feat(algorithms): add NSGA-III
Implementation of Deb & Jain 2014 NSGA-III — the canonical
many-objective MOEA. Replaces NSGA-II's crowding-distance niching
with a structured reference-point niching procedure that scales to
3+ objectives where crowding distance loses its diversity signal.
Each generation:
1. Random parent selection + variation + offspring evaluation, same as
NSGA-II.
2. Combine + non_dominated_sort, fill the next population front-by-
front until the next front would overflow (the splitting front F_l).
3. Survival on F_l uses reference-point niching:
- Translate by the ideal point z* (per-axis min in oriented space).
- Compute extreme points by ASF and intercepts; normalize by
intercepts (with a robust fallback to per-axis range if extreme
points are degenerate).
- Associate every member of the working pool with the closest
reference direction by perpendicular distance.
- Iteratively pick from F_l: prefer the niche with the smallest
count among references that have F_l candidates; if the niche is
empty in the already-selected set, take the closest associated
member by perpendicular distance, otherwise pick uniformly from
the niche.
Public API:
Nsga3Config { population_size, generations, reference_divisions, seed }
Nsga3 { config, initializer, variation }
impl<P, I, V> Optimizer<P> for Nsga3<I, V>
Re-exported from the prelude. Tests cover non-empty Pareto front,
exact final population size, deterministic reruns, and panic on
`population_size == 0`. Uses the existing tests_support problems.
This commit is contained in:
@@ -2,6 +2,7 @@
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pub mod differential_evolution;
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pub mod nsga2;
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pub mod nsga3;
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pub mod paes;
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pub(crate) mod parallel_eval;
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pub mod random_search;
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@@ -9,6 +10,7 @@ pub mod spea2;
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pub use differential_evolution::*;
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pub use nsga2::*;
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pub use nsga3::*;
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pub use paes::*;
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pub use random_search::*;
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pub use spea2::*;
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@@ -0,0 +1,486 @@
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//! NSGA-III — Deb & Jain 2014, the canonical many-objective MOEA.
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use rand::Rng as _;
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use rand::seq::IndexedRandom;
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use crate::algorithms::parallel_eval::evaluate_batch;
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use crate::core::candidate::Candidate;
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use crate::core::objective::ObjectiveSpace;
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use crate::core::population::Population;
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use crate::core::problem::Problem;
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use crate::core::result::OptimizationResult;
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use crate::core::rng::{Rng, rng_from_seed};
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use crate::pareto::front::{best_candidate, pareto_front};
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use crate::pareto::reference_points::das_dennis;
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use crate::pareto::sort::non_dominated_sort;
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use crate::traits::{Initializer, Optimizer, Variation};
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/// Configuration for [`Nsga3`].
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#[derive(Debug, Clone)]
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pub struct Nsga3Config {
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/// Constant population size carried across generations.
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pub population_size: usize,
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/// Number of generations to run.
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pub generations: usize,
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/// Number of divisions `H` for Das–Dennis reference points.
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/// Final reference set has `binomial(H + M - 1, M - 1)` points for
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/// `M = objectives`. Typical: `H = 12` for `M = 3` (91 points),
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/// `H = 6` for `M = 5` (210 points).
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pub reference_divisions: usize,
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/// Seed for the deterministic RNG.
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pub seed: u64,
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}
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impl Default for Nsga3Config {
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fn default() -> Self {
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Self {
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population_size: 100,
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generations: 250,
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reference_divisions: 12,
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seed: 42,
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}
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}
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}
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/// NSGA-III optimizer.
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#[derive(Debug, Clone)]
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pub struct Nsga3<I, V> {
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/// Algorithm configuration.
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pub config: Nsga3Config,
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/// Initial-decision sampler.
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pub initializer: I,
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/// Offspring-producing variation operator.
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pub variation: V,
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}
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impl<I, V> Nsga3<I, V> {
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/// Construct an `Nsga3` optimizer.
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pub fn new(config: Nsga3Config, initializer: I, variation: V) -> Self {
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Self { config, initializer, variation }
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}
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}
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impl<P, I, V> Optimizer<P> for Nsga3<I, V>
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where
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P: Problem + Sync,
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P::Decision: Send,
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I: Initializer<P::Decision>,
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V: Variation<P::Decision>,
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{
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fn run(&mut self, problem: &P) -> OptimizationResult<P::Decision> {
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assert!(
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self.config.population_size > 0,
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"Nsga3 population_size must be greater than 0",
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);
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let n = self.config.population_size;
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let objectives = problem.objectives();
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let m = objectives.len();
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let reference_points = das_dennis(m, self.config.reference_divisions);
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assert!(
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!reference_points.is_empty(),
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"Nsga3 reference set is empty — check reference_divisions",
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);
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let mut rng = rng_from_seed(self.config.seed);
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// Initial population.
