diff --git a/src/algorithms/rvea.rs b/src/algorithms/rvea.rs
index 5e4e7ae..87806d1 100644
--- a/src/algorithms/rvea.rs
+++ b/src/algorithms/rvea.rs
@@ -556,4 +556,41 @@ mod tests {
         );
         let _ = opt.run(&SchafferN1);
     }
+
+    // ---- Mutation-test pinned helpers --------------------------------------
+
+    #[test]
+    fn unit_normalize_produces_unit_vector() {
+        let v = unit_normalize(vec![3.0, 4.0]);
+        let norm: f64 = v.iter().map(|x| x * x).sum::<f64>().sqrt();
+        assert!((norm - 1.0).abs() < 1e-12);
+        assert!((v[0] - 0.6).abs() < 1e-12);
+        assert!((v[1] - 0.8).abs() < 1e-12);
+    }
+
+    #[test]
+    fn unit_normalize_zero_vector_unchanged() {
+        // A (near-)zero vector is left as-is (no division by ~0).
+        let v = unit_normalize(vec![0.0, 0.0]);
+        assert_eq!(v, vec![0.0, 0.0]);
+    }
+
+    #[test]
+    fn closest_reference_picks_smallest_angle() {
+        // References along the two axes; a point near the x-axis associates
+        // with reference 0 at a small angle.
+        let refs = vec![vec![1.0, 0.0], vec![0.0, 1.0]];
+        let (idx, angle) = closest_reference(&[1.0, 0.0], &refs);
+        assert_eq!(idx, 0);
+        assert!(angle.abs() < 1e-9, "angle = {angle}");
+        let (idx2, _) = closest_reference(&[0.1, 1.0], &refs);
+        assert_eq!(idx2, 1);
+    }
+
+    #[test]
+    fn smallest_neighbor_angle_of_orthogonal_refs_is_pi_over_2() {
+        let refs = vec![vec![1.0, 0.0], vec![0.0, 1.0]];
+        let a = smallest_neighbor_angle(&refs);
+        assert!((a - std::f64::consts::FRAC_PI_2).abs() < 1e-9, "angle = {a}");
+    }
 }
diff --git a/src/algorithms/simulated_annealing.rs b/src/algorithms/simulated_annealing.rs
index f021651..dc5f7d9 100644
--- a/src/algorithms/simulated_annealing.rs
+++ b/src/algorithms/simulated_annealing.rs
@@ -407,4 +407,26 @@ mod tests {
         );
         let _ = opt.run(&Sphere1D);
     }
+
+    // ---- Mutation-test pinned helpers --------------------------------------
+
+    use crate::core::evaluation::Evaluation;
+    use crate::core::objective::Direction;
+
+    #[test]
+    fn better_than_feasibility_first_and_direction() {
+        let feasible = Evaluation::new(vec![100.0]);
+        let infeasible = Evaluation::constrained(vec![0.0], 1.0);
+        assert!(better_than(&feasible, &infeasible, Direction::Minimize));
+        assert!(!better_than(&infeasible, &feasible, Direction::Minimize));
+        let lo = Evaluation::new(vec![1.0]);
+        let hi = Evaluation::new(vec![2.0]);
+        assert!(better_than(&lo, &hi, Direction::Minimize));
+        assert!(better_than(&hi, &lo, Direction::Maximize));
+        let eq = Evaluation::new(vec![1.0]);
+        assert!(!better_than(&lo, &eq, Direction::Minimize));
+        let v_lo = Evaluation::constrained(vec![0.0], 0.2);
+        let v_hi = Evaluation::constrained(vec![0.0], 0.8);
+        assert!(better_than(&v_lo, &v_hi, Direction::Minimize));
+    }
 }
diff --git a/src/algorithms/snes.rs b/src/algorithms/snes.rs
index a1e1916..7182673 100644
--- a/src/algorithms/snes.rs
+++ b/src/algorithms/snes.rs
@@ -457,4 +457,46 @@ mod tests {
         let mut opt = make_optimizer(0);
         let _ = opt.run(&SchafferN1);
     }
+
+    // ---- Mutation-test pinned helpers --------------------------------------
+
+    use crate::core::evaluation::Evaluation;
+    use crate::core::objective::Direction;
+
+    #[test]
+    fn nes_utilities_sum_to_zero_and_are_descending() {
+        // The NES utility weights are a shifted log-rank scheme; they sum
+        // to (approximately) zero and the first (best-ranked) is largest.
