[ANN] Metaheuristics.jl

[jmejia8]

After several years of development, I share with you Metaheuristics.jl

This package implements state-of-the-art metaheuristic algorithms for single and multi-objective optimization. The aim of this package is to provide easy to use (and fast) metaheuristics for numerical global optimization.

Metaheuristics.jl includes:

• Popular algorithms such as Differential Evolution, PSO, NSGA-II, NSGA-III, and more…
• Performance Indicators such as IGD, hypervolume, among others.
• Test Problems for single and multi-objective optimization.
• Some visualization features in terminal via UnicodePlots.jl

Example 1

Objective function:

julia> f(x) = 10length(x) + sum( x.^2 - 10cos.(2π*x)  )
f (generic function with 1 method)

Bounds for x∈ [-5,5]⁵ :

julia> bounds = [-5ones(5) 5ones(5)]
5×2 Matrix{Float64}:
 -5.0  5.0
 -5.0  5.0
 -5.0  5.0
 -5.0  5.0
 -5.0  5.0

Optimize:

julia> result = optimize(f, bounds)
+=========== RESULT ==========+
  iteration: 1429
    minimum: 0
  minimizer: [1.8792427588475406e-10, 1.6562253377998926e-9, -2.2532566630145983e-9, 1.649414863704028e-9, 4.005275371381464e-9]
    f calls: 49981
 total time: 0.2483 s
+============================+

Example 2

julia> f, bounds, front = Metaheuristics.TestProblems.ZDT3();

julia> optimize(f, bounds, NSGA2())
+=========== RESULT ==========+
  iteration: 500
...
non-dominated solution(s):
                           F space
          ┌────────────────────────────────────────┐ 
        2 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
          │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
          │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
          │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
          │⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
          │⢣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
          │⠀⠘⠲⠤⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
   f_2    │⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
          │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
          │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
          │⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⠍⠉⠉⠉⠉⠉⠉⢭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉│ 
          │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
          │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀│ 
          │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀│ 
       -1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
          └────────────────────────────────────────┘ 
          0                                      0.9
                             f_1
    f calls: 50000
  feasibles: 100 / 100 in final population
 total time: 1.4626 s
+============================+

Comments and suggestions are welcome.

[mohamed82008]

Congratulations on the package! I see you have some constraint handling in some of the algorithms. I think this might be the first Julia package for metaheuristics that can handle equality and inequality constraints natively. Would be great to create a wrapper for Metaheuristics in Nonconvex.jl.

[jmejia8]

Thanks for your comment. Good suggestion!

[PeterSimon]

Looks like a great package!

Very often I need to optimize expensive black-box functions, and having an optimizer that offers multi-threaded, simultaneous evaluation of multiple candidate solutions significantly reduces execution time. Please consider adding this option to your population-based optimizers.

[jmejia8]

That is a great suggestion. The evaluation of multiple solutions will be included in future versions.

[pierre-haessig]

@PeterSimon

Very often I need to optimize expensive black-box functions, and having an optimizer that offers multi-threaded, simultaneous evaluation of multiple candidate solutions significantly reduces execution time. Please consider adding this option to your population-based optimizers.

For the reference, parallel evaluation is now available (since?) in Metaheuristics.jl:

• Examples · Metaheuristics.jl
• Parallelization · Metaheuristics.jl

[jmejia8]

Parallel evaluation is available since v3.2.x (released mid-2022). BTW, v3.3 is coming with some new features:

New features coming in next release