109 lines
3.1 KiB
Rust
109 lines
3.1 KiB
Rust
//! Structured reference-point generators on the unit simplex.
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/// Das–Dennis reference points: all compositions of `divisions` into
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/// `num_objectives` non-negative integer parts, divided by `divisions`.
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///
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/// Returns `binomial(divisions + num_objectives - 1, num_objectives - 1)`
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/// points, each a `Vec<f64>` of length `num_objectives` summing to `1.0`.
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///
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/// This is the canonical NSGA-III / MOEA/D weight-vector generator.
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///
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/// # Panics
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/// If `num_objectives == 0`.
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pub fn das_dennis(num_objectives: usize, divisions: usize) -> Vec<Vec<f64>> {
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assert!(
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num_objectives > 0,
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"das_dennis requires num_objectives >= 1"
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);
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let mut out = Vec::new();
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let mut current = Vec::with_capacity(num_objectives);
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recurse(num_objectives, divisions, divisions, &mut current, &mut out);
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out
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}
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fn recurse(
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remaining_axes: usize,
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remaining_units: usize,
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total: usize,
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current: &mut Vec<usize>,
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out: &mut Vec<Vec<f64>>,
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) {
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if remaining_axes == 1 {
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current.push(remaining_units);
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let scale = (total as f64).max(1.0);
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out.push(current.iter().map(|&v| v as f64 / scale).collect());
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current.pop();
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return;
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}
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for take in 0..=remaining_units {
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current.push(take);
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recurse(
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remaining_axes - 1,
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remaining_units - take,
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total,
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current,
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out,
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);
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current.pop();
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}
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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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fn approx_eq(a: f64, b: f64) -> bool {
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(a - b).abs() < 1e-12
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}
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#[test]
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fn two_objective_four_divisions() {
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let pts = das_dennis(2, 4);
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// Expected: (0,4),(1,3),(2,2),(3,1),(4,0) → /4 → 5 points.
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assert_eq!(pts.len(), 5);
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for p in &pts {
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assert_eq!(p.len(), 2);
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assert!(approx_eq(p[0] + p[1], 1.0));
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}
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let first = &pts[0];
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let last = &pts[pts.len() - 1];
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assert!(approx_eq(first[0], 0.0) && approx_eq(first[1], 1.0));
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assert!(approx_eq(last[0], 1.0) && approx_eq(last[1], 0.0));
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}
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#[test]
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fn three_objective_twelve_divisions_has_91_points() {
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// C(12+3-1, 3-1) = C(14, 2) = 91 — the canonical NSGA-III 3-obj set.
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let pts = das_dennis(3, 12);
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assert_eq!(pts.len(), 91);
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for p in &pts {
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assert_eq!(p.len(), 3);
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assert!(approx_eq(p.iter().sum::<f64>(), 1.0));
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}
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}
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#[test]
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fn five_objective_six_divisions_has_210_points() {
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// C(6+5-1, 5-1) = C(10, 4) = 210.
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let pts = das_dennis(5, 6);
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assert_eq!(pts.len(), 210);
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for p in &pts {
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assert!(approx_eq(p.iter().sum::<f64>(), 1.0));
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}
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}
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#[test]
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fn zero_divisions_yields_one_zero_point() {
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// With 0 divisions every axis must take 0 → a single all-zero point.
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let pts = das_dennis(3, 0);
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assert_eq!(pts.len(), 1);
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assert_eq!(pts[0], vec![0.0, 0.0, 0.0]);
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}
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#[test]
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#[should_panic(expected = "num_objectives >= 1")]
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fn zero_objectives_panics() {
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let _ = das_dennis(0, 4);
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}
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}
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