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Add Dominguez-Rios algorithm (#28)
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‎README.md

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@@ -44,6 +44,7 @@ Set the algorithm using the `MOA.Algorithm()` attribute.
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The value must be one of the algorithms supported by MOA:
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* `MOA.EpsilonConstraint()`
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* `MOA.DominguezRios()`
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* `MOA.Hierarchical()`
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* `MOA.KirlikSayin()`
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* `MOA.Lexicographic()` [default]

‎src/algorithms/DominguezRios.jl

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# Copyright 2019, Oscar Dowson and contributors
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# This Source Code Form is subject to the terms of the Mozilla Public License,
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# v.2.0. If a copy of the MPL was not distributed with this file, You can
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# obtain one at http://mozilla.org/MPL/2.0/.
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"""
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DominguezRios()
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`DominguezRios` implements the algorithm of:
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Dominguez-Rios, M.A. & Chicano, F., & Alba, E. (2021). Effective anytime
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algorithm for multiobjective combinatorial optimization problems. Information
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Sciences, 565(7), 210-228.
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"""
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mutable struct DominguezRios <: AbstractAlgorithm end
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mutable struct _DominguezRiosBox
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l::Vector{Float64}
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u::Vector{Float64}
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priority::Float64
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function _DominguezRiosBox(
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l::Vector{Float64},
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u::Vector{Float64},
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p::Float64 = 0.0,
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)
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@assert length(l) == length(u) "Dimension mismatch between l and u"
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return new(l, u, p)
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end
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end
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function _reduced_scaled_priority(
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l::Vector{Float64},
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u::Vector{Float64},
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i::Int,
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z::Vector{Float64},
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yI::Vector{Float64},
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yN::Vector{Float64},
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)
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ret = prod((u - l) ./ (yN - yI))
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if i != length(z)
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return ret
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end
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return ret - prod((z - l) ./ (yN - yI))
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end
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function _p_partition(
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B::_DominguezRiosBox,
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z::Vector{Float64},
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yI::Vector{Float64},
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yN::Vector{Float64},
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)
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ẑ = max.(z, B.l)
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ret = _DominguezRiosBox[]
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for i in 1:length(z)
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new_l = vcat(B.l[1:i], ẑ[i+1:end])
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new_u = vcat(B.u[1:i-1], ẑ[i], B.u[i+1:end])
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new_priority = _reduced_scaled_priority(new_l, new_u, i, ẑ, yI, yN)
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push!(ret, _DominguezRiosBox(new_l, new_u, new_priority))
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end
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return ret
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end
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function _select_next_box(L::Vector{Vector{_DominguezRiosBox}}, k::Int)
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p = length(L)
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if any(.!isempty.(L))
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k = k % p + 1
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while isempty(L[k])
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k = k % p + 1
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end
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i = argmax([B.priority for B in L[k]])
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end
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return i, k
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end
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function _join(
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A::_DominguezRiosBox,
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B::_DominguezRiosBox,
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i::Int,
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z::Vector{Float64},
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yI::Vector{Float64},
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yN::Vector{Float64},
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)
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lᵃ, uᵃ, lᵇ, uᵇ = A.l, A.u, B.l, B.u
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@assert all(uᵃ .<= uᵇ) "`join` operation not valid. (uᵃ ≰ uᵇ)"
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lᶜ, uᶜ = min.(lᵃ, lᵇ), uᵇ
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ẑ = max.(z, lᶜ)
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priority = _reduced_scaled_priority(lᶜ, uᶜ, i, ẑ, yI, yN)
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return _DominguezRiosBox(lᶜ, uᶜ, priority)
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end
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function Base.isempty(B::_DominguezRiosBox)
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return any(isapprox(B.l[i], B.u[i]) for i in 1:length(B.u))
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end
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function _update!(
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L::Vector{Vector{_DominguezRiosBox}},
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z::Vector{Float64},
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yI::Vector{Float64},
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yN::Vector{Float64},
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)
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T = [_DominguezRiosBox[] for _ in 1:length(L)]
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for j in 1:length(L)
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for B in L[j]
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if all(z .< B.u)
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for (i, Bᵢ) in enumerate(_p_partition(B, z, yI, yN))
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if !isempty(Bᵢ)
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push!(T[i], Bᵢ)
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end
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end
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else
