[Bridges] add IntegerToZeroOneBridge (#2205)

docs/src/submodules/Bridges/list_of_bridges.md

@@ -64,6 +64,7 @@ Bridges.Constraint.IndicatorLessToGreaterThanBridge
 Bridges.Constraint.IndicatorSOS1Bridge
 Bridges.Constraint.SemiToBinaryBridge
 Bridges.Constraint.ZeroOneBridge
+Bridges.Constraint.IntegerToZeroOneBridge
 Bridges.Constraint.NumberConversionBridge
 Bridges.Constraint.AllDifferentToCountDistinctBridge
 Bridges.Constraint.ReifiedAllDifferentToCountDistinctBridge

src/Bridges/Constraint/Constraint.jl

@@ -35,6 +35,7 @@ include("bridges/geomean.jl")
 include("bridges/indicator_activate_on_zero.jl")
 include("bridges/indicator_flipsign.jl")
 include("bridges/indicator_sos.jl")
+include("bridges/integer_to_zeroone.jl")
 include("bridges/interval.jl")
 include("bridges/ltgt_to_interval.jl")
 include("bridges/norm_infinity.jl")
@@ -128,6 +129,7 @@ function add_all_bridges(bridged_model, ::Type{T}) where {T}
     MOI.Bridges.add_bridge(bridged_model, IndicatorGreaterToLessThanBridge{T})
     MOI.Bridges.add_bridge(bridged_model, SemiToBinaryBridge{T})
     MOI.Bridges.add_bridge(bridged_model, ZeroOneBridge{T})
+    MOI.Bridges.add_bridge(bridged_model, IntegerToZeroOneBridge{T})
     # Do not add by default
     # MOI.Bridges.add_bridge(bridged_model, NumberConversionBridge{T})
     # Constraint programming bridges