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let initial_decisions = self.initializer.initialize(n, &mut rng);
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assert_eq!(
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initial_decisions.len(),
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n,
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"NSGA-III initializer must return exactly population_size decisions",
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);
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let mut population: Vec<Candidate<P::Decision>> =
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evaluate_batch(problem, initial_decisions);
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let mut evaluations = population.len();
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for _ in 0..self.config.generations {
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// --- Random parent selection + variation ---
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let mut offspring_decisions: Vec<P::Decision> = Vec::with_capacity(n);
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while offspring_decisions.len() < n {
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let p1 = rng.random_range(0..population.len());
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let p2 = rng.random_range(0..population.len());
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let parents =
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vec![population[p1].decision.clone(), population[p2].decision.clone()];
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let children = self.variation.vary(&parents, &mut rng);
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assert!(
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!children.is_empty(),
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"NSGA-III variation returned no children",
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);
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for child_decision in children {
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if offspring_decisions.len() >= n {
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break;
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}
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offspring_decisions.push(child_decision);
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}
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}
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let offspring = evaluate_batch(problem, offspring_decisions);
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evaluations += offspring.len();
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// --- Combine + survival selection ---
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let mut combined: Vec<Candidate<P::Decision>> =
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Vec::with_capacity(2 * n);
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combined.extend(population.into_iter());
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combined.extend(offspring);
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population = environmental_selection(&combined, &objectives, &reference_points, n, &mut rng);
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}
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let front = pareto_front(&population, &objectives);
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let best = best_candidate(&population, &objectives);
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OptimizationResult::new(
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Population::new(population),
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front,
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best,
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evaluations,
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self.config.generations,
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)
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}
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}
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/// NSGA-III environmental selection: front-by-front + reference-point niching
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/// on the splitting front.
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fn environmental_selection<D: Clone>(
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combined: &[Candidate<D>],
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objectives: &ObjectiveSpace,
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reference_points: &[Vec<f64>],
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n: usize,
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rng: &mut Rng,
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) -> Vec<Candidate<D>> {
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let fronts = non_dominated_sort(combined, objectives);
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let mut selected: Vec<usize> = Vec::with_capacity(n);
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let mut splitting: &[usize] = &[];
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for front in &fronts {
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if selected.len() + front.len() <= n {
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selected.extend(front.iter().copied());
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} else {
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splitting = front;
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break;
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}
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if selected.len() == n {
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break;
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}
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}
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if selected.len() == n {
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return selected.into_iter().map(|i| combined[i].clone()).collect();
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}
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// The "working pool" is everything that might end up in the next pop:
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// already-selected plus the splitting front. Normalization and
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// association are computed on this pool only.
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let mut working: Vec<usize> = selected.clone();
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working.extend(splitting.iter().copied());
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let normalized = normalize(combined, &working, objectives);
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let m = objectives.len();
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let (assoc, dist): (Vec<usize>, Vec<f64>) = associate(&normalized, reference_points, m);
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// Niche counts over already-selected members only.
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let mut niche_count = vec![0_usize; reference_points.len()];
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for k in 0..selected.len() {
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niche_count[assoc[k]] += 1;
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}
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// Set of reference indices still available; we won't actually drop them
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// permanently — instead we track which references currently have any
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// candidate in F_l associated.
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let f_l_offset = selected.len();
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let mut available_in_fl: Vec<Vec<usize>> = vec![Vec::new(); reference_points.len()];
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for k in 0..splitting.len() {
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let working_idx = f_l_offset + k;
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available_in_fl[assoc[working_idx]].push(k); // store F_l-local index
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}
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while selected.len() < n {
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// Find min niche count among references with at least one F_l candidate.
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let mut min_count = usize::MAX;
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for j in 0..reference_points.len() {
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if !available_in_fl[j].is_empty() && niche_count[j] < min_count {
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min_count = niche_count[j];
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}
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}
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if min_count == usize::MAX {
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// No more F_l candidates anywhere. Should not happen if we still
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// need members, but guard anyway.
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break;
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}
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let candidate_refs: Vec<usize> = (0..reference_points.len())
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.filter(|&j| !available_in_fl[j].is_empty() && niche_count[j] == min_count)
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.collect();
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let &chosen_ref = candidate_refs.choose(rng).expect("non-empty by construction");
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let pool = &available_in_fl[chosen_ref];
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let pick_local = if niche_count[chosen_ref] == 0 {
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// Take the F_l member closest to the reference direction.
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*pool
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.iter()
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.min_by(|&&a, &&b| {
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let da = dist[f_l_offset + a];
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let db = dist[f_l_offset + b];
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da.partial_cmp(&db).unwrap_or(std::cmp::Ordering::Equal)
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})
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.unwrap()
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} else {
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*pool.choose(rng).unwrap()
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};
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let combined_idx = splitting[pick_local];
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selected.push(combined_idx);
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niche_count[chosen_ref] += 1;
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// Remove pick_local from available_in_fl[chosen_ref].
