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.
Add the following to your Cargo.toml:
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:
rust
use eviolite::prelude::*;
Then import a few other things that'll be helpful:
rust
use ndarray::Array1;
use ndarray_rand::RandomExt;
use rand::distributions::Uniform;
use std::f64::consts::FRAC_PI_2;
```rust
struct Polynomial(Array1
The elements of this array will represent the coefficientsa,b,c, and
dof the polynomiala + bx + cx² + dx³. Now let's define a method to
evaluate our polynomial for a givenx`:
rust
impl Polynomial {
fn apply(&self, x: f64) -> f64 {
self.0[0]
+ 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.
rust
lazy_static::lazy_static! {
static ref TEST_POINTS: Array1<f64> = Array1::range(0., FRAC_PI_2, FRAC_PI_2 / 100.);
}
SolutionNow we're ready to implement the Solution trait:
rust
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:
rust
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.
rust
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.
rust
fn evaluate(&self) -> f64 {
-TEST_POINTS.mapv(
|x| (self.apply(x) - x.sin()).abs()
).mean().unwrap()
}
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:
rust
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.
rust
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.
Let's create our
);
``` 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:
```rust
let start = std::time::Instant::now(); let log = evo.rununtil(
|gen| -gen.hallof_fame[0].evaluate() < 0.001
); let time = start.elapsed();
``` Now, let's extract our shiny new less-than-0.001-average-error polynomial from
the run log and print it to console:
```rust
let (best, ) = log.halloffame[0].clone().intoinner(); println!("found in {:.3} secs: sin(x) ≈ {:.3} + {:.3}x + {:.3}x² + {:.3}x³",
time.assecsf64(), best.0[0], best.0[1], best.0[2], best.0[3]
);
``` And that's everything! See
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:
Activity: Set the environment variable The
Taylor series expansion
for 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():
```rust
let evo: Evolutionhof::BestN::new(1),
25000
.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.examples/approx_sin.rs
for the full code.
found in 3.982 secs: sin(x) ≈ 0.001 + 1.017x + -0.059x² + -0.118x³
EVIOLITE_SEED to 1175913497836025702 and run the program again to get the exact same output as above! (Except the run time, of course.)sin(x) starts x - (x³ / 3!) + ..., so it's a nice sanity check to see
that the coefficients roughly match 0, 1, 0, and -1/6.