Added basic NOMAD integration

Added basic NOMAD integration with tests and documentation

Author: jonasmac16

docs/make.jl

@@ -34,6 +34,7 @@ makedocs(
             "MathOptInterface.jl" => "optimization_packages/mathoptinterface.md",
             "MultistartOptimization.jl" => "optimization_packages/multistartoptimization.md",
             "Metaheuristics.jl" => "optimization_packages/metaheuristics.md",
+            "NOMAD.jl" => "optimization_packages/nomad.md",
             "NLopt.jl" => "optimization_packages/nlopt.md",
             "Nonconvex.jl" => "optimization_packages/nonconvex.md",
             "Optim.jl" => "optimization_packages/optim.md",

docs/src/optimization_packages/nomad.md

@@ -0,0 +1,28 @@
+# NOMAD.jl
+[`NOMAD`](https://github.com/bbopt/NOMAD.jl) is Julia package interfacing to NOMAD,which is a C++ implementation of the Mesh Adaptive Direct Search algorithm (MADS), designed for difficult blackbox optimization problems. These problems occur when the functions defining the objective and constraints are the result of costly computer simulations. [`NOMAD.jl documentation`](https://bbopt.github.io/NOMAD.jl/stable/)
+
+The NOMAD algorithm is called by `NOMADOpt()`
+
+## Global Optimizer
+### Without Constraint Equations
+
+The method in [`NOMAD`](https://github.com/bbopt/NOMAD.jl) is performing global optimization on problems both with and without
+constraint equations. Currently however, linear and nonlinear constraints  defined in `GalacticOPtim` are not passed.
+
+NOMAD works both with and without lower and upper boxconstraints set by `lb` and `ub` in the `OptimizationProblem`.
+
+
+The Rosenbrock function can optimized using the `NOMADOpt()` with and without boxcontraints as follows:
+
+```julia
+rosenbrock(x, p) =  (p[1] - x[1])^2 + p[2] * (x[2] - x[1]^2)^2
+x0 = zeros(2)
+p  = [1.0, 100.0]
+f = OptimizationFunction(rosenbrock)
+
+prob = OptimizationProblem(f, x0, _p)
+sol = GalacticOptim.solve(prob,NOMADOpt())
+
+prob = OptimizationProblem(f, x0, _p, lb = [-1.0,-1.0], ub = [1.5,1.5])
+sol = GalacticOptim.solve(prob,NOMADOpt())
+```

src/GalacticOptim.jl

@@ -43,6 +43,7 @@ function __init__()
         end
     end
     @require Metaheuristics="bcdb8e00-2c21-11e9-3065-2b553b22f898" include("solve/metaheuristics.jl")
+    @require NOMAD="02130f1c-4665-5b79-af82-ff1385104aa0" include("solve/nomad.jl")
 