src/Bridges/Constraint/bridges/integer_to_zeroone.jl

@@ -0,0 +1,175 @@
+# Copyright (c) 2017: Miles Lubin and contributors
+# Copyright (c) 2017: Google Inc.
+#
+# Use of this source code is governed by an MIT-style license that can be found
+# in the LICENSE.md file or at https://opensource.org/licenses/MIT.
+
+"""
+    IntegerToZeroOneBridge{T} <: Bridges.Constraint.AbstractBridge
+
+`IntegerToZeroOneBridge` implements the following reformulation:
+
+  * ``x \\in \\mathbf{Z}`` into ``y_i \\in \\{0, 1\\}``,
+    ``x == lb + \\sum 2^{i-1} y_i``.
+
+## Source node
+
+`IntegerToZeroOneBridge` supports:
+
+  * `VariableIndex` in [`MOI.Integer`](@ref)
+
+## Target nodes
+
+`IntegerToZeroOneBridge` creates:
+
+  * [`MOI.VariableIndex`](@ref) in [`MOI.ZeroOne`](@ref)
+  * [`MOI.ScalarAffineFunction{T}`](@ref) in [`MOI.EqualTo{T}`](@ref)
+
+## Developer note
+
+This bridge is implemented as a constraint bridge instead of a variable bridge
+because we don't want to substitute the linear combination of `y` for every
+instance of `x`. Doing so would be expensive and greatly reduce the sparsity of
+the constraints.
+"""
+mutable struct IntegerToZeroOneBridge{T} <: AbstractBridge
+    x::MOI.VariableIndex
+    y::Vector{MOI.VariableIndex}
+    ci::MOI.ConstraintIndex{MOI.ScalarAffineFunction{T},MOI.EqualTo{T}}
+    last_bounds::Union{Nothing,NTuple{2,T}}
+
+    function IntegerToZeroOneBridge{T}(x::MOI.VariableIndex) where {T}
+        return new{T}(
+            x,
+            MOI.VariableIndex[],
+            MOI.ConstraintIndex{MOI.ScalarAffineFunction{T},MOI.EqualTo{T}}(0),
+            nothing,
+        )
+    end
+end
+
+const IntegerToZeroOne{T,OT<:MOI.ModelLike} =
+    SingleBridgeOptimizer{IntegerToZeroOneBridge{T},OT}
+
+function bridge_constraint(
+    ::Type{IntegerToZeroOneBridge{T}},
+    ::MOI.ModelLike,
+    x::MOI.VariableIndex,
+    ::MOI.Integer,
+) where {T}
+    # !!! info
+    #     Postpone creation until final_touch.
+    return IntegerToZeroOneBridge{T}(x)
+end
+
+function MOI.supports_constraint(
+    ::Type{IntegerToZeroOneBridge{T}},
+    ::Type{MOI.VariableIndex},
+    ::Type{MOI.Integer},
+) where {T}
+    return true
+end
+
+function MOI.Bridges.added_constrained_variable_types(
+    ::Type{<:IntegerToZeroOneBridge},
+)
+    return Tuple{Type}[(MOI.ZeroOne,)]
+end
+
+function MOI.Bridges.added_constraint_types(
+    ::Type{IntegerToZeroOneBridge{T}},
+) where {T}
+    return Tuple{Type,Type}[(MOI.ScalarAffineFunction{T}, MOI.EqualTo{T})]
+end
+
+function concrete_bridge_type(
+    ::Type{IntegerToZeroOneBridge{T}},
+    ::Type{MOI.VariableIndex},
+    ::Type{MOI.Integer},
+) where {T}
+    return IntegerToZeroOneBridge{T}
+end
+
+function MOI.get(
+    ::MOI.ModelLike,
+    ::MOI.ConstraintFunction,
+    bridge::IntegerToZeroOneBridge,
+)
+    return bridge.x
+end
+
+function MOI.get(::MOI.ModelLike, ::MOI.ConstraintSet, ::IntegerToZeroOneBridge)
+    return MOI.Integer()
+end
+
+function MOI.delete(model::MOI.ModelLike, bridge::IntegerToZeroOneBridge)
+    MOI.delete(model, bridge.ci)
+    MOI.delete(model, bridge.y)
+    return
+end
+
+function MOI.get(bridge::IntegerToZeroOneBridge, ::MOI.NumberOfVariables)::Int64
+    return length(bridge.y)
+end
+
+function MOI.get(bridge::IntegerToZeroOneBridge, ::MOI.ListOfVariableIndices)
+    return copy(bridge.y)
+end
+
+function MOI.get(
+    bridge::IntegerToZeroOneBridge,
+    ::MOI.NumberOfConstraints{MOI.VariableIndex,MOI.ZeroOne},
+)::Int64
+    return length(bridge.y)
+end
+
+function MOI.get(
+    bridge::IntegerToZeroOneBridge,
+    ::MOI.ListOfConstraintIndices{MOI.VariableIndex,MOI.ZeroOne},
+)
+    return map(bridge.y) do y
+        return MOI.ConstraintIndex{MOI.VariableIndex,MOI.ZeroOne}(y.value)
+    end
+end
+
+function MOI.get(
+    bridge::IntegerToZeroOneBridge{T},
+    ::MOI.NumberOfConstraints{MOI.ScalarAffineFunction{T},MOI.EqualTo{T}},
+)::Int64 where {T}
+    return 1
+end
+
+function MOI.get(
+    bridge::IntegerToZeroOneBridge{T},
+    ::MOI.ListOfConstraintIndices{MOI.ScalarAffineFunction{T},MOI.EqualTo{T}},
+) where {T}
+    return [bridge.ci]
+end
+
+MOI.Bridges.needs_final_touch(::IntegerToZeroOneBridge) = true
+
+function MOI.Bridges.final_touch(
+    bridge::IntegerToZeroOneBridge{T},
+    model::MOI.ModelLike,
+) where {T}
+    ret = MOI.Utilities.get_bounds(model, T, bridge.x)
+    if ret === bridge.last_bounds
+        return nothing  # final_touch already called
+    elseif ret[1] == typemin(T) || ret[2] == typemax(T)
+        error(
+            "Unable to use IntegerToZeroOneBridge because the variable " *
+            "$(bridge.x) has a non-finite domain",
+        )
+    end
+    f = MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(T(1), bridge.x)], T(0))
+    lb, ub = ceil(Int, ret[1]), floor(Int, ret[2])
+    N = floor(Int, log2(ub - lb)) + 1
+    for i in 1:N
+        y, _ = MOI.add_constrained_variable(model, MOI.ZeroOne())
+        push!(bridge.y, y)
+        push!(f.terms, MOI.ScalarAffineTerm(-(T(2)^(i - 1)), y))
+    end
+    bridge.ci = MOI.add_constraint(model, f, MOI.EqualTo{T}(lb))
+    bridge.last_bounds = ret
+    return
+end

