NOMAD.jl

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This package provides a Julia interface for 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.

If you use NOMAD.jl in your work, please cite using the format given in CITATION.bib.

NOMAD can be installed and tested through the Julia package manager:

julia> ]
pkg> add NOMAD
pkg> test NOMAD

Let's say you want to minimize some objective function :

function f(x)
  return x[1]^2 + x[2]^2
end

while keeping some constraint inferior to 0 :

function c(x)
  return 1 - x[1]
end

You first need to declare a function eval_fct(x::Vector{Float64}) that returns a Vector{Float64} containing the objective function and the constraint evaluated for x, along with two booleans.

function eval_fct(x)
  bb_outputs = [f(x), c(x)]
  success = true
  count_eval = true
  return (success, count_eval, bb_outputs)
end

success is a boolean set to false if the evaluation should not be taken into account by NOMAD. Here, every evaluation will be considered as a success. count_eval is also a boolean, it decides weather the evaluation's counter will be incremented. Here, it is always equal to true so every evaluation will be counted.

Then, create an object of type NomadProblem that will contain settings for the optimization.

The classic constructor takes as arguments the initial point x0 and the types of the outputs contained in bb_outputs (as a Vector{String}).

pb = NomadProblem(2, # number of inputs of the blackbox
                  2, # number of outputs of the blackbox
                  ["OBJ", "EB"], # type of outputs of the blackbox
                  eval_fct;
                  lower_bound=[-5.0, -5.0],
                  upper_bound=[5.0, 5.0])

Here, first element of bb_outputs is the objective function (f(x)), second is a constraint treated with the Extreme Barrier method (c(x)). In this example, lower and upper bounds have been added but it is not compulsory.

Now call the function solve(p::NomadProblem, x0::Vector{Float64}) where x0 is the initial starting point to launch a NOMAD optimization process.

result = solve(pb, [3.0, 3.0])

The object returned by solve() contains information about the run.

Note: NOMAD is already precompiled with Yggdrasil for all platforms.

To use your custom NOMAD, set the environmental variables JULIA_NOMAD_LIBRARY_PATH to point the shared library. Note that NOMAD version 4.3.1 is needed.

For example:

ENV["JULIA_NOMAD_LIBRARY_PATH"] = "~/Applications/nomad-4.3.1/build/lib"
using NOMAD

Alternatively, you can create an entry in .julia/config/startup.jl or set these permanently through your operating system.