Metaheuristics - an Intuitive Package for Global Optimization

Author: Jesús-Adolfo Mejía-de-Dios (@jmejia8)

High-performance algorithms for optimization coded purely in a high-performance language.

Source Build Status codecov DOI


Optimization is one of the most common tasks in the scientific and industrial field but real-world problems require high-performance algorithms to optimize non-differentiable, non-convex, discontinuous functions. Different metaheuristics algorithms have been proposed to solve optimization problems but without strong assumptions about the objective function.

This package implements state-of-the-art metaheuristics algorithms for global optimization. The package aims to provide easy-to-use (and fast) metaheuristics for numerical global optimization.


Open the Julia (Julia 1.1 or Later) REPL and press ] to open the Pkg prompt. To add this package, use the add command:

pkg> add Metaheuristics

Or, equivalently, via the Pkg API:

julia> import Pkg; Pkg.add("Metaheuristics")

Quick Start

Assume you want to solve the following minimization problem.

Rastrigin Surface


\[f(x) = 10D + \sum_{i=1}^{D} x_i^2 - 10\cos(2\pi x_i)\]

where $x\in[-5, 5]^{D}$, i.e., $-5 \leq x_i \leq 5$ for $i=1,\ldots,D$. $D$ is the dimension number, assume $D=10$.


Firstly, import the Metaheuristics package:

using Metaheuristics

Code the objective function:

f(x) = 10length(x) + sum( x.^2 - 10cos.(2π*x)  )

Instantiate the bounds:

D = 10
bounds = boxconstraints(lb = -5ones(D), ub = 5ones(D))

Also, bounds can be a $2\times 10$ Matrix where the first row corresponds to the lower bounds whilst the second row corresponds to the upper bounds.

Approximate the optimum using the function optimize.

result = optimize(f, bounds)
Optimization Result
  Iteration:       883
  Minimum:         0.994959
  Minimizer:       [-4.48345e-09, -9.30599e-10, 3.25831e-10, …, -0.994959]
  Function calls:  61810
  Total time:      0.3276 s
  Stop reason:     Due to Convergence Termination criterion.

Optimize returns a State datatype which contains some information about the approximation. For instance, you may use mainly two functions to obtain such an approximation.

10-element Vector{Float64}:


How to cite?

Please cite the package using the bibtex entry

  doi = {10.21105/joss.04723}, 
  url = {}, 
  year = {2022}, 
  publisher = {The Open Journal}, 
  volume = {7}, 
  number = {78}, 
  pages = {4723}, 
  author = {Jesús-Adolfo Mejía-de-Dios and Efrén Mezura-Montes}, 
  title = {Metaheuristics: A Julia Package for Single- and Multi-Objective Optimization}, 
 journal = {Journal of Open Source Software} }

or the citation string

Mejía-de-Dios et al., (2022). Metaheuristics: A Julia Package for Single- and Multi-Objective Optimization. Journal of Open Source Software, 7(78), 4723,

in your scientific paper if you use Metaheristics.jl.


Jesús Mejía acknowledges support from the Mexican Council for Science and Technology (CONACyT) through a scholarship to pursue graduate studies at the University of Veracruz, MEXICO. This allowed the development of Metaheuristics.jl from August 2018 to July 2022.