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:

Select promising individuals
Build probabilistic model from selected
Sample new individuals from model
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

Fugue-Evo Documentation