/
feasibility.jl
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/
feasibility.jl
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# MIT License
#
# Copyright (c) 2018 Martin Biel
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
abstract type AbstractFeasibilityAlgorithm end
abstract type AbstractFeasibilityStrategy end
"""
NoFeasibilityAlgorithm
Empty functor object for running an L-shaped algorithm without dealing with second-stage feasibility.
"""
struct NoFeasibilityAlgorithm <: AbstractFeasibilityAlgorithm end
handle_feasibility(::NoFeasibilityAlgorithm) = false
num_cuts(::NoFeasibilityAlgorithm) = 0
active!(::MOI.ModelLike, ::NoFeasibilityAlgorithm) = nothing
deactive!(::MOI.ModelLike, ::NoFeasibilityAlgorithm) = nothing
restore!(::MOI.ModelLike, ::NoFeasibilityAlgorithm) = nothing
"""
FeasibilityCutsMaster
Master functor object for using feasibility cuts in an L-shaped algorithm. Create by supplying a [`FeasibilityCuts`](@ref) object through `feasibility_strategy` in `LShaped.Optimizer` or set the [`FeasibilityStrategy`](@ref) attribute.
"""
struct FeasibilityCutsMaster{T <: AbstractFloat} <: AbstractFeasibilityAlgorithm
cuts::Vector{SparseFeasibilityCut{T}}
function FeasibilityCutsMaster(::Type{T}) where T <: AbstractFloat
return new{T}(Vector{SparseFeasibilityCut{T}}())
end
end
handle_feasibility(::FeasibilityCutsMaster) = true
worker_type(::FeasibilityCutsMaster) = FeasibilityCutsWorker
num_cuts(feasibility::FeasibilityCutsMaster) = length(feasibility.cuts)
active!(::MOI.ModelLike, ::FeasibilityCutsMaster) = nothing
deactive!(::MOI.ModelLike, ::FeasibilityCutsMaster) = nothing
restore!(::MOI.ModelLike, ::FeasibilityCutsMaster) = nothing
"""
FeasibilityCutsWorker
Worker functor object for using feasibility cuts in an L-shaped algorithm. Create by supplying a [`FeasibilityCuts`](@ref) object through `feasibility_strategy` in `LShaped.Optimizer` or set the [`FeasibilityStrategy`](@ref) attribute.
"""
mutable struct FeasibilityCutsWorker <: AbstractFeasibilityAlgorithm
objective::MOI.AbstractScalarFunction
linking_constraints::Vector{MOI.ConstraintIndex}
feasibility_variables::Vector{MOI.VariableIndex}
aux_constraint::MOI.ConstraintIndex{MOI.ScalarAffineFunction{Float64}, MOI.EqualTo{Float64}}
function FeasibilityCutsWorker(objective::MOI.AbstractScalarFunction,
linking_constraints::Vector{MOI.ConstraintIndex},
feasibility_variables::Vector{MOI.VariableIndex})
return new(objective, linking_constraints, feasibility_variables, CI{MOI.ScalarAffineFunction{Float64}, MOI.EqualTo{Float64}}(0))
end
end
handle_feasibility(::FeasibilityCutsWorker) = true
num_cuts(::FeasibilityCutsWorker) = 0
function prepare!(model::MOI.ModelLike, worker::FeasibilityCutsWorker)
# Set objective to zero
G = MOI.ScalarAffineFunction{Float64}
MOI.set(model, MOI.ObjectiveFunction{G}(), zero(MOI.ScalarAffineFunction{Float64}))
i = 1
# Create auxiliary feasibility variables
for ci in worker.linking_constraints
i = add_auxiliary_variables!(model, worker, ci, i)
end
return nothing
end
function prepared(worker::FeasibilityCutsWorker)
return length(worker.feasibility_variables) > 0
end
function add_auxiliary_variables!(model::MOI.ModelLike,
worker::FeasibilityCutsWorker,