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push!(T[j], B)
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end
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end
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end
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L .= T
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for k in 1:length(L)
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i = 1
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N = length(L[k])
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while i < N
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index_to_remove = Int[]
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for j in i:N
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if i != j
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if all(L[k][i].u .<= L[k][j].u)
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L[k][i] = _join(L[k][i], L[k][j], k, z, yI, yN)
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push!(index_to_remove, j)
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elseif all(L[k][i].u .>= L[k][j].u)
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L[k][i] = _join(L[k][j], L[k][i], k, z, yI, yN)
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push!(index_to_remove, j)
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end
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end
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end
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i += 1
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N -= length(index_to_remove)
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deleteat!(L[k], index_to_remove)
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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 optimize_multiobjective!(algorithm::DominguezRios, model::Optimizer)
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sense = MOI.get(model.inner, MOI.ObjectiveSense())
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if sense == MOI.MAX_SENSE
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old_obj, neg_obj = copy(model.f), -model.f
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MOI.set(model, MOI.ObjectiveFunction{typeof(neg_obj)}(), neg_obj)
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MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
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status, solutions = optimize_multiobjective!(algorithm, model)
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MOI.set(model, MOI.ObjectiveFunction{typeof(old_obj)}(), old_obj)
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MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
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if solutions !== nothing
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solutions = [SolutionPoint(s.x, -s.y) for s in solutions]
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end
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return status, solutions
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end
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n = MOI.output_dimension(model.f)
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L = [_DominguezRiosBox[] for i in 1:n]
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scalars = MOI.Utilities.scalarize(model.f)
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variables = MOI.get(model.inner, MOI.ListOfVariableIndices())
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yI, yN = zeros(n), zeros(n)
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# Ideal and Nadir point estimation
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for (i, f_i) in enumerate(scalars)
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MOI.set(model.inner, MOI.ObjectiveFunction{typeof(f_i)}(), f_i)
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MOI.set(model.inner, MOI.ObjectiveSense(), sense)
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MOI.optimize!(model.inner)
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status = MOI.get(model.inner, MOI.TerminationStatus())
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if !_is_scalar_status_optimal(status)
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return status, nothing
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end
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_, Y = _compute_point(model, variables, f_i)
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yI[i] = Y
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rev_sense = sense == MOI.MIN_SENSE ? MOI.MAX_SENSE : MOI.MIN_SENSE
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MOI.set(model.inner, MOI.ObjectiveSense(), rev_sense)
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MOI.optimize!(model.inner)
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status = MOI.get(model.inner, MOI.TerminationStatus())
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if !_is_scalar_status_optimal(status)
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@warn(
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"Unable to solve problem using `DominguezRios()` because " *
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"objective $i does not have a finite domain.",
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)
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return status, nothing
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end
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_, Y = _compute_point(model, variables, f_i)
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yN[i] = Y
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end
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MOI.set(model.inner, MOI.ObjectiveSense(), sense)
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ϵ = 1 / (2 * n * (maximum(yN - yI) - 1))
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push!(L[1], _DominguezRiosBox(yI, yN, 0.0))
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t_max = MOI.add_variable(model.inner)
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solutions = SolutionPoint[]
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k = 0
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while any(!isempty(l) for l in L)
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i, k = _select_next_box(L, k)
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B = L[k][i]
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w = 1 ./ max.(1, B.u - yI)
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constraints = [
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MOI.Utilities.normalize_and_add_constraint(
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model.inner,
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t_max - (w[i] * (scalars[i] - yI[i])),
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MOI.GreaterThan(0.0),
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) for i in 1:n
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]
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new_f = t_max + ϵ * sum(w[i] * (scalars[i] - yI[i]) for i in 1:n)
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MOI.set(model.inner, MOI.ObjectiveFunction{typeof(new_f)}(), new_f)
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MOI.optimize!(model.inner)
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if MOI.get(model.inner, MOI.TerminationStatus()) == MOI.OPTIMAL
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X, Y = _compute_point(model, variables, model.f)
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obj = MOI.get(model.inner, MOI.ObjectiveValue())
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if (obj < 1) && all(yI .< B.u)
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push!(solutions, SolutionPoint(X, Y))
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_update!(L, Y, yI, yN)
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else
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deleteat!(L[k], i)
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end
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end
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MOI.delete.(model.inner, constraints)
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end
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MOI.delete(model.inner, t_max)
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return MOI.OPTIMAL, solutions
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end

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