Swarm

Black-box optimisation tool written in Rust. Clean API for solving complex single-objective and multi-objective optimisation problems using powerful metaheuristic algorithms. Swarm has the following features:

• NSGA-II for single/multi-objective problems.
• Particle Swarm Optimisation (PSO) for single-objective problems.
• Optional Parallel Execution (massively improves performance for expensive blackbox functions).
• Flexible Function Support.

Getting Started

Rust

To use Swarm in your project, add it as a dependency in your Cargo.toml:

[dependencies]
swarm = "0.1.2"  # (replace with current version)

This by default includes the parallel feature. This allows the use of solve_par which is very useful for computationally expensive objective functions. To disable it (for more lightweight build, or if parallel not necessary) use default-features = false.

Python

pip install swarm_py

Examples in Rust

All functions provided to Swarm must be of the signature:

FnMut(&[f64]) -> (Vec<f64>, Option<Vec<f64>>)

• The first argument is a reference to a vector of f64 values representing the variables. Variable types are currently limited to f64.
• The first return vector contains the objective values.
• The second return vector contains the constraint values (if any).
• For parallel execution, the function must also be thread-safe (i.e., Fn + Sync + Send).

Single-Objective Optimisation with Particle Swarm (PSO)

Problem: Minimise f(x, y) = (x² + y - 11)² + (x + y² - 7)²

use swarm::{error::Result, pso::PsoParams, Optimiser, Variable};

// Define the function (can also use closure)
fn himmelblau(x: &[f64]) -> (Vec<f64>, Option<Vec<f64>>) {
    let f = (x[0].powi(2) + x[1] - 11.0).powi(2) + (x[0] + x[1].powi(2) - 7.0).powi(2);
    (vec![f], None)
}

fn main() -> Result<(), Box<dyn std::error::Error>> {
    // 1. Define the search space for the variables
    let vars = vec![Variable(-5.0, 5.0), Variable(-5.0, 5.0)];

    // 2. Configure the optimiser
    let optimiser = Optimiser::Pso {
        n_particles: 100,
        params: PsoParams::default(),
        constraint_handler: None,
        seed: None,
    };

    // 3. Find the minimum
    let max_iter = 200;
    let result = optimiser.solve(&mut himmelblau, &vars, max_iter)?;
    // Note: 1. You can also call the pso function directly.
    // Note: 2. You can pass a closure directly.
    // Note: 3. For parallel execution use `solve_par` 
    // (if feature `parallel` is enabled)
    
    // 4. Get the best solution found
    let best = &result.solutions[0];
    println!("Min at x = {:.4?}, f(x) = {:.4}", best.x, best.f[0]);
    Ok(())
}

Multi-Objective Optimisation with NSGA-II

This example solves the constrained Binh and Korn problem. NSGA-II is ideal for this as it finds a set of trade-off solutions, known as the Pareto Front, rather than a single point.

Problem: Minimise two objectives, f1(x, y) and f2(x, y), subject to two constraints.

use swarm::{Optimiser, Variable, SbxParams, PmParams};

// Define the problem (can also use closure)
fn binh_and_korn(x: &[f64]) -> (Vec<f64>, Option<Vec<f64>>) {
    // Objectives
    let f1 = 4.0 * x[0].powi(2) + 4.0 * x[1].powi(2);
    let f2 = (x[0] - 5.0).powi(2) + (x[1] - 5.0).powi(2);

    // Constraints
    let g1 = (x[0] - 5.0).powi(2) + x[1].powi(2) - 25.0;
    let g2 = 7.7 - (x[0] - 8.0).powi(2) - (x[1] + 3.0).powi(2);

    (vec![f1, f2], Some(vec![g1, g2]))
}

fn main() -> Result<(), Box<dyn std::error::Error>> {
    // 1. Define the search space
    let vars = vec![Variable(0.0, 5.0), Variable(0.0, 3.0)];

    // 2. Configure the NSGA-II optimiser
    let optimiser = Optimiser::Nsga {
        pop_size: 50,
        crossover: SbxParams::default(),
        mutation: PmParams::default(),
        seed: None,
    };

    // 3. Solve the problem
    let result = optimiser.solve(&mut binh_and_korn, &vars, 250)?;
    
    // 4. Get the Pareto front
    println!("Found {} solutions on the Pareto front.", result.solutions.len());
    
    Ok(())
}

After running the Binh and Korn example and plotting the solutions, you should see a Pareto front similar to the one shown below.

Examples in Python

Similar to the Rust examples all blackbox functions must have signatures of the form:

def blackbox(x: list[float]) -> tuple[list[float], list[float] | None]

Here's the same Binh and Korn example in Python:

import swarm_py as sp

def binh_and_korn_problem(x):
    f1 = 4.0 * x[0]**2 + 4.0 * x[1]**2
    f2 = (x[0] - 5.0)**2 + (x[1] - 5.0)**2

    g1 = (x[0] - 5.0)**2 + x[1]**2 - 25.0
    g2 = 7.7 - (x[0] - 8.0)**2 - (x[1] + 3.0)**2
    return ([f1, f2], [g1, g2])

if __name__ == "__main__":
    # Define variable bounds and optimisation settings
    variables = [sp.Variable(0, 5), sp.Variable(0, 3)]

    # Configure the NSGA-II optimiser
    # Other properties are default unless specified
    optimiser = sp.Optimiser.nsga(pop_size=100)

    # Run the optimisation
    result = optimiser.solve(binh_and_korn_problem, variables, 250)

    # For parallel execution, use the following:
    result = optimiser.solve_par(binh_and_korn_problem, variables, 250)

    print(result.solutions)

Performance (Python)

Serial Execution

Comparing to the same configuration Pymoo NSGA-II optimiser for the ZDT1 problem:

Parallel Execution

For expensive blackbox functions it makes sense to run swarm in parallel. If we simulate an expensive blackbox function by adding a sleep delay to the ZDT1 problem, i.e.,

def expensive_blackbox(x):
    time.sleep(0.0005)  # Artificial delay
    n_vars = len(x)
    f1 = x[0]
    g = 1.0 + 9.0 * sum(x[1:]) / (n_vars - 1)
    h = 1.0 - np.sqrt(f1 / (g + 1e-8))
    f2 = g * h
    return ([f1, f2], None)

then running swarm with NSGA-II in parallel is a massive improvement:

Build python from source

These instructions assume that Python3 and Cargo are installed on your system. To set up this project, follow these steps:

1. Clone the repository:

   git clone https://github.com/alexlovric/swarm.git
   cd swarm/swarm_py
   

2. Create a virtual environment and install build system:

   python3 -m venv .venv
   source .venv/bin/activate # In windows /Scripts/activate
   python3 -m pip install -r requirements.txt
   

3. Build the release binary:

   maturin develop --release
   

4. Build the python wheel:

   maturin build --release
   

License

MIT License - See LICENSE for details.

Support

If you'd like to support the project consider:

• Identifying the features you'd like to see implemented or bugs you'd like to fix and open an issue.
• Contributing to the code by resolving existing issues, I'm happy to have you.
• Donating to help me continue development, Buy Me a Coffee