ci::CI{F,S},
idx::Integer) where {F <: MOI.AbstractFunction, S <: MOI.AbstractSet}
# Nothing to do for most most constraints
return idx
end
function add_auxiliary_variables!(model::MOI.ModelLike,
worker::FeasibilityCutsWorker,
ci::CI{F,S},
idx::Integer) where {F <: AffineDecisionFunction, S <: MOI.AbstractScalarSet}
G = MOI.ScalarAffineFunction{Float64}
obj_sense = MOI.get(model, MOI.ObjectiveSense())
# Positive feasibility variable
pos_aux_var = MOI.add_variable(model)
name = add_subscript(:v⁺, idx)
MOI.set(model, MOI.VariableName(), pos_aux_var, name)
push!(worker.feasibility_variables, pos_aux_var)
# Nonnegativity constraint
MOI.add_constraint(model, MOI.VariableIndex(pos_aux_var.value),
MOI.GreaterThan{Float64}(0.0))
# Add to objective
MOI.modify(model, MOI.ObjectiveFunction{G}(),
MOI.ScalarCoefficientChange(pos_aux_var, obj_sense == MOI.MAX_SENSE ? -1.0 : 1.0))
# Add to constraint
MOI.modify(model, ci, MOI.ScalarCoefficientChange(pos_aux_var, 1.0))
# Negative feasibility variable
neg_aux_var = MOI.add_variable(model)
name = add_subscript(:v⁻, idx)
MOI.set(model, MOI.VariableName(), neg_aux_var, name)
push!(worker.feasibility_variables, neg_aux_var)
# Nonnegativity constraint
MOI.add_constraint(model, MOI.VariableIndex(neg_aux_var.value),
MOI.GreaterThan{Float64}(0.0))
# Add to objective
MOI.modify(model, MOI.ObjectiveFunction{G}(),
MOI.ScalarCoefficientChange(neg_aux_var, obj_sense == MOI.MAX_SENSE ? -1.0 : 1.0))
# Add to constraint
MOI.modify(model, ci, MOI.ScalarCoefficientChange(neg_aux_var, -1.0))
# Return updated identification index
return idx + 1
end
function add_auxiliary_variables!(model::MOI.ModelLike,
worker::FeasibilityCutsWorker,
ci::CI{F,S},
idx::Integer) where {F <: VectorAffineDecisionFunction, S <: MOI.AbstractVectorSet}
G = MOI.ScalarAffineFunction{Float64}
obj_sense = MOI.get(model, MOI.ObjectiveSense())
n = MOI.dimension(MOI.get(model, MOI.ConstraintSet(), ci))
for (i, id) in enumerate(idx:(idx + n - 1))
# Positive feasibility variable
pos_aux_var = MOI.add_variable(model)
name = add_subscript(:v⁺, id)
MOI.set(model, MOI.VariableName(), pos_aux_var, name)
push!(worker.feasibility_variables, pos_aux_var)
# Nonnegativity constraint
MOI.add_constraint(model, MOI.VariableIndex(pos_aux_var.value),
MOI.GreaterThan{Float64}(0.0))
# Add to objective
MOI.modify(model, MOI.ObjectiveFunction{G}(),
MOI.ScalarCoefficientChange(pos_aux_var, obj_sense == MOI.MAX_SENSE ? -1.0 : 1.0))
# Add to constraint
MOI.modify(model, ci, MOI.MultirowChange(pos_aux_var, [(i, 1.0)]))
end
for (i, id) in enumerate(idx:(idx + n - 1))
# Negative feasibility variable
neg_aux_var = MOI.add_variable(model)
name = add_subscript(:v⁻, id)
MOI.set(model, MOI.VariableName(), neg_aux_var, name)
push!(worker.feasibility_variables, neg_aux_var)
# Nonnegativity constraint
MOI.add_constraint(model, MOI.VariableIndex(neg_aux_var.value),
MOI.GreaterThan{Float64}(0.0))
# Add to objective
MOI.modify(model, MOI.ObjectiveFunction{G}(),
MOI.ScalarCoefficientChange(neg_aux_var, obj_sense == MOI.MAX_SENSE ? -1.0 : 1.0))
# Add to constraint
MOI.modify(model, ci, MOI.MultirowChange(neg_aux_var, [(i, -1.0)]))
end
# Return updated identification index
return idx + n + 1
