[ANN] ExtremalOptimization.jl: gradient-free optimizer over continuous spaces

Hi everyone,

i made a super tiny package which could be useful to people attempting to optimize functions which have many multiple local minima and/or jumps, this algorithm finds solutions via a non-greedy policy, it does not improve on the best solutions, it improves the worst solutions in a rejection-free approach, this package is still in the process of being registered, let me know if you have suggestions or if you find it useful in your work :slight_smile:


for functions of continuous variables.

Build Status

This package implements the basic mechanism of Extremal Optimization (τ-EO) as described in Boettcher, Stefan; Percus, Allon G. (2001-06-04). “Optimization with Extremal Dynamics”. Physical Review Letters.

The only twist w.r.t. classical EO is an affine invariant update equation for the worst performing solutions,

X \to X_1 + \beta \cdot Z \cdot (X_2 - X_3), \,\,\,\, Z \sim \mathcal{N}(0,1)

where X₁, X₂, X₃ are chosen random inside the pool of candidate solutions, this update mechanism allows EO to work on continuous spaces, and be invariant w.r.t. affine transformations of X and monotonous tranformations of the cost function.


function optimize(
    reps_per_particle = 100,
    β = 1.0,
    τ = 1.2,
    atol = 0.0,
    rtol = sqrt(eps(1.0)),
    f_atol = 0.0,
    f_rtol = sqrt(eps(1.0)),
    verbose = false,
    rng = Random.GLOBAL_RNG,
    callback = state -> nothing,
  • f : cost function to minimize, whose argument is either a scalar or a vector, must returns a scalar value.
  • s : function whose input is the particle number and output is a random initial point to be ranked by f.
  • N : number of particles to use, choose a number greater than d+4 where d is the number of dimensions.
  • reps_per_particle : maximum number of iterations per particle.

Usage example:

using ExtremalOptimization
rosenbrock2d(x) = (x[1]-1)^2+(x[2]-x[1]^2)^2
initpoint(i) = randn(2)
optimize(rosenbrock2d, initpoint, 50)


(x = [1.000000001, 1.000000004], fx = 4.0e-18, f_nevals = 2726)

as expected the algorithm has found the optimum at (1, 1), up to the specified tolerance.


the package is now registered and can be added via ]add ExtremalOptimization in julia >= 1.5