61,21 +61,46 @@ function test_runtests_VectorOfVariables()
  return
 end
 
+function test_runtests_VectorOfVariables_NotEqualTo()
+ MOI.Bridges.runtests(
+ MOI.Bridges.Constraint.CountDistinctToMILPBridge,
+ """
+ variables: n, x, y
+ [n, x, y] in CountDistinct(3)
+ x in Interval(1.0, 4.0)
+ y >= 2.0
+ y <= 5.0
+ n == 2.0
+ """,
+ """
+ variables: n, x, y, z
+ 1.0 * x + -1.0 * y + -3.0 * z <= -1.0
+ 1.0 * y + -1.0 * x + 5.0 * z <= 4.0
+ x in Interval(1.0, 4.0)
+ y >= 2.0
+ y <= 5.0
+ n == 2.0
+ z in ZeroOne()
+ """,
+ )
+ return
+end
+
 function test_runtests_VectorAffineFunction()
  MOI.Bridges.runtests(
  MOI.Bridges.Constraint.CountDistinctToMILPBridge,
  """
- variables: x, y
- [2.0, 2.0 * x + -1.0, y] in CountDistinct(3)
+ variables: d, x, y
+ [d, 2.0 * x + -1.0, y] in CountDistinct(3)
  x in Interval(1.0, 2.0)
  y >= 2.0
  y <= 3.0
  """,
  """
- variables: x, y, z_x1, z_x2, z_x3, z_y2, z_y3, a_1, a_2, a_3
+ variables: d, x, y, z_x1, z_x2, z_x3, z_y2, z_y3, a_1, a_2, a_3
  2.0 * x + -1.0 * z_x1 + -2.0 * z_x2 + -3.0 * z_x3 == 1.0
  1.0 * y + -2.0 * z_y2 + -3.0 * z_y3 == 0.0
- a_1 + a_2 + a_3 == 2.0
+ a_1 + a_2 + a_3 + -1.0 * d == 0.0
  z_x1 + z_x2 + z_x3 == 1.0
  z_y2 + z_y3 == 1.0
  z_x1 + -1.0 * a_1 <= 0.0
@@ -146,6 +171,22 @@ function test_runtests_error_affine()
  return
 end
 
+function test_resolve_with_modified_not_equal_to()
+ inner = MOI.Utilities.Model{Int}()
+ model = MOI.Bridges.Constraint.CountDistinctToMILP{Int}(inner)
+ x = MOI.add_variables(model, 3)
+ c = MOI.add_constraint.(model, x[2:3], MOI.Interval(0, 2))
+ MOI.add_constraint(model, x[1], MOI.EqualTo(2))
+ MOI.add_constraint(model, MOI.VectorOfVariables(x), MOI.CountDistinct(3))
+ @test MOI.get(inner, MOI.NumberOfVariables()) == 3
+ MOI.Bridges.final_touch(model)
+ @test MOI.get(inner, MOI.NumberOfVariables()) == 4
+ MOI.set(model, MOI.ConstraintSet(), c[2], MOI.Interval(0, 1))
+ MOI.Bridges.final_touch(model)
+ @test MOI.get(inner, MOI.NumberOfVariables()) == 4
+ return
+end
+
 end # module
 
 TestConstraintCountDistinct.runtests()