The NOMAD module for Julia v0.6

This module provides a Julia-language interface to the free/open-source NOMAD library for nonlinear optimization of black-box functions. Currently only a limited set of features of NOMAD is available through this interface. Currently it works only for julia v0.6; if you wish to update it to later versions of Julia, please consider opening a PR.

Installation

Currently the installation is only tested on Linux. Please adapt deps/build.jl for other platforms.

Within Julia, you can install the NOMAD.jl package with the package manager: Pkg.add("NOMAD")

Basic Usage

using NOMAD
function rosenbrock(x)
    res = 0.
    for i in 1:length(x) - 1
    	res += 100 * (x[i+1] - x[i]^2)^2 + (1 - x[i])^2
    end
    res
end
ev = Evaluator(rosenbrock, [], 5)
opt = Opt(ev, UPPER_BOUND = 10*ones(5), LOWER_BOUND = -10*ones(5), 
          X0 = zeros(5), DISPLAY_DEGREE = 0)
optimize(opt)

The Evaluator takes an objective function rosenbrock, an array of constraints (the empty array []), and the dimensionality of the problem 5. Opt takes an evaluator ev and any number of keyword arguments that are allowed in NOMAD (c.f NOMAD.help())

using NOMAD
NOMAD.help(:CONSTRAINTS)
ev = Evaluator((x, y) -> - x^2 + (y - 1)^2, [(:EB, (x, y) -> x - y)], 2, vectorin = false)
opt = Opt(ev, UPPER_BOUND = [5, 6], LOWER_BOUND = [-2, -6], X0 = [1, 2])
optimize(opt)

The array of constraints can contain functions (for which the default type :PB is assumed) or tuples of the form (type of constraint, function). The keyword argument vectorin = false (default true) is set to indicate that the functions provided in this examples do not take a vector as input but 2 scalar arguments.

using NOMAD
ev = Evaluator(x -> x[5], [(:PB, x -> (norm(x-1)^2 - 25)), (:EB, x -> 25 - norm(x + 1)^2)], 5)
opt = Opt(ev, UPPER_BOUND = [5, 6, 7, Inf64, Inf64], LOWER_BOUND = -6*ones(5), 
          X0 = zeros(5), MAX_BB_EVAL = 100, SEED = 11)
optimize(opt)

Using JuMP

NOMAD implements the MathProgBase interface for nonlinear optimization, which means that it can be used interchangeably with other optimization packages from modeling packages like JuMP.

using JuMP, NOMAD
m = Model(solver = NOMAD.NOMADSolver(DISPLAY_DEGREE = 2, constrainttype = :EB))
a1 = 2
b1 = 0
a2 = -1
b2 = 1

@variable(m, x1)
@variable(m, x2 >= 0)

@NLobjective(m, Min, sqrt(x2))
@NLconstraint(m, x2 >= (a1*x1+b1)^3)
@NLconstraint(m, x2 >= (a2*x1+b2)^3)

setvalue(x1, 1.234)
setvalue(x2, 5.678)

status = solve(m)
println("got ", getobjectivevalue(m), " at ", [getvalue(x1),getvalue(x2)])

Help on NOMAD Parameters

NOMAD.help()
NOMAD.help(:UPPER_BOUND)