end
function activate!(model::MOI.ModelLike, worker::FeasibilityCutsWorker)
# Set objective to zero
G = MOI.ScalarAffineFunction{Float64}
MOI.set(model, MOI.ObjectiveFunction{G}(), zero(MOI.ScalarAffineFunction{Float64}))
obj_sense = MOI.get(model, MOI.ObjectiveSense())
# Add auxiliary variables to objective and linking constraints
idx = 0
for ci in worker.linking_constraints
dim = MOI.dimension(MOI.get(model, MOI.ConstraintSet(), ci))
for i in 1:dim
pos_aux_var = worker.feasibility_variables[idx + 2*(i-1) + 1]
MOI.modify(model, MOI.ObjectiveFunction{G}(),
MOI.ScalarCoefficientChange(pos_aux_var, obj_sense == MOI.MAX_SENSE ? -1.0 : 1.0))
neg_aux_var = worker.feasibility_variables[idx + 2*(i-1) + 2]
MOI.modify(model, MOI.ObjectiveFunction{G}(),
MOI.ScalarCoefficientChange(neg_aux_var, obj_sense == MOI.MAX_SENSE ? -1.0 : 1.0))
end
idx += 2*dim
end
if MOI.is_valid(model, worker.aux_constraint)
MOI.delete(model, worker.aux_constraint)
end
return nothing
end
function deactivate!(model::MOI.ModelLike, worker::FeasibilityCutsWorker)
# Force auxiliary variables to zero
func_type = MOI.get(model, MOI.ObjectiveFunctionType())
obj = MOI.get(model, MOI.ObjectiveFunction{func_type}())
worker.aux_constraint = MOI.add_constraint(model, obj, MOI.EqualTo{Float64}(0.0))
# Restore objective
F = typeof(worker.objective)
MOI.set(model, MOI.ObjectiveFunction{F}(), worker.objective)
return nothing
end
function restore!(model::MOI.ModelLike, worker::FeasibilityCutsWorker)
# Remove aux constraint
if MOI.is_valid(model, worker.aux_constraint)
MOI.delete(model, worker.aux_constraint)
end
worker.aux_constraint = CI{MOI.ScalarAffineFunction{Float64}, MOI.EqualTo{Float64}}(0)
# Delete any feasibility variables
if prepared(worker)
MOI.delete(model, worker.feasibility_variables)
end
empty!(worker.feasibility_variables)
# Restore objective
F = typeof(worker.objective)
MOI.set(model, MOI.ObjectiveFunction{F}(), worker.objective)
return nothing
end
# API
# ------------------------------------------------------------
"""
IgnoreFeasibility
Factory object for [`NoFeasibilityAlgorithm`](@ref). Passed by default to `feasibility_strategy` in `LShaped.Optimizer`.
"""
struct IgnoreFeasibility <: AbstractFeasibilityStrategy end
function master(::IgnoreFeasibility, ::Type{T}) where T <: AbstractFloat
return NoFeasibilityAlgorithm()
end
function worker(::IgnoreFeasibility, ::Vector{MOI.ConstraintIndex}, ::MOI.ModelLike)
return NoFeasibilityAlgorithm()
end
function worker_type(::IgnoreFeasibility)
return NoFeasibilityAlgorithm
end
"""
IgnoreFeasibility
Factory object for using feasibility cuts in an L-shaped algorithm.
"""
struct FeasibilityCuts <: AbstractFeasibilityStrategy end
function master(::FeasibilityCuts, ::Type{T}) where T <: AbstractFloat
return FeasibilityCutsMaster(T)
end
function worker(::FeasibilityCuts, linking_constraints::Vector{MOI.ConstraintIndex}, model::MOI.ModelLike)
# Cache objective
func_type = MOI.get(model, MOI.ObjectiveFunctionType())
obj = MOI.get(model, MOI.ObjectiveFunction{func_type}())
return FeasibilityCutsWorker(obj, linking_constraints, Vector{MOI.VariableIndex}())
end
function worker_type(::FeasibilityCuts)
return FeasibilityCutsWorker
end