From 2965955874e3b11dcbefcef104cdbdd18f13c78b Mon Sep 17 00:00:00 2001
From: Stephen Waits <steve@waits.net>
Date: Mon, 4 May 2026 19:54:16 -0600
Subject: [PATCH] feat(pareto): add Das-Dennis reference-point generator
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The standard structured weight/reference vector generator for
many-objective MOEAs (NSGA-III, MOEA/D). Generates (H+M-1 choose M-1)
points uniformly distributed on the unit simplex by enumerating all
integer compositions of `divisions` into `num_objectives` parts and
dividing each by `divisions`.

Lives in src/pareto/reference_points.rs. Re-exported from the prelude
as `das_dennis`.

Tests cover: M=2/H=4 → 5 points along the diagonal; M=3/H=12 → 91
points (the canonical NSGA-III 3-objective ref set); each generated
point has exactly M components summing to 1 within float tolerance.
---
 src/pareto/mod.rs              |  2 +
 src/pareto/reference_points.rs | 99 ++++++++++++++++++++++++++++++++++
 src/prelude.rs                 |  4 +-
 3 files changed, 103 insertions(+), 2 deletions(-)
 create mode 100644 src/pareto/reference_points.rs

diff --git a/src/pareto/mod.rs b/src/pareto/mod.rs
index 41dfa51..c78db97 100644
--- a/src/pareto/mod.rs
+++ b/src/pareto/mod.rs
@@ -4,10 +4,12 @@ pub mod archive;
 pub mod crowding;
 pub mod dominance;
 pub mod front;
+pub mod reference_points;
 pub mod sort;
 
 pub use archive::*;
 pub use crowding::*;
 pub use dominance::*;
 pub use front::*;
+pub use reference_points::*;
 pub use sort::*;
diff --git a/src/pareto/reference_points.rs b/src/pareto/reference_points.rs
new file mode 100644
index 0000000..dc74189
--- /dev/null
+++ b/src/pareto/reference_points.rs
@@ -0,0 +1,99 @@
+//! Structured reference-point generators on the unit simplex.
+
+/// Das–Dennis reference points: all compositions of `divisions` into
+/// `num_objectives` non-negative integer parts, divided by `divisions`.
+///
+/// Returns `binomial(divisions + num_objectives - 1, num_objectives - 1)`
+/// points, each a `Vec<f64>` of length `num_objectives` summing to `1.0`.
+///
+/// This is the canonical NSGA-III / MOEA/D weight-vector generator.
+///
+/// # Panics
+/// If `num_objectives == 0`.
+pub fn das_dennis(num_objectives: usize, divisions: usize) -> Vec<Vec<f64>> {
+    assert!(num_objectives > 0, "das_dennis requires num_objectives >= 1");
+    let mut out = Vec::new();
+    let mut current = Vec::with_capacity(num_objectives);
+    recurse(num_objectives, divisions, divisions, &mut current, &mut out);
+    out
+}
+
+fn recurse(
+    remaining_axes: usize,
+    remaining_units: usize,
+    total: usize,
+    current: &mut Vec<usize>,
+    out: &mut Vec<Vec<f64>>,
+) {
+    if remaining_axes == 1 {
+        current.push(remaining_units);
+        let scale = (total as f64).max(1.0);
+        out.push(current.iter().map(|&v| v as f64 / scale).collect());
+        current.pop();
+        return;
+    }
+    for take in 0..=remaining_units {
+        current.push(take);
+        recurse(remaining_axes - 1, remaining_units - take, total, current, out);
+        current.pop();
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn approx_eq(a: f64, b: f64) -> bool {
+        (a - b).abs() < 1e-12
+    }
+
+    #[test]
+    fn two_objective_four_divisions() {
+        let pts = das_dennis(2, 4);
+        // Expected: (0,4),(1,3),(2,2),(3,1),(4,0) → /4 → 5 points.
+        assert_eq!(pts.len(), 5);
+        for p in &pts {
+            assert_eq!(p.len(), 2);
+            assert!(approx_eq(p[0] + p[1], 1.0));
+        }
+        let first = &pts[0];
+        let last = &pts[pts.len() - 1];
+        assert!(approx_eq(first[0], 0.0) && approx_eq(first[1], 1.0));
+        assert!(approx_eq(last[0], 1.0) && approx_eq(last[1], 0.0));
+    }
+
+    #[test]
+    fn three_objective_twelve_divisions_has_91_points() {
+        // C(12+3-1, 3-1) = C(14, 2) = 91 — the canonical NSGA-III 3-obj set.
+        let pts = das_dennis(3, 12);
+        assert_eq!(pts.len(), 91);
+        for p in &pts {
+            assert_eq!(p.len(), 3);
+            assert!(approx_eq(p.iter().sum::<f64>(), 1.0));
+        }
+    }
+
+    #[test]
+    fn five_objective_six_divisions_has_210_points() {
+        // C(6+5-1, 5-1) = C(10, 4) = 210.
+        let pts = das_dennis(5, 6);
+        assert_eq!(pts.len(), 210);
+        for p in &pts {
+            assert!(approx_eq(p.iter().sum::<f64>(), 1.0));
+        }
+    }
+
+    #[test]
+    fn zero_divisions_yields_one_zero_point() {
+        // With 0 divisions every axis must take 0 → a single all-zero point.
+        let pts = das_dennis(3, 0);
+        assert_eq!(pts.len(), 1);
+        assert_eq!(pts[0], vec![0.0, 0.0, 0.0]);
+    }
+
+    #[test]
+    #[should_panic(expected = "num_objectives >= 1")]
+    fn zero_objectives_panics() {
+        let _ = das_dennis(0, 4);
+    }
+}
diff --git a/src/prelude.rs b/src/prelude.rs
index a4e9fe5..8535c1a 100644
--- a/src/prelude.rs
+++ b/src/prelude.rs
@@ -12,8 +12,8 @@ pub use crate::core::{
 pub use crate::traits::{Initializer, Optimizer, Variation};
 
 pub use crate::pareto::{
-    Dominance, ParetoArchive, best_candidate, crowding_distance, non_dominated_sort,
-    pareto_compare, pareto_front,
+    Dominance, ParetoArchive, best_candidate, crowding_distance, das_dennis,
+    non_dominated_sort, pareto_compare, pareto_front,
 };
 
 pub use crate::operators::{