Update __loss function for MOO using OptimizationMetaheuristics.jl

lib/OptimizationMetaheuristics/src/OptimizationMetaheuristics.jl

@@ -107,9 +107,14 @@ function SciMLBase.__solve(cache::OptimizationCache{
     maxiters = Optimization._check_and_convert_maxiters(cache.solver_args.maxiters)
     maxtime = Optimization._check_and_convert_maxtime(cache.solver_args.maxtime)
 
+    f=cache.f
     _loss = function (θ)
-        x = cache.f(θ, cache.p)
-        return first(x)
+        if isa(f,MultiObjectiveOptimizationFunction)
+            return cache.f(θ, cache.p)
+        else
+            x = cache.f(θ, cache.p)
+            return first(x)
+        end
     end
 
     if !isnothing(cache.lb) & !isnothing(cache.ub)

lib/OptimizationMetaheuristics/test/runtests.jl

@@ -1,6 +1,7 @@
-using OptimizationMetaheuristics, Optimization
+using OptimizationMetaheuristics, Optimization, Random
 using Test
 
+Random.seed!(42)
 @testset "OptimizationMetaheuristics.jl" begin
     rosenbrock(x, p) = (p[1] - x[1])^2 + p[2] * (x[2] - x[1]^2)^2
     x0 = zeros(2)
@@ -50,4 +51,144 @@ using Test
 
