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kofgokhankofgokhan
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Add Chalmet algorithm (#41)
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‎README.md

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@@ -43,6 +43,7 @@ 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.Chalmet()`
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* `MOA.EpsilonConstraint()`
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* `MOA.Dichotomy()`
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* `MOA.DominguezRios()`

‎src/algorithms/Chalmet.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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Chalmet()
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`Chalmet` implements the algorithm of:
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Chalmet, L.G., and Lemonidis, L., and Elzinga, D.J. (1986). An algorithm for the
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bi-criterion integer programming problem. European Journal of Operational
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Research. 25(2), 292-300
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"""
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mutable struct Chalmet <: AbstractAlgorithm end
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function _solve_constrained_model(
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model::Optimizer,
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::Chalmet,
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rhs::Vector{Float64},
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)
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f = MOI.Utilities.scalarize(model.f)
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MOI.set(model.inner, MOI.ObjectiveFunction{typeof(sum(f))}(), sum(f))
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constraints = [
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MOI.add_constraint(model.inner, f[1], MOI.LessThan(rhs[1] - 1))
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MOI.add_constraint(model.inner, f[2], MOI.LessThan(rhs[2] - 1))
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]
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MOI.optimize!(model.inner)
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MOI.delete.(model, constraints)
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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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variables = MOI.get(model.inner, MOI.ListOfVariableIndices())
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X, Y = _compute_point(model, variables, model.f)
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return status, SolutionPoint(X, Y)
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end
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function optimize_multiobjective!(algorithm::Chalmet, model::Optimizer)
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if MOI.output_dimension(model.f) != 2
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error("Chalmet requires exactly two objectives")
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end
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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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solutions = SolutionPoint[]
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E = Tuple{Int,Int}[]
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Q = Tuple{Int,Int}[]
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variables = MOI.get(model.inner, MOI.ListOfVariableIndices())
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f1, f2 = MOI.Utilities.scalarize(model.f)
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y1, y2 = zeros(2), zeros(2)
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MOI.set(model.inner, MOI.ObjectiveFunction{typeof(f2)}(), f2)
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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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_, y1[2] = _compute_point(model, variables, f2)
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MOI.set(model.inner, MOI.ObjectiveFunction{typeof(f1)}(), f1)
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y1_constraint = MOI.add_constraint(model.inner, f2, MOI.LessThan(y1[2]))
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MOI.optimize!(model.inner)
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x1, y1[1] = _compute_point(model, variables, f1)
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MOI.delete(model.inner, y1_constraint)
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push!(solutions, SolutionPoint(x1, y1))
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MOI.set(model.inner, MOI.ObjectiveFunction{typeof(f1)}(), f1)
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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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_, y2[1] = _compute_point(model, variables, f1)
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if y2[1] ≈ solutions[1].y[1]
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return MOI.OPTIMAL, [solutions]
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end
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MOI.set(model.inner, MOI.ObjectiveFunction{typeof(f2)}(), f2)
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y2_constraint = MOI.add_constraint(model.inner, f1, MOI.LessThan(y2[1]))
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MOI.optimize!(model.inner)
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x2, y2[2] = _compute_point(model, variables, f2)
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MOI.delete(model.inner, y2_constraint)
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push!(solutions, SolutionPoint(x2, y2))
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push!(Q, (1, 2))
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t = 3
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while !isempty(Q)
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r, s = pop!(Q)
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yr, ys = solutions[r].y, solutions[s].y
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rhs = [max(yr[1], ys[1]), max(yr[2], ys[2])]
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status, solution = _solve_constrained_model(model, algorithm, rhs)
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if !_is_scalar_status_optimal(status)
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push!(E, (r, s))
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continue
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end
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push!(solutions, solution)
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append!(Q, [(r, t), (t, s)])
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t += 1
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end
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return MOI.OPTIMAL, solutions
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end

