[ANN] Metaheuristics.jl

jmejia8 · September 20, 2021, 4:00pm

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 · September 20, 2021, 4:24pm

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 · September 21, 2021, 1:06am

Thanks for your comment. Good suggestion!

PeterSimon · September 21, 2021, 3:36pm

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 · September 21, 2021, 3:52pm

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

pierre-haessig · April 18, 2023, 7:31pm

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

jmejia8 · April 18, 2023, 9:00pm

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

github.com/jmejia8/Metaheuristics.jl

New features coming in next release

opened 08:44PM - 12 Apr 23 UTC

jmejia8

new features

Install the unstable version hosted in the `develop` branch. ```julia pkg> …add Metaheuristics#develop ``` **Optimizers with default parameters** ```julia f, bounds, pareto_solutions = Metaheuristics.TestProblems.get_problem(:sphere); optimize(f, bounds, ECA) ``` Pass parameters and `Options` via as `kargs...` ```julia optimize(f, bounds, ECA, N = 20, iterations = 10, seed = 1) ``` is similar to ```julia optimize(f, bounds, ECA(N = 20, options=Options(iterations = 10, seed = 1)) ``` **Using the [`SearchSpaces`](https://jmejia8.github.io/SearchSpaces.jl/stable/searchspaces/) module to define search spaces.** ```julia fn(x) = abs(sum(diff(x))) space = boxconstraints(zeros(10), 100ones(10)) # float optimize(fn, space, ECA) # bounds space = boxconstraints(zeros(10), 100ones(10), rigid = false) # float optimize(fn, space, ECA) space = boxconstraints(zeros(Int, 10), 100ones(Int, 10)) # integers optimize(fn, space, ECA) # discrete space = BitArraySpace(10) # 10D array of booleans optimize(fn, space, GA) space = PermutationSpace(10) # 10-permutation optimize(fn, space, GA) ``` **Termination criteria based on convergence** **Other performance improvements** **Clear message errors (https://github.com/jmejia8/Metaheuristics.jl/issues/65)** ```julia ff(x) = "abcd" optimize(ff, [zeros(2) ones(2)] , ECA ) ``` output: ``` ERROR: Objective function should return either a numerical value or a Tuple depending on the problem. Current output: abcd of type String Examples at https://jmejia8.github.io/Metaheuristics.jl/stable/examples Stacktrace: [1] error(s::String) ```

compleat · June 9, 2024, 11:55am

Say, I am only an occasional user to this interesting package.

After working fine earlier, now it seems that it does not regocnize ‘BitArraySpace’

UndefVarError: `BitArraySpace` not defined

I have tried Metaheuristics.BitArraySpace, etc and looked all over, but cannot figure out why the same code which worked earlier now does not work
Thanks for any hints

jmejia8 · June 12, 2024, 8:13am

Which version are you using?