     sol = solve(prob, WOA(), use_initial = true)
     @test 10 * sol.objective < l1
+
+    # Define the benchmark functions as multi-objective problems
+function sphere(x)
+    f1 = sum(x .^ 2)
+    f2 = sum((x .- 2.0) .^ 2)
+    gx = [0.0]
+    hx = [0.0]
+    return [f1, f2], gx, hx
+end
+
+function rastrigin(x)
+    f1 = sum(x .^ 2 .- 10 .* cos.(2 .* π .* x) .+ 10)
+    f2 = sum((x .- 2.0) .^ 2 .- 10 .* cos.(2 .* π .* (x .- 2.0)) .+ 10)
+    gx = [0.0]
+    hx = [0.0]
+    return [f1, f2], gx, hx
+end
+
+function rosenbrock(x)
+    f1 = sum(100 .* (x[2:end] .- x[1:end-1] .^ 2) .^ 2 .+ (x[1:end-1] .- 1) .^ 2)
+    f2 = sum(100 .* ((x[2:end] .- 2.0) .- (x[1:end-1] .^ 2)) .^ 2 .+ ((x[1:end-1] .- 1.0) .^ 2))
+    gx = [0.0]
+    hx = [0.0]
+    return [f1, f2], gx, hx
+end
+
+function ackley(x)
+    f1 = -20 * exp(-0.2 * sqrt(sum(x .^ 2) / length(x))) - exp(sum(cos.(2 * π .* x)) / length(x)) + 20 + ℯ
+    f2 = -20 * exp(-0.2 * sqrt(sum((x .- 2.0) .^ 2) / length(x))) - exp(sum(cos.(2 * π .* (x .- 2.0))) / length(x)) + 20 + ℯ
+    gx = [0.0]
+    hx = [0.0]
+    return [f1, f2], gx, hx
+end
+
+
+function dtlz2(x)
+    g = sum((x[3:end] .- 0.5) .^ 2)
+    f1 = (1 + g) * cos(x[1] * π / 2) * cos(x[2] * π / 2)
+    f2 = (1 + g) * cos(x[1] * π / 2) * sin(x[2] * π / 2)
+    gx = [0.0]
+    hx = [0.0]
+    return [f1, f2], gx, hx
+end
+
+function schaffer_n2(x)
+    f1 = x[1]^2
+    f2 = (x[1] - 2.0)^2
+    gx = [0.0]
+    hx = [0.0]
+    return [f1, f2], gx, hx
+end
+OBJECTIVES = Dict(
+            "Metaheuristics.Algorithm{NSGA2} for sphere"=> [2.1903011284699687, 3.9825426762781477],
+            "Metaheuristics.Algorithm{NSGA3} for sphere"=>  [0.36916068436590516, 8.256797942777018],
+            "Metaheuristics.Algorithm{SPEA2} for sphere"=> [0.6866588142724173, 7.18284015333389],
+            "Metaheuristics.Algorithm{CCMO{NSGA2}} for sphere"=> [1.6659983952552437, 4.731690734657798],
+            "Metaheuristics.Algorithm{MOEAD_DE} for sphere"=> [1.3118335977331483, 5.478715622895562],
+            "Metaheuristics.Algorithm{SMS_EMOA} for sphere"=> [0.5003293369817386, 7.837151299208113],
+            "Metaheuristics.Algorithm{NSGA2} for rastrigin"=> [0.0, 12.0],
+            "Metaheuristics.Algorithm{NSGA3} for rastrigin"=> [9.754810555001253, 11.123569741993528],
+            "Metaheuristics.Algorithm{SPEA2} for rastrigin"=> [0.0, 12.0],
+            "Metaheuristics.Algorithm{CCMO{NSGA2}} for rastrigin"=> [2.600961284360525, 3.4282466721631755],
+            "Metaheuristics.Algorithm{MOEAD_DE} for rastrigin"=> [2.4963842982482607, 10.377445766099369],
+            "Metaheuristics.Algorithm{SMS_EMOA} for rastrigin"=> [0.0, 12.0],
+            "Metaheuristics.Algorithm{NSGA2} for rosenbrock"=> [17.500214034475118, 586.5039366722865],
+            "Metaheuristics.Algorithm{NSGA3} for rosenbrock"=> [60.58413196101549, 427.34913230512063] ,
+            "Metaheuristics.Algorithm{SPEA2} for rosenbrock"=> [37.42314302223994, 498.8799375425481],
+            "Metaheuristics.Algorithm{CCMO{NSGA2}} for rosenbrock"=> [2.600961284360525, 3.4282466721631755],
+            "Metaheuristics.Algorithm{MOEAD_DE} for rosenbrock"=> [12.969698120217537, 642.4135236259822],
+            "Metaheuristics.Algorithm{SMS_EMOA} for rosenbrock"=> [61.6898556398449, 450.62433057243777],
+            "Metaheuristics.Algorithm{NSGA2} for ackley"=> [2.240787163704834, 5.990002878952371],
+            "Metaheuristics.Algorithm{NSGA3} for ackley"=> [3.408535107623966, 5.459538604033934],
+            "Metaheuristics.Algorithm{SPEA2} for ackley"=> [4.440892098500626e-16, 6.593599079287213],
+            "Metaheuristics.Algorithm{CCMO{NSGA2}} for ackley"=> [2.600961284360525, 3.4282466721631755],
+            "Metaheuristics.Algorithm{MOEAD_DE} for ackley"=> [4.440892098500626e-16, 6.593599079287213],
+            "Metaheuristics.Algorithm{SMS_EMOA} for ackley"=> [3.370770500897429, 5.510527199861947],
+            "Metaheuristics.Algorithm{NSGA2} for dtlz2"=> [0.013283104966270814, 0.010808186786590583],
+            "Metaheuristics.Algorithm{NSGA3} for dtlz2"=> [0.013428265441897881, 0.03589930489326534],
+            "Metaheuristics.Algorithm{SPEA2} for dtlz2"=> [0.019006068021099495, 0.0009905093731377751],
+            "Metaheuristics.Algorithm{CCMO{NSGA2}} for dtlz2"=> [2.600961284360525, 3.4282466721631755],
+            "Metaheuristics.Algorithm{MOEAD_DE} for dtlz2"=> [0.027075258566241527, 0.00973958317460759],
+            "Metaheuristics.Algorithm{SMS_EMOA} for dtlz2"=> [0.056304481489060705, 0.026075248436234502],
+            "Metaheuristics.Algorithm{NSGA2} for schaffer_n2"=> [1.4034569322987955, 0.6647534264038837],
+            "Metaheuristics.Algorithm{NSGA3} for schaffer_n2"=> [2.7987535368174363, 0.10696329884083178],
+            "Metaheuristics.Algorithm{SPEA2} for schaffer_n2"=> [0.0007534237111212252, 3.8909591643988075],
+            "Metaheuristics.Algorithm{CCMO{NSGA2}} for schaffer_n2"=> [3.632401400816196e-17, 4.9294679997494206e-17],
+            "Metaheuristics.Algorithm{MOEAD_DE} for schaffer_n2"=> [2.50317097527324, 0.17460592430221922],
+            "Metaheuristics.Algorithm{SMS_EMOA} for schaffer_n2"=> [0.4978888767998813, 1.67543922644328],
+    )
+    # Define the testset
+@testset "Multi-Objective Optimization with Various Functions and Metaheuristics" begin
+    # Define the problems and their bounds
+    problems = [
+        (sphere, [0.0, 0.0, 0.0], [1.0, 1.0, 1.0]),
+        (rastrigin, [0.0, 0.0, 0.0], [1.0, 1.0, 1.0]),
+        (rosenbrock, [0.0, 0.0, 0.0], [1.0, 1.0, 1.0]),
+        (ackley, [0.0, 0.0, 0.0], [1.0, 1.0, 1.0]),
+        (dtlz2, [0.0, 0.0, 0.0], [1.0, 1.0, 1.0]),
+        (schaffer_n2, [0.0, 0.0, 0.0], [2.0, 0.0, 0.0])
+    ]
+
+    nobjectives = 2
+    npartitions = 100
+
+    # Define the different algorithms
+    algs = [
+        NSGA2(),
+        NSGA3(),
+        SPEA2(),
+        CCMO(NSGA2(N=100, p_m=0.001)),
+        MOEAD_DE(gen_ref_dirs(nobjectives, npartitions), options=Options(debug=false, iterations = 250)),
+        SMS_EMOA()
+    ]
+
+    # Run tests for each problem and algorithm
+    for (prob_func, lb, ub) in problems
+        prob_name = string(prob_func)
+        for alg in algs
+            alg_name = string(typeof(alg))
+            @testset "$alg_name on $prob_name" begin
+                multi_obj_fun = MultiObjectiveOptimizationFunction((x, p) -> prob_func(x))
+                prob = OptimizationProblem(multi_obj_fun, lb; lb = lb, ub = ub)
+                if (alg_name=="Metaheuristics.Algorithm{CCMO{NSGA2}}")
+                    sol = solve(prob, alg)
+                else
+                    sol = solve(prob, alg; maxiters = 100, use_initial = true)
+                end
+
+                # Tests
+                @test !isempty(sol.minimizer)  # Check that a solution was found
+
+                # Use sol.objective to get the objective values
+                key = "$alg_name for $prob_name"
+                value = OBJECTIVES[key]
+                objectives = sol.objective
+                @test value ≈ objectives atol=1e-1
+                end
+            end
+        end
+    end
 end