moors

Evolution is a mystery

Overview

moors is the core crate of the moo-rs project for solving multi-objective optimization problems with evolutionary algorithms. It's a pure-Rust crate for high-performance implementations of genetic algorithms

Features

• Single Objective Genetic Algorithms (SO-GA)
• NSGA-II, NSGA-III, R-NSGA-II, Age-MOEA, REVEA, SPEA-II, IBEA (many more coming soon!)
• Pluggable operators: sampling, crossover, mutation, duplicates removal
• Flexible fitness & constraints via user-provided closures
• Built on ndarray and faer

Installation

[dependencies]
moors = "0.2.3"

Quickstart

use ndarray::{Array1, Array2, Axis, stack};

use moors::{
    algorithms::{AlgorithmError, Nsga2Builder},
    duplicates::ExactDuplicatesCleaner,
    operators::{SinglePointBinaryCrossover, BitFlipMutation, RandomSamplingBinary},
};

// problem data
const WEIGHTS: [f64; 5] = [12.0, 2.0, 1.0, 4.0, 10.0];
const VALUES: [f64; 5] = [4.0, 2.0, 1.0, 5.0, 3.0];
const CAPACITY: f64 = 15.0;

/// Compute multi-objective fitness [–total_value, total_weight]
/// Returns an Array2<f64> of shape (population_size, 2)
fn fitness_knapsack(population_genes: &Array2<f64>) -> Array2<f64> {
    let weights_arr = Array1::from_vec(WEIGHTS.to_vec());
    let values_arr = Array1::from_vec(VALUES.to_vec());

    let total_values = population_genes.dot(&values_arr);
    let total_weights = population_genes.dot(&weights_arr);

    // stack two columns: [-total_values, total_weights]
    stack(Axis(1), &[(-&total_values).view(), total_weights.view()]).expect("stack failed")
}

fn constraints_knapsack(population_genes: &Array2<f64>) -> Array1<f64> {
    let weights_arr = Array1::from_vec(WEIGHTS.to_vec());
    population_genes.dot(&weights_arr) - CAPACITY
}

fn main() -> Result<(), AlgorithmError> {
    // build the NSGA-II algorithm
    let mut algorithm = Nsga2Builder::default()
        .fitness_fn(fitness_knapsack)
        .constraints_fn(constraints_knapsack)
        .sampler(RandomSamplingBinary::new())
        .crossover(SinglePointBinaryCrossover::new())
        .mutation(BitFlipMutation::new(0.5))
        .duplicates_cleaner(ExactDuplicatesCleaner::new())
        .num_vars(5)
        .population_size(100)
        .crossover_rate(0.9)
        .mutation_rate(0.1)
        .num_offsprings(32)
        .num_iterations(2)
        .build()?;

    algorithm.run()?;
    let population = algorithm.population()?;
    println!("Done! Population size: {}", population.len());

    Ok(())
}

Duplicates Cleaner

In the example above, we use ExactDuplicatesCleaner to remove duplicated individuals that are exactly the same (hash-based deduplication). The CloseDuplicatesCleaner is also available—it accepts an epsilon parameter to drop any individuals within an ε-ball. Note that eliminating duplicates can be computationally expensive; if you do not want to use a duplicate cleaner, pass moors::NoDuplicatesCleaner to the builder.

Constraints

In moors, constraints (if provided) are used to enforce feasibility:

• Feasibility dominates everything: any individual with all constraint values ≤ 0 is preferred over any infeasible one.

• If both tournament participants are infeasible, the one with the smaller sum of positive violations wins.

• All constraints must evaluate to ≤ 0. For “>” constraints, invert the inequality in your function (multiply by –1).

• Equality constraints use an ε-tolerance:

  $$g_{\text{ineq}}(x) = \bigl|g_{\text{eq}}(x)\bigr| - \varepsilon ;\le; 0.$$

use ndarray::{Array2, Array1, Axis};

const EPSILON: f64 = 1e-6;

/// Returns an Array2 of shape (n, 2) containing two constraints for each row [x, y]:
/// - Column 0: |x + y - 1| - EPSILON ≤ 0 (equality with ε-tolerance)
/// - Column 1: x² + y² - 1.0 ≤ 0 (unit circle inequality)
fn constraints(genes: &Array2<f64>) -> Array2<f64> {
    // Constraint 1: |x + y - 1| - EPSILON
    let eq = genes.map_axis(Axis(1), |row| (row[0] + row[1] - 1.0).abs() - EPSILON);
    // Constraint 2: x^2 + y^2 - 1
    let ineq = genes.map_axis(Axis(1), |row| row[0].powi(2) + row[1].powi(2) - 1.0);
    // Stack into two columns
    stack(Axis(1), &[eq.view(), ineq.view()]).unwrap()
}

We know! we don't want to be stacking and using the epsilon technique everywhere. We have a helper macro to build the constraints for us

use ndarray::{Array2, Array1, Axis};

use moors::impl_constraints_fn;

const EPSILON: f64 = 1e-6;

/// Equality constraint x + y = 1
fn constraints_eq(genes: &Array2<f64>) -> Array1<f64> {
    genes.map_axis(Axis(1), |row| row[0] + row[1] - 1.0)
}

/// Inequality constraint: x² + y² - 1 ≤ 0
fn constraints_ineq(genes: &Array2<f64>) -> Array1<f64> {
    genes.map_axis(Axis(1), |row| row[0].powi(2) + row[1].powi(2) - 1.0)
}

constraints_fn!(
    MyConstraints,
    ineq = [constraints_ineq],
    eq   = [constraints_eq],
);

The macro above will generate a struct MyConstraints that can be passed to any moors algorithm. This macro accepts optional arguments lower_bound and upper_bound both for now f64 that are used to control the lower and upper bound of each gene.

If the optimization problem does not have any constraint, then use in the builder the struct moors::NoConstraints

Contributing

Contributions welcome! Please read the contribution guide and open issues or PRs in the relevant crate’s repository

License

This project is licensed under the MIT License.