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let pos = available_in_fl[chosen_ref]
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.iter()
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.position(|&v| v == pick_local)
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.unwrap();
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available_in_fl[chosen_ref].swap_remove(pos);
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}
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selected.into_iter().map(|i| combined[i].clone()).collect()
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}
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/// Translate by ideal, compute extreme points + intercepts, return per-member
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/// normalized objective vectors. Falls back to per-axis range when the
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/// extreme-point hyperplane is degenerate.
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fn normalize<D>(
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combined: &[Candidate<D>],
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working: &[usize],
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objectives: &ObjectiveSpace,
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) -> Vec<Vec<f64>> {
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let m = objectives.len();
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let mut oriented: Vec<Vec<f64>> = working
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.iter()
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.map(|&i| objectives.as_minimization(&combined[i].evaluation.objectives))
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.collect();
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// Ideal point z*: per-axis min over `working`.
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let mut ideal = vec![f64::INFINITY; m];
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for o in &oriented {
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for (k, &v) in o.iter().enumerate() {
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if v < ideal[k] {
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ideal[k] = v;
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}
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}
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}
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// Translate.
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for o in oriented.iter_mut() {
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for (k, v) in o.iter_mut().enumerate() {
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*v -= ideal[k];
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}
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}
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// Extreme points by Achievement Scalarizing Function:
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// ASF_k(x) = max_i(x[i] / w_k[i]), w_k[i] = 1 if i==k else 1e-6
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let extremes: Vec<usize> = (0..m)
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.map(|axis| {
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let mut best = 0usize;
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let mut best_asf = f64::INFINITY;
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for (idx, o) in oriented.iter().enumerate() {
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let asf = o
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.iter()
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.enumerate()
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.map(|(k, &v)| {
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let w = if k == axis { 1.0 } else { 1e-6 };
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v / w
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})
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.fold(f64::NEG_INFINITY, f64::max);
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if asf < best_asf {
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best_asf = asf;
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best = idx;
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}
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}
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best
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})
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.collect();
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// Intercepts: solve A * a = 1 where rows of A are the extreme points.
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// If the system is singular or yields non-positive intercepts, fall back
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// to per-axis range (max value per axis in `oriented`).
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let intercepts = solve_intercepts(&oriented, &extremes).unwrap_or_else(|| {
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(0..m)
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.map(|k| {
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oriented
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.iter()
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.map(|o| o[k])
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.fold(f64::NEG_INFINITY, f64::max)
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.max(1e-12)
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})
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.collect()
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});
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for o in oriented.iter_mut() {
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for (k, v) in o.iter_mut().enumerate() {
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*v /= intercepts[k].max(1e-12);
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}
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}
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oriented
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}
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/// Try to compute axis intercepts from M extreme points by Gaussian
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/// elimination. Returns `None` if singular or degenerate.
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fn solve_intercepts(oriented: &[Vec<f64>], extremes: &[usize]) -> Option<Vec<f64>> {
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let m = extremes.len();
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if m == 0 {
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return None;
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}
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// Build the M×M matrix of extreme points (each row = one extreme).
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let mut a: Vec<Vec<f64>> = extremes.iter().map(|&i| oriented[i].clone()).collect();
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let mut b: Vec<f64> = vec![1.0; m];
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// Forward elimination with partial pivoting.
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for k in 0..m {
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let mut pivot = k;
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for i in (k + 1)..m {
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if a[i][k].abs() > a[pivot][k].abs() {
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pivot = i;
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}
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}
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if a[pivot][k].abs() < 1e-12 {
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return None;
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}
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a.swap(k, pivot);
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b.swap(k, pivot);
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for i in (k + 1)..m {
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let factor = a[i][k] / a[k][k];
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for j in k..m {
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a[i][j] -= factor * a[k][j];
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}
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b[i] -= factor * b[k];
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}
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}
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// Back-substitution.
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let mut x = vec![0.0_f64; m];
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for i in (0..m).rev() {
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let mut sum = b[i];
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for j in (i + 1)..m {
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sum -= a[i][j] * x[j];
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}
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if a[i][i].abs() < 1e-12 {
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return None;
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}
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x[i] = sum / a[i][i];
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}
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// Intercept along axis k is 1 / x[k].
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let intercepts: Vec<f64> = x
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.into_iter()
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.map(|v| if v.abs() < 1e-12 { return f64::NAN } else { 1.0 / v })
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.collect();
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if intercepts.iter().any(|v| !v.is_finite() || *v <= 0.0) {
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return None;
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}
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Some(intercepts)
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}
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/// Associate each normalized point with the closest reference direction by
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/// perpendicular distance. Returns parallel `(ref_index, perp_dist)` vectors.
