[Bridge] implement special case for x != y in CountDistinctToMILPBridge (#2416)

Author: odow

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()