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EDA/UMDA Reference

Estimation of Distribution Algorithms using probabilistic models.

Module

use fugue_evo::algorithms::eda::{Umda, UmdaBuilder, UmdaConfig};

Overview

EDAs replace crossover/mutation with probabilistic model building:

  1. Select promising individuals
  2. Build probabilistic model from selected
  3. Sample new individuals from model
  4. Repeat

UMDA (Univariate Marginal Distribution Algorithm) assumes variables are independent.

Builder API

Required Configuration

Method Type Description
bounds(bounds) MultiBounds Search space bounds
fitness(fit) impl Fitness Fitness function

Optional Configuration

Method Type Default Description
population_size(n) usize 100 Population size
selection_size(n) usize 50 Individuals for model building
max_generations(n) usize 100 Max generations

Usage

Basic Example

use fugue_evo::prelude::*;

let result = UmdaBuilder::<RealVector, f64, _>::new()
    .population_size(100)
    .selection_size(30)  // Top 30% for model
    .bounds(MultiBounds::symmetric(5.12, 10))
    .fitness(Sphere::new(10))
    .max_generations(200)
    .build()?
    .run(&mut rng)?;

Algorithm Details

Model Building (Univariate)

For continuous variables:

μᵢ = mean of selected individuals' gene i
σᵢ = std dev of selected individuals' gene i

Sampling

New individuals sampled from:

xᵢ ~ N(μᵢ, σᵢ²)

When to Use

Good for:

  • Separable problems (variables independent)
  • Problems where crossover is disruptive
  • Understanding variable distributions

Not good for:

  • Non-separable problems (use CMA-ES instead)
  • Problems with variable interactions

Comparison with GA

Aspect GA EDA (UMDA)
Variation Crossover + Mutation Model sampling
Interactions Crossover preserves building blocks Assumes independence
Parameters Crossover rate, mutation rate Selection ratio

See Also