Module multiobjective 

Clean Vec-based multi-objective optimisation algorithms.

This module provides self-contained, easy-to-use implementations of multi-objective evolutionary algorithms that work directly with Rust Vec<f64> slices — no ndarray wrappers required.

Modules

Module	Algorithm
[nsga2]	NSGA-II — Non-dominated Sorting Genetic Algorithm II (Deb 2002)
[nsga3]	NSGA-III — Many-objective NSGA with reference-point niching (Deb 2014)
[moead]	MOEA/D — Decomposition-based MOEA (Zhang 2007)
pareto	Pareto dominance, ranking, hypervolume, and distance metrics
indicators	Quality indicators: HV, IGD, IGD+, GD, ε-indicator, R2, spacing

Quick start

use scirs2_optimize::multiobjective::nsga2::{nsga2, Nsga2Config};

// 2-variable, 2-objective ZDT1 benchmark
let bounds = vec![(0.0_f64, 1.0_f64); 5];
let mut cfg = Nsga2Config::default();
cfg.population_size = 20;
cfg.n_generations   = 5;

let result = nsga2(2, &bounds, |x| {
    let f1 = x[0];
    let g  = 1.0 + 9.0 * x[1..].iter().sum::<f64>() / (x.len()-1) as f64;
    vec![f1, g * (1.0 - (f1 / g).sqrt())]
}, cfg).expect("valid input");

println!("Pareto front size: {}", result.pareto_front.len());

Many-objective (≥ 4 objectives) example

use scirs2_optimize::multiobjective::nsga3::{nsga3, Nsga3Config};

let n_obj = 4;
let bounds: Vec<(f64, f64)> = vec![(0.0, 1.0); n_obj + 3];
let mut cfg = Nsga3Config::default();
cfg.population_size = 30;
cfg.n_generations   = 10;
cfg.n_divisions     = 3;

let result = nsga3(n_obj, &bounds, |x| {
    let n = x.len();
    let k = n - n_obj + 1;
    let g: f64 = x[n-k..].iter().map(|&xi| (xi - 0.5).powi(2)).sum();
    let mut f = vec![0.0f64; n_obj];
    for i in 0..n_obj {
        let mut val = 1.0 + g;
        for j in 0..n_obj - 1 - i {
            val *= (x[j] * std::f64::consts::FRAC_PI_2).cos();
        }
        if i > 0 { val *= (x[n_obj - 1 - i] * std::f64::consts::FRAC_PI_2).sin(); }
        f[i] = val;
    }
    f
}, cfg).expect("valid input");

println!("Reference points: {}", result.reference_points.len());

Re-exports

pub use hypervolume::exclusive_hypervolume;

pub use hypervolume::hypervolume_2d as hv_2d;

pub use hypervolume::hypervolume_3d;

pub use hypervolume::hypervolume_contribution_wfg;

pub use hypervolume::hypervolume_wfg;

pub use indicators::additive_epsilon_indicator;

pub use indicators::delta_metric;

pub use indicators::dominates;

pub use indicators::generational_distance;

pub use indicators::hypervolume_2d;

pub use indicators::hypervolume_contribution;

pub use indicators::hypervolume_mc;

pub use indicators::igd;

pub use indicators::igd_plus;

pub use indicators::non_dominated_sort;

pub use indicators::r2_indicator;

pub use indicators::spacing_metric;

pub use indicators::spread;

pub use indicators::R2Utility;

pub use moead::build_neighborhood;

pub use moead::generate_weight_vectors;

pub use moead::moead;

pub use moead::tchebycheff_scalarization;

pub use moead::MoeadConfig;

pub use moead::MoeadResult;

pub use nsga2::nsga2;

pub use nsga2::Individual;

pub use nsga2::Nsga2Config;

pub use nsga2::Nsga2Result;

pub use nsga3::adapt_reference_points;

pub use nsga3::associate_to_reference_points;

pub use nsga3::generate_reference_points;

pub use nsga3::generate_reference_points_inner;

pub use nsga3::nsga3;

pub use nsga3::reference_line_distance;

pub use nsga3::Nsga3Config;

pub use nsga3::Nsga3Result;

pub use pareto::crowding_distance;

pub use pareto::dominates as pareto_dominates;

pub use pareto::epsilon_indicator;

pub use pareto::generational_distance as pareto_gd;

pub use pareto::hypervolume_2d as pareto_hv2d;

pub use pareto::hypervolume_indicator as pareto_hv;

pub use pareto::igd as pareto_igd;

pub use pareto::non_dominated_sort as pareto_nds;

pub use pareto::pareto_front;

pub use pareto::pareto_front_2d;

pub use pareto::pareto_rank;

pub use pareto::spread_metric;

Modules

hypervolume

Hypervolume indicator computation for multi-objective optimization.

indicators

Performance indicators for multi-objective optimization

moead

MOEA/D: Multi-Objective Evolutionary Algorithm based on Decomposition

nsga2

NSGA-II: Non-dominated Sorting Genetic Algorithm II

nsga3

NSGA-III: Non-dominated Sorting Genetic Algorithm III

pareto

Pareto front utilities for multi-objective optimization.