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Add Tamby Vanderpooten algorithm (#67)
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‎README.md‎

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@@ -53,6 +53,7 @@ The value must be one of the algorithms supported by MOA:
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* `MOA.Hierarchical()`
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* `MOA.KirlikSayin()`
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* `MOA.Lexicographic()` [default]
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* `MOA.TambyVanderpooten()`
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Consult their docstrings for details.
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‎src/algorithms/TambyVanderpooten.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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TambyVanderpooten()
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`TambyVanderpooten` implements the algorithm of:
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Satya Tamby, Daniel Vanderpooten (2021) Enumeration of the Nondominated Set
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of Multiobjective Discrete Optimization Problems. INFORMS Journal on
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Computing 33(1):72-85.
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This is an algorithm to generate all nondominated solutions for multi-objective
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discrete optimization problems. The algorithm maintains upper bounds (for
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minimization problems) and their associated defining points. At each iteration,
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one of the objectives and an upper bound is picked and the single objective
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reformulation is solved using one of the defining points as a starting solution.
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## Supported optimizer attributes
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* `MOI.TimeLimitSec()`: terminate if the time limit is exceeded and return the
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list of current solutions.
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"""
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mutable struct TambyVanderpooten <: AbstractAlgorithm end
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function _project(x::Vector{Float64}, axis::Int)
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return [x[i] for i in 1:length(x) if i != axis]
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end
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_volume(r::_Rectangle, l::Vector{Float64}) = prod(r.u - l)
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function _update_search_region(
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U_N::Dict{Vector{Float64},Vector{Vector{Vector{Float64}}}},
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y::Vector{Float64},
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yN::Vector{Float64},
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)
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bounds_to_remove = Vector{Float64}[]
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p = length(y)
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for u in keys(U_N)
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if all(y .< u)
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push!(bounds_to_remove, u)
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for l in 1:p
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u_l = _get_child(u, y, l)
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N = [
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k != l ? [yi for yi in U_N[u][k] if yi[l] < y[l]] : [y]
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for k in 1:p
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]
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if all(!isempty(N[k]) for k in 1:p if u_l[k] ≠ yN[k])
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U_N[u_l] = N
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end
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end
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else
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for k in 1:p
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if (y[k] == u[k]) && all(_project(y, k) .< _project(u, k))
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push!(U_N[u][k], y)
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end
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end
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end
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end
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for bound_to_remove in bounds_to_remove
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delete!(U_N, bound_to_remove)
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end
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return
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end
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function _get_child(u::Vector{Float64}, y::Vector{Float64}, k::Int)
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@assert length(u) == length(y)
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return vcat(u[1:k-1], y[k], u[k+1:length(y)])
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end
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function _select_search_zone(
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U_N::Dict{Vector{Float64},Vector{Vector{Vector{Float64}}}},
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yI::Vector{Float64},
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)
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i, j =
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argmax([
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prod(_project(u, k) - _project(yI, k)) for k in 1:length(yI),
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u in keys(U_N)
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]).I
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return i, collect(keys(U_N))[j]
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end
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function optimize_multiobjective!(
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algorithm::TambyVanderpooten,
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model::Optimizer,
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)
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start_time = time()
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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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warm_start_supported = false
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if MOI.supports(model, MOI.VariablePrimalStart(), MOI.VariableIndex)
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warm_start_supported = true
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end
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solutions = Dict{Vector{Float64},Dict{MOI.VariableIndex,Float64}}()
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YN = Vector{Float64}[]
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variables = MOI.get(model.inner, MOI.ListOfVariableIndices())
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n = MOI.output_dimension(model.f)
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yI, yN = zeros(n), zeros(n)
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scalars = MOI.Utilities.scalarize(model.f)
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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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MOI.set(model.inner, MOI.ObjectiveSense(), MOI.MAX_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_on_nonfinite_anti_ideal(algorithm, sense, i)
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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(), MOI.MIN_SENSE)
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U_N = Dict{Vector{Float64},Vector{Vector{Vector{Float64}}}}()
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V = [Tuple{Vector{Float64},Vector{Float64}}[] for k in 1:n]
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U_N[yN] = [[_get_child(yN, yI, k)] for k in 1:n]
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status = MOI.OPTIMAL
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while !isempty(U_N)
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if _time_limit_exceeded(model, start_time)
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status = MOI.TIME_LIMIT
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break
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end
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k, u = _select_search_zone(U_N, yI)
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MOI.set(
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model.inner,
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MOI.ObjectiveFunction{typeof(scalars[k])}(),
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scalars[k],
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)
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ε_constraints = Any[]
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for (i, f_i) in enumerate(scalars)
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if i != k
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ci = MOI.add_constraint(
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model.inner,
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f_i,
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MOI.LessThan{Float64}(u[i] - 1),
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)
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push!(ε_constraints, ci)
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end
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end
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if u[k] ≠ yN[k]
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if warm_start_supported
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variables_start = solutions[first(U_N[u][k])]
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for x_i in variables
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MOI.set(
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model.inner,
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MOI.VariablePrimalStart(),
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x_i,
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variables_start[x_i],
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)
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end
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end
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end
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MOI.optimize!(model.inner)
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if !_is_scalar_status_optimal(model)
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return status, nothing
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end
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y_k = MOI.get(model.inner, MOI.ObjectiveValue())
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sum_f = sum(1.0 * s for s in scalars)
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MOI.set(model.inner, MOI.ObjectiveFunction{typeof(sum_f)}(), sum_f)
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y_k_constraint =
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MOI.add_constraint(model.inner, scalars[k], MOI.EqualTo(y_k))
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MOI.optimize!(model.inner)
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if !_is_scalar_status_optimal(model)
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return status, nothing
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end
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X, Y = _compute_point(model, variables, model.f)
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MOI.delete.(model, ε_constraints)
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MOI.delete(model, y_k_constraint)
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push!(V[k], (u, Y))
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if Y ∉ U_N[u][k]
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_update_search_region(U_N, Y, yN)
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solutions[Y] = X
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end
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bounds_to_remove = Vector{Float64}[]
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for u_i in keys(U_N)
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for k in 1:n
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if u_i[k] == yI[k]
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push!(bounds_to_remove, u_i)
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else
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for (u_j, y_j) in V[k]
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if all(_project(u_i, k) .<= _project(u_j, k)) &&
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(y_j[k] == u_i[k])
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push!(bounds_to_remove, u_i)
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end
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end
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end
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end
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end
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if !isempty(bounds_to_remove)
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for bound_to_remove in bounds_to_remove
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delete!(U_N, bound_to_remove)
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end
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end
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end
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solutions = [SolutionPoint(X, Y) for (Y, X) in solutions]
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return status, solutions
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end

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