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fn associate(
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normalized: &[Vec<f64>],
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reference_points: &[Vec<f64>],
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_m: usize,
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) -> (Vec<usize>, Vec<f64>) {
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let mut assoc = vec![0_usize; normalized.len()];
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let mut dist = vec![0.0_f64; normalized.len()];
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let ref_norms: Vec<f64> = reference_points
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.iter()
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.map(|r| r.iter().map(|v| v * v).sum::<f64>().sqrt().max(1e-12))
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.collect();
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for (i, x) in normalized.iter().enumerate() {
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let mut best = 0usize;
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let mut best_d = f64::INFINITY;
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for (j, r) in reference_points.iter().enumerate() {
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// Perpendicular distance from x to the line spanned by r:
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// t = (x · r) / ||r||²
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// d = ||x - t·r||
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let dot: f64 = x.iter().zip(r.iter()).map(|(a, b)| a * b).sum();
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let t = dot / (ref_norms[j] * ref_norms[j]);
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let mut sq = 0.0_f64;
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for (a, b) in x.iter().zip(r.iter()) {
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let proj = t * b;
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let diff = a - proj;
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sq += diff * diff;
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}
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let d = sq.sqrt();
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if d < best_d {
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best_d = d;
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best = j;
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}
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}
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assoc[i] = best;
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dist[i] = best_d;
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}
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(assoc, dist)
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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use crate::operators::{
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CompositeVariation, PolynomialMutation, RealBounds, SimulatedBinaryCrossover,
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};
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use crate::tests_support::SchafferN1;
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fn make_optimizer(
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seed: u64,
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) -> Nsga3<
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RealBounds,
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CompositeVariation<SimulatedBinaryCrossover, PolynomialMutation>,
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> {
|
||||
let bounds = vec![(-5.0, 5.0)];
|
||||
let initializer = RealBounds::new(bounds.clone());
|
||||
let variation = CompositeVariation {
|
||||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0),
|
||||
};
|
||||
Nsga3::new(
|
||||
Nsga3Config {
|
||||
population_size: 20,
|
||||
generations: 8,
|
||||
reference_divisions: 12,
|
||||
seed,
|
||||
},
|
||||
initializer,
|
||||
variation,
|
||||
)
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn produces_pareto_front() {
|
||||
let mut opt = make_optimizer(1);
|
||||
let r = opt.run(&SchafferN1);
|
||||
assert_eq!(r.population.len(), 20);
|
||||
assert!(!r.pareto_front.is_empty());
|
||||
assert_eq!(r.generations, 8);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn deterministic_with_same_seed() {
|
||||
let mut a = make_optimizer(99);
|
||||
let mut b = make_optimizer(99);
|
||||
let ra = a.run(&SchafferN1);
|
||||
let rb = b.run(&SchafferN1);
|
||||
let oa: Vec<Vec<f64>> =
|
||||
ra.pareto_front.iter().map(|c| c.evaluation.objectives.clone()).collect();
|
||||
let ob: Vec<Vec<f64>> =
|
||||
rb.pareto_front.iter().map(|c| c.evaluation.objectives.clone()).collect();
|
||||
assert_eq!(oa, ob);
|
||||
}
|
||||
|
||||
#[test]
|
||||
#[should_panic(expected = "population_size must be greater than 0")]
|
||||
fn zero_population_size_panics() {
|
||||
let bounds = vec![(0.0, 1.0)];
|
||||
let initializer = RealBounds::new(bounds.clone());
|
||||
let variation = CompositeVariation {
|
||||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0),
|
||||
};
|
||||
let mut opt = Nsga3::new(
|
||||
Nsga3Config {
|
||||
population_size: 0,
|
||||
generations: 1,
|
||||
reference_divisions: 4,
|
||||
seed: 0,
|
||||
},
|
||||
initializer,
|
||||
variation,
|
||||
);
|
||||
let _ = opt.run(&SchafferN1);
|
||||
}
|
||||
}
|
||||
+2
-2
@@ -22,6 +22,6 @@ pub use crate::operators::{
|
||||
};
|
||||
|
||||
pub use crate::algorithms::{
|
||||
DifferentialEvolution, DifferentialEvolutionConfig, Nsga2, Nsga2Config, Paes, PaesConfig,
|
||||
RandomSearch, RandomSearchConfig, Spea2, Spea2Config,
|
||||
DifferentialEvolution, DifferentialEvolutionConfig, Nsga2, Nsga2Config, Nsga3,
|
||||
Nsga3Config, Paes, PaesConfig, RandomSearch, RandomSearchConfig, Spea2, Spea2Config,
|
||||
};
|
||||
|
||||
Reference in New Issue
Block a user