     # AD backends
     @require FiniteDiff="6a86dc24-6348-571c-b903-95158fe2bd41" include("function/finitediff.jl")

src/solve/nomad.jl

@@ -0,0 +1,84 @@
+export NOMADOpt
+struct NOMADOpt end
+
+
+function __map_optimizer_args(prob::OptimizationProblem, opt::NOMAD.NomadProblem;
+    cb=nothing,
+    maxiters::Union{Number, Nothing}=nothing,
+    maxtime::Union{Number, Nothing}=nothing,
+    abstol::Union{Number, Nothing}=nothing, 
+    reltol::Union{Number, Nothing}=nothing, 
+    kwargs...)
+
+    for j in kwargs
+        setproperty!(opt.options, j.first, j.second)
+    end
+
+    if !isnothing(maxiters)
+        opt.options.max_bb_eval=maxiters
+    end
+
+    if !isnothing(maxtime)
+        opt.options.max_time=maxtime
+    end
+
+    if !isnothing(reltol)
+        @warn "common reltol is currently not used by $(opt)"
+    end
+
+    if !isnothing(abstol)
+        @warn "common abstol is currently not used by $(opt)"
+  end
+  
+    return nothing
+end
+
+function __solve(prob::OptimizationProblem, opt::NOMADOpt;
+                 maxiters::Union{Number, Nothing} = nothing,
+                 maxtime::Union{Number, Nothing} = nothing,
+                 abstol::Union{Number, Nothing}=nothing,
+                 reltol::Union{Number, Nothing}=nothing,
+                 progress = false,
+                 kwargs...)
+
+    local x
+
+    maxiters = _check_and_convert_maxiters(maxiters)
+    maxtime = _check_and_convert_maxtime(maxtime)
+
+
+    _loss = function(θ)
+        x = prob.f(θ, prob.p)
+        return first(x)
+    end
+
+    function bb(x)
+        bb_outputs = [_loss(x)]
+        success = true
+        count_eval = true
+        return (success, count_eval, bb_outputs)
+    end
+
+    if !isnothing(prob.lcons) | !isnothing(prob.ucons)
+        @warn "Linear and nonlinear constraints defined in OptimizationProblem are currently not used by $(opt)"
+    end
+
+    bounds=(;)
+    if !isnothing(prob.lb)
+        bounds = (; bounds..., lower_bound=prob.lb)
+    end
+    
+    if !isnothing(prob.ub)
+        bounds = (; bounds..., upper_bound=prob.ub)
+    end
+
+    opt_setup = NOMAD.NomadProblem(length(prob.u0), 1, ["OBJ"], bb; bounds...)
+
+    _map_optimizer_args(prob, opt_setup, maxiters=maxiters, maxtime=maxtime,abstol=abstol, reltol=reltol; kwargs...)
+
+    t0 = time()
+    opt_res = NOMAD.solve(opt_setup, prob.u0)
+    t1 = time()
+    
+    SciMLBase.build_solution(prob, opt, opt_res.x_best_feas, first(opt_res.bbo_best_feas); original=opt_res)
+end

test/Project.toml

@@ -14,6 +14,7 @@ Metaheuristics = "bcdb8e00-2c21-11e9-3065-2b553b22f898"
 ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
 MultistartOptimization = "3933049c-43be-478e-a8bb-6e0f7fd53575"
 NLopt = "76087f3c-5699-56af-9a33-bf431cd00edd"
+NOMAD = "02130f1c-4665-5b79-af82-ff1385104aa0"
 Nonconvex = "01bcebdf-4d21-426d-b5c4-6132c1619978"
 NonconvexBayesian = "fb352abc-de7b-48de-9ebd-665b54b5d9b3"
 NonconvexIpopt = "bf347577-a06d-49ad-a669-8c0e005493b8"
@@ -49,6 +50,7 @@ Metaheuristics = ">=3.0.2"
 ModelingToolkit = ">= 6.4.7"
 MultistartOptimization = ">= 0.1.2"
 NLopt = ">= 0.6"
+NOMAD = ">= 2.1"
 Nonconvex = ">= 1.0"
 NonconvexBayesian = ">= 0.1"
 NonconvexIpopt = ">= 0.1"
@@ -65,4 +67,4 @@ ReverseDiff = ">= 1.9.0"
 SafeTestsets = ">= 0.0.1"
 Tracker = ">= 0.2"
 Zygote = ">= 0.5"
-julia = "1.5"
+julia = "1.5"

test/rosenbrock.jl

@@ -173,7 +173,7 @@ end
 # sol = solve(prob, QuadDirect(); splits = ([-0.5, 0.0, 0.5],[-0.5, 0.0, 0.5]))
 # @test 10*sol.minimum < l1
 
-@testset "Evolutionary, BlackBoxOptim, Metaheuristics, Nonconvex" begin
+@testset "Evolutionary, BlackBoxOptim, Metaheuristics, Nonconvex, NOMAD" begin
     optprob = OptimizationFunction(rosenbrock, GalacticOptim.AutoZygote())
     using Evolutionary
     prob = GalacticOptim.OptimizationProblem(optprob, x0, _p)
@@ -426,4 +426,15 @@ end
 
     sol = solve(prob, BayesOptAlg(NLoptAlg(:LN_NELDERMEAD)), sub_options=(;maxeval=100))
     @test 10*sol.minimum < l1
+
+    using NOMAD
+    f = OptimizationFunction(rosenbrock)
+
+    prob = OptimizationProblem(f, x0, _p)
+    sol = GalacticOptim.solve(prob,NOMADOpt())
+    @test 10*sol.minimum < l1
+
+    prob = OptimizationProblem(f, x0, _p; lb = [-1.0,-1.0], ub = [1.5,1.5])
+    sol = GalacticOptim.solve(prob,NOMADOpt())
+    @test 10*sol.minimum < l1
 end