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[Utilities] add FeasibilityRelaxation
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‎src/Utilities/Utilities.jl

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@@ -77,7 +77,7 @@ include("mockoptimizer.jl")
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include("cachingoptimizer.jl")
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include("universalfallback.jl")
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include("print.jl")
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include("feasibility_relaxation.jl")
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include("lazy_iterators.jl")
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include("precompile.jl")

‎src/Utilities/feasibility_relaxation.jl

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# Copyright (c) 2017: Miles Lubin and contributors
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# Copyright (c) 2017: Google Inc.
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#
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# Use of this source code is governed by an MIT-style license that can be found
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# in the LICENSE.md file or at https://opensource.org/licenses/MIT.
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"""
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FeasibilityRelaxation(
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penalties = Dict{MOI.ConstraintIndex,Float64}(),
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) <: MOI.AbstractModelAttribute
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A model attribute that, when set, destructively modifies the model in-place to
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create a feasibility relxation.
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!!! warning
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This is a destructive routine that modifies the model in-place. If you don't
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want to modify the original model, use `copy_model` to create a copy before
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setting this attribute.
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## Reformulation
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The feasibility relaxation modifies constraints of the form ``f(x) \\in S`` into
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``f(x) + y - z \\in S``, where ``y, z \\ge 0``, and then it introduces a penalty
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term into the objective of ``a \\times (y + z)`` (if minimizing, else ``-a``),
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where `a` is the value in the `penalties` dictionary associated with the
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constraint that is being relaxed. If no value exists, the default is `1.0`.
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The feasibility relaxation is limited to modifying constraint types for which
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`MOI.supports(model, ::FeasibilityRelaxation, MOI.ConstraintIndex{F,S})` is
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`true`. By default, this is only true for [`MOI.ScalarAffineFunction`](@ref) and
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[`MOI.MOI.ScalarQuadraticFunction`](@ref) constraints in the linear sets
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[`MOI.LessThan`](@ref), [`MOI.GreaterThan`](@ref), [`MOI.EqualTo`](@ref) and
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[`MOI.Interval`](@ref). It does not include variable bound or integrality
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constraints, because these cannot be modified in-place.
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## Example
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```jldoctest
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julia> model = MOI.Utilities.Model{Float64}();
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julia> x = MOI.add_variable(model);
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julia> c = MOI.add_constraint(model, 1.0 * x, MOI.LessThan(2.0));
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julia> MOI.set(model, MOI.Utilities.FeasibilityRelaxation(Dict(c => 2.0)))
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julia> print(model)
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Minimize ScalarAffineFunction{Float64}:
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0.0 + 2.0 v[2]
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Subject to:
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ScalarAffineFunction{Float64}-in-LessThan{Float64}
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0.0 + 1.0 v[1] - 1.0 v[2] <= 2.0
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VariableIndex-in-GreaterThan{Float64}
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v[2] >= 0.0
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```
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"""
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mutable struct FeasibilityRelaxation{T} <: MOI.AbstractModelAttribute
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penalties::Dict{MOI.ConstraintIndex,T}
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scale::T
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function FeasibilityRelaxation(p::Dict{MOI.ConstraintIndex,T}) where {T}
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return new{T}(p, zero(T))
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end
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end
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function FeasibilityRelaxation()
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return FeasibilityRelaxation(Dict{MOI.ConstraintIndex,Float64}())
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end
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function FeasibilityRelaxation(d::Dict{<:MOI.ConstraintIndex,T}) where {T}
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return FeasibilityRelaxation(convert(Dict{MOI.ConstraintIndex,T}, d))
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end
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function MOI.set(
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model::MOI.ModelLike,
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relax::FeasibilityRelaxation{T},
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) where {T}
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sense = MOI.get(model, MOI.ObjectiveSense())
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if sense == MOI.FEASIBILITY_SENSE
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relax.scale = one(T)
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MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
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f = zero(MOI.ScalarAffineFunction{T})
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MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
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elseif sense == MOI.MIN_SENSE