test/Bridges/Constraint/integer_to_zeroone.jl

@@ -0,0 +1,102 @@
+# Copyright (c) 2017: Miles Lubin and contributors
+# Copyright (c) 2017: Google Inc.
+#
+# Use of this source code is governed by an MIT-style license that can be found
+# in the LICENSE.md file or at https://opensource.org/licenses/MIT.
+
+module TestConstraintIntegerToZeroOne
+
+using Test
+
+import MathOptInterface as MOI
+
+function runtests()
+    for name in names(@__MODULE__; all = true)
+        if startswith("$(name)", "test_")
+            @testset "$(name)" begin
+                getfield(@__MODULE__, name)()
+            end
+        end
+    end
+    return
+end
+
+function test_runtests()
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.IntegerToZeroOneBridge,
+        """
+        variables: x, z
+        x in Integer()
+        x in Interval(1.0, 3.0)
+        z in ZeroOne()
+        """,
+        """
+        variables: x, z, y1, y2
+        y1 in ZeroOne()
+        y2 in ZeroOne()
+        x + -1.0 * y1 + -2.0 * y2 == 1.0
+        x in Interval(1.0, 3.0)
+        z in ZeroOne()
+        """,
+    )
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.IntegerToZeroOneBridge,
+        """
+        variables: x
+        x in Integer()
+        x in Interval(-1.0, 2.0)
+        """,
+        """
+        variables: x, y1, y2
+        y1 in ZeroOne()
+        y2 in ZeroOne()
+        x + -1.0 * y1 + -2.0 * y2 == -1.0
+        x in Interval(-1.0, 2.0)
+        """,
+    )
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.IntegerToZeroOneBridge,
+        """
+        variables: x
+        x in Integer()
+        x in Interval(-2.0, 2.0)
+        """,
+        """
+        variables: x, y1, y2, y3
+        y1 in ZeroOne()
+        y2 in ZeroOne()
+        y3 in ZeroOne()
+        x + -1.0 * y1 + -2.0 * y2 + -4.0 * y3 == -2.0
+        x in Interval(-2.0, 2.0)
+        """,
+    )
+    return
+end
+
+function test_finite_domain_error()
+    inner = MOI.Utilities.Model{Int}()
+    model = MOI.Bridges.Constraint.IntegerToZeroOne{Int}(inner)
+    x, _ = MOI.add_constrained_variable(model, MOI.Integer())
+    @test_throws(
+        ErrorException(
+            "Unable to use IntegerToZeroOneBridge because the variable " *
+            "$(x) has a non-finite domain",
+        ),
+        MOI.Bridges.final_touch(model),
+    )
+    return
+end
+
+function test_final_touch_twice()
+    inner = MOI.Utilities.Model{Int}()
+    model = MOI.Bridges.Constraint.IntegerToZeroOne{Int}(inner)
+    x, _ = MOI.add_constrained_variable(model, MOI.Integer())
+    MOI.add_constraint(model, x, MOI.Interval(1, 3))
+    MOI.Bridges.final_touch(model)
+    MOI.Bridges.final_touch(model)
+    return
+end
+
+end  # module
+
+TestConstraintIntegerToZeroOne.runtests()