#evolution #genetic #algorithm #optimization #random


Toolkit for working with evolutionary algorithms

3 unstable releases

0.1.1 Mar 6, 2023
0.1.0 Mar 2, 2023
0.0.0 Feb 17, 2023

#195 in Algorithms

MIT license

1.5K SLoC


Published on crates.io! Read the docs on docs.rs!

Eviolite is a set of tools and algorithms for using evolutionary algorithms in Rust. It is written in a performance-minded, minimal-copy style, and uses rayon to parallelize the most computationally intensive parts. It also includes a drop-in replacement for rand's thread_rng that is fully reproducible and can be seeded from an environment variable. This means that if you get a run you like, you can share that seed with someone else alongside your program and they will be guaranteed to get the same output you got.

Getting Started

Add the following to your Cargo.toml:

eviolite = "0.1"

Then continue reading for a simple example, or take a look at the docs if you're not the tutorial type.


Let's go step by step over a complete program that uses a genetic algorithm to find a polynomial that approximates the sine function. This program is nice and short, but nicely demonstrates the general workflow of using Eviolite.

First, we'll import everything we need from Eviolite:

use eviolite::prelude::*;

Then import a few other things that'll be helpful:

use ndarray::Array1;
use ndarray_rand::RandomExt;
use rand::distributions::Uniform;
use std::f64::consts::FRAC_PI_2;

Defining Our Solution Type

struct Polynomial(Array1<f64>);

The elements of this array will represent the coefficients a, b, c, and d of the polynomial a + bx + cx² + dx³. Now let's define a method to evaluate our polynomial for a given x:

impl Polynomial {
    fn apply(&self, x: f64) -> f64 {
        + self.0[1] * x
        + self.0[2] * x.powi(2)
        + self.0[3] * x.powi(3)

Next, we'll create an array of test points. We can't evaluate how good our approximation is at every point, since that would take forever, so we'll use 100 evenly spaced points between 0 and π/2. We'll wrap this in a lazy_static so it's globally accessible.

lazy_static::lazy_static! {
    static ref TEST_POINTS: Array1<f64> = Array1::range(0., FRAC_PI_2, FRAC_PI_2 / 100.);

Implementing Solution

Now we're ready to implement the Solution trait:

impl Solution for Polynomial {

First, we define what type our fitness values will be. For now, we'll keep it simple, and say that how good an approximation is can be represented as a single f64:

type Fitness = f64;

Next, we need to define the four genetic algorithm primitives: generation, evaluation, crossover, and mutation.


Eviolite needs to be able to create a population of randomly generated individuals as a starting point for the algorithm. We'll use the handy random_using method from ndarray-rand to generate four random f64s between 0 and 1 with Eviolite's reproducible RNG. These numbers will represent the coefficients a, b, c, and d in our polynomial a + bx + cx² + dx³.

fn generate() -> Polynomial {
        Polynomial(Array1::random_using(4, Uniform::new_inclusive(0.0, 1.0), &mut thread_rng()))


We need to be able to tell the algorithm how good a given polynomial is at approximating sin. We'll do this by evaluating our polynomial for every test point x and taking the absolute difference between that value and sin(x), then averaging all of those differences to get the mean error across all test points.

fn evaluate(&self) -> f64 {
            |x| (self.apply(x) - x.sin()).abs()

Genetic algorithms assume that a higher fitness value is better, so we stick a negative sign in front.

Activity: Think of other ways we could measure the fitness of these approximations!


If you were to compare genetic algorithms to real-life selective breeding, this would be the breeding part. We need to mix together the coefficients of two polynomials so that they both get some information from the other while retaining some of their own. We'll just use a simple one-point crossover, which there's conveniently a built-in for:

fn crossover(a: &mut Self, b: &mut Self) {
        crossover::one_point(&mut a.0, &mut b.0);


Just like in real-life evolution, this is where "new ideas" come from. We need to randomly modify a polynomial just a little bit. One way to do this is by adding some Gaussian noise to the coefficients. Fortunately, there's a built-in for that. We'll apply a 50% chance to mutate each coefficient, and add noise with a standard deviation of 0.1 to the ones that are chosen for mutation.

fn mutate(&mut self) {
        mutation::gaussian(&mut self.0, 0.5, 0.1);

And that's it! We've implemented Solution, and that means Eviolite has everything it needs to evolve a polynomial to approximate sin(x). Now we can write our main() function and actually get a result.

Running an Evolution

Let's create our Evolution instance. We'll use the (μ + λ) algorithm, with some somewhat arbitrarily chosen parameters. We'll pass it a Tournament selector, which will repeatedly choose 10 polynomials at random and pick the best. We'll also create a BestN hall of fame with a size of 1, which will automatically track the best polynomial that's been found so far. Finally, we'll completely delete the population and generate a fresh one every 25,000 generations as a failsafe in case the algorithm gets stuck. In main():

let evo: Evolution<Polynomial, _, _, ()> = Evolution::with_resets(
        // population size (μ)
        // offspring size (λ)
        // crossover chance (cxpb)
        // mutation chance (mutpb)
        // selection operator



Activity: Try playing around with these parameters to see how they affect the evolution!

Now we just have to run it! We'll have the evolution run until it finds a polynomial whose mean error across all the test points is less than 0.001. We'll also time it for good measure:

let start = std::time::Instant::now();

let log = evo.run_until(
    |gen| -gen.hall_of_fame[0].evaluate() < 0.001

let time = start.elapsed();

.run_until() takes a closure that receives information about the current state of the run and decides whether to stop it, so we just check if the best solution we've seen has a mean error less than 0.001.

Now, let's extract our shiny new less-than-0.001-average-error polynomial from the run log and print it to console:

let (best, _) = log.hall_of_fame[0].clone().into_inner();

println!("found in {:.3} secs: sin(x) ≈ {:.3} + {:.3}x + {:.3}x² + {:.3}",
    time.as_secs_f64(), best.0[0], best.0[1], best.0[2], best.0[3]

And that's everything! See examples/approx_sin.rs for the full code.

When you compile and run this example (on release build - genetic algorithms are very computationally intensive!), after a moment you should get an output that looks a bit like this:

found in 3.982 secs: sin(x)0.001 + 1.017x + -0.059+ -0.118

Activity: Set the environment variable EVIOLITE_SEED to 1175913497836025702 and run the program again to get the exact same output as above! (Except the run time, of course.)

The Taylor series expansion for sin(x) starts x - (/ 3!) + ..., so it's a nice sanity check to see that the coefficients roughly match 0, 1, 0, and -1/6.


~47K SLoC