‎test/algorithms/Chalmet.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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module TestChalmet
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using Test
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import HiGHS
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import MultiObjectiveAlgorithms as MOA
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const MOI = MOA.MOI
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function run_tests()
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for name in names(@__MODULE__; all = true)
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if startswith("$name", "test_")
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@testset "$name" begin
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getfield(@__MODULE__, name)()
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end
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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 test_knapsack_min()
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n = 10
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W = 2137.0
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C = Float64[
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566 611 506 180 817 184 585 423 26 317
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62 84 977 979 874 54 269 93 881 563
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]
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w = Float64[557, 898, 148, 63, 78, 964, 246, 662, 386, 272]
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model = MOA.Optimizer(HiGHS.Optimizer)
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MOI.set(model, MOA.Algorithm(), MOA.Chalmet())
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MOI.set(model, MOI.Silent(), true)
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x = MOI.add_variables(model, n)
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MOI.add_constraint.(model, x, MOI.ZeroOne())
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MOI.add_constraint(
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model,
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MOI.ScalarAffineFunction(
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[MOI.ScalarAffineTerm(w[j], x[j]) for j in 1:n],
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0.0,
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),
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MOI.LessThan(W),
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)
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f = MOI.VectorAffineFunction(
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[
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MOI.VectorAffineTerm(i, MOI.ScalarAffineTerm(-C[i, j], x[j]))
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for i in 1:2 for j in 1:n
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],
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[0.0, 0.0],
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)
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MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
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MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
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MOI.optimize!(model)
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X_E = Float64[
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0 0 1 1 1 0 1 1 1 1
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1 0 1 1 1 0 1 1 0 1
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0 1 1 1 1 0 1 0 1 1
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]
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Y_N = Float64[
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-2854 -4636
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-3394 -3817
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-3042 -4627
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]
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N = MOI.get(model, MOI.ResultCount())
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x_sol = hcat([MOI.get(model, MOI.VariablePrimal(i), x) for i in 1:N]...)
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@test isapprox(x_sol, X_E'; atol = 1e-6)
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y_sol = hcat([MOI.get(model, MOI.ObjectiveValue(i)) for i in 1:N]...)
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@test isapprox(y_sol, Y_N'; atol = 1e-6)
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return
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end
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function test_knapsack_max()
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n = 10
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W = 2137.0
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C = Float64[
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566 611 506 180 817 184 585 423 26 317
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62 84 977 979 874 54 269 93 881 563
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]
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w = Float64[557, 898, 148, 63, 78, 964, 246, 662, 386, 272]
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model = MOA.Optimizer(HiGHS.Optimizer)
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MOI.set(model, MOA.Algorithm(), MOA.Chalmet())
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MOI.set(model, MOI.Silent(), true)
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x = MOI.add_variables(model, n)
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MOI.add_constraint.(model, x, MOI.ZeroOne())
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MOI.add_constraint(
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model,
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MOI.ScalarAffineFunction(
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[MOI.ScalarAffineTerm(w[j], x[j]) for j in 1:n],
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0.0,
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),
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MOI.LessThan(W),
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)
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f = MOI.VectorAffineFunction(
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[
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MOI.VectorAffineTerm(i, MOI.ScalarAffineTerm(C[i, j], x[j])) for
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i in 1:2 for j in 1:n
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],
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[0.0, 0.0],
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)
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MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
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MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
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MOI.optimize!(model)
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X_E = Float64[
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0 0 1 1 1 0 1 1 1 1
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1 0 1 1 1 0 1 1 0 1
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0 1 1 1 1 0 1 0 1 1
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]
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Y_N = Float64[
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2854 4636
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3394 3817
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3042 4627
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]
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N = MOI.get(model, MOI.ResultCount())
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x_sol = hcat([MOI.get(model, MOI.VariablePrimal(i), x) for i in 1:N]...)
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@test isapprox(x_sol, X_E'; atol = 1e-6)
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y_sol = hcat([MOI.get(model, MOI.ObjectiveValue(i)) for i in 1:N]...)
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@test isapprox(y_sol, Y_N'; atol = 1e-6)
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return
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end
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function test_unbounded()
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model = MOA.Optimizer(HiGHS.Optimizer)
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MOI.set(model, MOA.Algorithm(), MOA.Chalmet())
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MOI.set(model, MOI.Silent(), true)
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x = MOI.add_variables(model, 2)
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MOI.add_constraint.(model, x, MOI.GreaterThan(0.0))
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f = MOI.Utilities.operate(vcat, Float64, 1.0 .* x...)
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MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
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MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
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MOI.optimize!(model)
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@test MOI.get(model, MOI.TerminationStatus()) == MOI.DUAL_INFEASIBLE
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@test MOI.get(model, MOI.PrimalStatus()) == MOI.NO_SOLUTION
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@test MOI.get(model, MOI.DualStatus()) == MOI.NO_SOLUTION
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return
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end
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function test_infeasible()
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model = MOA.Optimizer(HiGHS.Optimizer)
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MOI.set(model, MOA.Algorithm(), MOA.Chalmet())
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MOI.set(model, MOI.Silent(), true)
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x = MOI.add_variables(model, 2)
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MOI.add_constraint.(model, x, MOI.GreaterThan(0.0))
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MOI.add_constraint(model, 1.0 * x[1] + 1.0 * x[2], MOI.LessThan(-1.0))
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f = MOI.Utilities.operate(vcat, Float64, 1.0 .* x...)
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MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
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MOI.optimize!(model)
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@test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
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@test MOI.get(model, MOI.PrimalStatus()) == MOI.NO_SOLUTION
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@test MOI.get(model, MOI.DualStatus()) == MOI.NO_SOLUTION
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return
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end
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end
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TestChalmet.run_tests()

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