CMA-ES Reference

Covariance Matrix Adaptation Evolution Strategy for continuous optimization.

Module

use fugue_evo::algorithms::cmaes::{CmaEs, CmaEsState, CmaEsFitness};

Constructor

pub fn new(initial_mean: Vec<f64>, initial_sigma: f64) -> Self

Configuration Methods

Fitness Trait

CMA-ES uses a different fitness trait (minimization):

pub trait CmaEsFitness: Send + Sync {
    /// Evaluate solution - return value to MINIMIZE
    fn evaluate(&self, x: &RealVector) -> f64;
}

Usage

Basic Example

use fugue_evo::prelude::*;

struct MyFitness;

impl CmaEsFitness for MyFitness {
    fn evaluate(&self, x: &RealVector) -> f64 {
        // Return value to minimize
        x.genes().iter().map(|g| g * g).sum()
    }
}

let mut cmaes = CmaEs::new(vec![0.0; 10], 0.5)
    .with_bounds(MultiBounds::symmetric(5.0, 10));

let best = cmaes.run_generations(&MyFitness, 1000, &mut rng)?;

println!("Best fitness: {}", best.fitness_value());

Step-by-Step

let mut cmaes = CmaEs::new(vec![0.0; 10], 1.0);

for _ in 0..100 {
    cmaes.step(&fitness, &mut rng)?;

    println!("Generation {}: sigma = {:.6}",
        cmaes.state.generation,
        cmaes.state.sigma);

    // Early stopping
    if cmaes.state.sigma < 1e-10 {
        break;
    }
}

State Structure

pub struct CmaEsState {
    pub generation: usize,
    pub evaluations: usize,
    pub mean: Vec<f64>,
    pub sigma: f64,
    pub covariance: Vec<Vec<f64>>,
    // ... internal adaptation parameters
}

Algorithm Parameters

CMA-ES automatically sets most parameters based on problem dimension:

Convergence Criteria

CMA-ES converges when:

• sigma becomes very small (< 1e-12)
• Condition number of covariance matrix is too high
• No improvement for many generations

Memory Usage

CMA-ES stores a full covariance matrix:

For high dimensions (>1000), consider alternatives.

Best Practices

1. Initial sigma: Should cover ~1/3 of the search range
2. Initial mean: Start near expected optimum if known
3. Bounds: Use soft bounds (CMA-ES handles them gracefully)
4. Restarts: For multimodal problems, use multiple restarts

See Also

• CMA-ES Tutorial
• Choosing an Algorithm