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relax.scale = one(T)
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elseif sense == MOI.MAX_SENSE
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relax.scale = -one(T)
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end
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for (F, S) in MOI.get(model, MOI.ListOfConstraintTypesPresent())
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MOI.set(model, relax, F, S)
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end
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return
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end
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function MOI.set(
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model::MOI.ModelLike,
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relax::FeasibilityRelaxation,
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::Type{F},
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::Type{S},
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) where {F,S}
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if MOI.supports(model, relax, MOI.ConstraintIndex{F,S})
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for ci in MOI.get(model, MOI.ListOfConstraintIndices{F,S}())
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MOI.set(model, relax, ci)
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end
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end
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return
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end
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function MOI.supports(
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::MOI.ModelLike,
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::FeasibilityRelaxation,
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::Type{MOI.ConstraintIndex{F,<:MOI.AbstractScalarSet}},
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) where {T,F<:Union{MOI.ScalarAffineFunction{T},MOI.ScalarQuadraticFunction{T}}}
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return true
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end
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function MOI.supports_fallback(
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::MOI.ModelLike,
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::FeasibilityRelaxation,
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::Type{MOI.ConstraintIndex{F,S}},
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) where {F,S}
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return false
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end
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function MOI.set(
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model::MOI.ModelLike,
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relax::FeasibilityRelaxation,
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ci::MOI.ConstraintIndex{F,<:MOI.AbstractScalarSet},
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) where {T,F<:Union{MOI.ScalarAffineFunction{T},MOI.ScalarQuadraticFunction{T}}}
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y = MOI.add_variable(model)
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z = MOI.add_variable(model)
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MOI.add_constraint(model, y, MOI.GreaterThan(zero(T)))
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MOI.add_constraint(model, z, MOI.GreaterThan(zero(T)))
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MOI.modify(model, ci, MOI.ScalarCoefficientChange(y, one(T)))
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MOI.modify(model, ci, MOI.ScalarCoefficientChange(z, -one(T)))
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a = relax.scale * get(relax.penalties, ci, one(T))
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O = MOI.get(model, MOI.ObjectiveFunctionType())
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obj = MOI.ObjectiveFunction{O}()
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MOI.modify(model, obj, MOI.ScalarCoefficientChange(y, a))
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MOI.modify(model, obj, MOI.ScalarCoefficientChange(z, a))
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return
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end
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function MOI.set(
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model::MOI.ModelLike,
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relax::FeasibilityRelaxation,
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ci::MOI.ConstraintIndex{F,MOI.GreaterThan{T}},
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) where {T,F<:Union{MOI.ScalarAffineFunction{T},MOI.ScalarQuadraticFunction{T}}}
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# Performance optimization: we don't need the z relaxation variable.
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y = MOI.add_variable(model)
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MOI.add_constraint(model, y, MOI.GreaterThan(zero(T)))
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MOI.modify(model, ci, MOI.ScalarCoefficientChange(y, one(T)))
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a = relax.scale * get(relax.penalties, ci, one(T))
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O = MOI.get(model, MOI.ObjectiveFunctionType())
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obj = MOI.ObjectiveFunction{O}()
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MOI.modify(model, obj, MOI.ScalarCoefficientChange(y, a))
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return
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end
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function MOI.set(
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model::MOI.ModelLike,
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relax::FeasibilityRelaxation,
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ci::MOI.ConstraintIndex{F,MOI.LessThan{T}},
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) where {T,F<:Union{MOI.ScalarAffineFunction{T},MOI.ScalarQuadraticFunction{T}}}
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# Performance optimization: we don't need the y relaxation variable.
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z = MOI.add_variable(model)
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MOI.add_constraint(model, z, MOI.GreaterThan(zero(T)))
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MOI.modify(model, ci, MOI.ScalarCoefficientChange(z, -one(T)))
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a = relax.scale * get(relax.penalties, ci, one(T))
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O = MOI.get(model, MOI.ObjectiveFunctionType())
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obj = MOI.ObjectiveFunction{O}()
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MOI.modify(model, obj, MOI.ScalarCoefficientChange(z, a))
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return
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end

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