Math Audio Differential Evolution

This crate provides a pure Rust implementation of Differential Evolution (DE) global optimization algorithm with advanced features including L-SHADE.

Features

• Pure Rust Implementation: No external dependencies for core optimization
• Multiple DE Strategies: Various mutation and crossover strategies
• L-SHADE: Linear population size reduction for faster convergence
• External Archive: Maintains diversity by storing discarded solutions
• Current-to-pbest/1: SHADE mutation strategy for balanced exploration
• Constraint Handling: Linear and nonlinear constraint support
• Adaptive Parameters: Self-adjusting F and CR parameters (SHADE-style)
• Evaluation Recording: Track optimization progress and convergence
• Visualization Tools: Plot test functions and optimization traces

Optimization Strategies

Mutation Strategies

• DE/rand/1: x_trial = x_r1 + F * (x_r2 - x_r3)
• DE/best/1: x_trial = x_best + F * (x_r1 - x_r2)
• DE/current-to-best/1: Combines current and best vectors
• DE/rand/2: Uses five random vectors for mutation
• DE/current-to-pbest/1: Blends current with top-p% individual (SHADE)

L-SHADE Strategy

L-SHADE combines three key improvements:

1. Linear Population Reduction: Starts with large population (18×dim), reduces to minimum (4)
2. External Archive: Stores discarded solutions for diversity
3. Current-to-pbest/1: Selects pbest from top p% of population

use math_audio_optimisation::{
    differential_evolution, DEConfigBuilder, Strategy, LShadeConfig
};

let bounds = vec![(-5.0, 5.0); 10];  // 10D problem

let lshade_config = LShadeConfig {
    np_init: 18,      // Initial NP = 18 × dim = 180
    np_final: 4,      // Final NP = 4
    p: 0.11,          // Select from top 11%
    arc_rate: 2.1,    // Archive size = 2.1 × current NP
    ..Default::default()
};

let config = DEConfigBuilder::new()
    .maxiter(500)
    .strategy(Strategy::LShadeBin)
    .lshade(lshade_config)
    .seed(42)
    .build()
    .expect("invalid config");

let result = differential_evolution(
    &|x| x.iter().map(|&xi| xi * xi).sum(),
    &bounds,
    config,
).expect("optimization should succeed");

Crossover Strategies

• Binomial: Random parameter-wise crossover
• Exponential: Sequential parameter crossover

Usage

use math_audio_optimisation::{differential_evolution, DEConfigBuilder, Strategy, Mutation};
use ndarray::Array1;

// Example objective function (Rosenbrock)
let objective = |x: &Array1<f64>| {
    let a = 1.0;
    let b = 100.0;
    (a - x[0]).powi(2) + b * (x[1] - x[0].powi(2)).powi(2)
};

// Define bounds for 2D problem
let bounds = vec![(-5.0, 5.0), (-5.0, 5.0)];

let config = DEConfigBuilder::new()
    .strategy(Strategy::Rand1Bin)
    .maxiter(1000)
    .popsize(50)
    .mutation(Mutation::Factor(0.8))
    .recombination(0.9)
    .seed(42)
    .build()
    .expect("invalid config");

let result = differential_evolution(&objective, &bounds, config)
    .expect("optimization should succeed");
println!("Best solution: {:?}", result.x);
println!("Best fitness: {}", result.fun);

Constraint Support

Linear Constraints

use math_audio_optimisation::{LinearConstraintHelper, DEConfig};
use ndarray::{Array1, Array2};

// Linear constraint: x1 + x2 <= 1.0
let constraint = LinearConstraintHelper {
    a: Array2::from_shape_vec((1, 2), vec![1.0, 1.0]).unwrap(),
    lb: Array1::from_vec(vec![f64::NEG_INFINITY]),
    ub: Array1::from_vec(vec![1.0]),
};

// Apply to configuration with penalty weight
let mut config = DEConfig::default();
constraint.apply_to(&mut config, 1000.0); // penalty weight

Nonlinear Constraints

let nonlinear_constraint = |x: &[f64]| -> f64 {
    x[0].powi(2) + x[1].powi(2) - 1.0 // circle constraint
};

Visualization

The crate includes a plot_functions binary for visualizing test functions and optimization traces:

# Plot test functions as contour plots
cargo run --bin plot_functions -- --functions rosenbrock,sphere

# Show optimization traces from CSV files
cargo run --bin plot_functions -- --csv-dir traces/ --show-traces

Integration

This crate is part of the Math Audio ecosystem:

• Used by autoeq for filter parameter optimization
• Integrates with math-audio-testfunctions for validation
• Works with math-audio-iir-fir for audio filter optimization

Examples

The crate includes several example programs demonstrating different DE capabilities:

• basic_de: Simple unconstrained optimization
• linear_constraints: Linear constraint handling
• nonlinear_constraints: Complex constraint optimization

Performance Tips

1. Use L-SHADE for high-dimensional problems (>10 dimensions)
2. Start with default LShadeConfig and tune p if needed
3. Lower p values (0.05-0.1) favor exploitation
4. Higher p values (0.15-0.25) favor exploration

References

License

GPL-3.0-or-later