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

**URL:** <https://discourse.julialang.org/t/ann-extremaloptimization-jl-gradient-free-optimizer-over-continuous-spaces/45085>\
**Category:** Package Announcements\
**Created:** [August 17, 2020, 8:27am UTC](https://discourse.julialang.org/t/ann-extremaloptimization-jl-gradient-free-optimizer-over-continuous-spaces/45085 "2020-08-17T08:27:15Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![francesco.alemanno](https://avatars.discourse-cdn.com/v4/letter/f/e8c25b/32.png) [@francesco.alemanno](https://discourse.julialang.org/u/francesco.alemanno)\
**Post date:** [August 17, 2020, 8:27am UTC](https://discourse.julialang.org/t/ann-extremaloptimization-jl-gradient-free-optimizer-over-continuous-spaces/45085/1 "2020-08-17T08:27:15Z")

</div>

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 🙂

[https://github.com/francescoalemanno/ExtremalOptimization.jl](https://github.com/francescoalemanno/ExtremalOptimization.jl)

# ExtremalOptimization

for functions of continuous variables.

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](https://arxiv.org/pdf/cond-mat/0010337.pdf).

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.

## API:

```julia
function optimize(
    f,
    s,
    N;
    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:

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

```

output

```julia-auto
(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.

---

<div class="post-metadata">

**Author:** ![francesco.alemanno](https://avatars.discourse-cdn.com/v4/letter/f/e8c25b/32.png) [@francesco.alemanno](https://discourse.julialang.org/u/francesco.alemanno)\
**Post date:** [August 19, 2020, 5:33pm UTC](https://discourse.julialang.org/t/ann-extremaloptimization-jl-gradient-free-optimizer-over-continuous-spaces/45085/2 "2020-08-19T17:33:17Z")

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