+        let u = nes_utilities(10);
+        assert_eq!(u.len(), 10);
+        let sum: f64 = u.iter().sum();
+        assert!(sum.abs() < 1e-9, "utilities sum = {sum}");
+        // Descending: best rank gets the most weight.
+        for w in u.windows(2) {
+            assert!(w[0] >= w[1] - 1e-12, "not descending: {:?}", u);
+        }
+        // The first utility is positive (it gets above-average weight).
+        assert!(u[0] > 0.0);
+    }
+
+    #[test]
+    fn compare_feasibility_first_and_direction() {
+        let feasible = Evaluation::new(vec![100.0]);
+        let infeasible = Evaluation::constrained(vec![0.0], 1.0);
+        assert_eq!(compare(&feasible, &infeasible, Direction::Minimize), std::cmp::Ordering::Less);
+        let lo = Evaluation::new(vec![1.0]);
+        let hi = Evaluation::new(vec![2.0]);
+        assert_eq!(compare(&lo, &hi, Direction::Minimize), std::cmp::Ordering::Less);
+        assert_eq!(compare(&lo, &hi, Direction::Maximize), std::cmp::Ordering::Greater);
+    }
+
+    #[test]
+    fn better_is_strict_less() {
+        let lo = Evaluation::new(vec![1.0]);
+        let hi = Evaluation::new(vec![2.0]);
+        assert!(better(&lo, &hi, Direction::Minimize));
+        assert!(!better(&hi, &lo, Direction::Minimize));
+        let eq = Evaluation::new(vec![1.0]);
+        assert!(!better(&lo, &eq, Direction::Minimize));
+    }
 }
diff --git a/src/algorithms/spea2.rs b/src/algorithms/spea2.rs
index b9fcb32..118ae4b 100644
--- a/src/algorithms/spea2.rs
+++ b/src/algorithms/spea2.rs
@@ -601,4 +601,30 @@ mod tests {
         );
         let _ = opt.run(&SchafferN1);
     }
+
+    // ---- Mutation-test pinned helpers --------------------------------------
+
+    #[test]
+    fn euclidean_distance_basics() {
+        // (0,0) to (3,4) = 5.
+        assert!((euclidean(&[0.0, 0.0], &[3.0, 4.0]) - 5.0).abs() < 1e-12);
+        // symmetric and zero-to-self.
+        assert!((euclidean(&[3.0, 4.0], &[0.0, 0.0]) - 5.0).abs() < 1e-12);
+        assert_eq!(euclidean(&[1.0, 2.0, 3.0], &[1.0, 2.0, 3.0]), 0.0);
+    }
+
+    #[test]
+    fn binary_tournament_prefers_lower_fitness() {
+        // SPEA2 fitness is "lower is better" — index 1 here is the best.
+        use crate::core::rng::rng_from_seed;
+        let fitness = vec![5.0_f64, 0.5];
+        let mut wins1 = 0;
+        for seed in 0..200 {
+            let mut rng = rng_from_seed(seed);
+            if binary_tournament(&fitness, &mut rng) == 1 {
+                wins1 += 1;
+            }
+        }
+        assert!(wins1 > 130, "lower-fitness index won only {wins1}/200");
+    }
 }
diff --git a/src/algorithms/tabu_search.rs b/src/algorithms/tabu_search.rs
index bf53533..128cdac 100644
--- a/src/algorithms/tabu_search.rs
+++ b/src/algorithms/tabu_search.rs
@@ -421,4 +421,24 @@ mod tests {
             rb.best.unwrap().evaluation.objectives,
         );
     }
+
+    // ---- Mutation-test pinned helpers --------------------------------------
+
+    #[test]
+    fn better_than_feasibility_first_and_direction() {
+        use crate::core::objective::Direction;
+        let feasible = Evaluation::new(vec![100.0]);
+        let infeasible = Evaluation::constrained(vec![0.0], 1.0);
+        assert!(better_than(&feasible, &infeasible, Direction::Minimize));
+        assert!(!better_than(&infeasible, &feasible, Direction::Minimize));
+        let lo = Evaluation::new(vec![1.0]);
+        let hi = Evaluation::new(vec![2.0]);
+        assert!(better_than(&lo, &hi, Direction::Minimize));
+        assert!(better_than(&hi, &lo, Direction::Maximize));
+        let eq = Evaluation::new(vec![1.0]);
+        assert!(!better_than(&lo, &eq, Direction::Minimize));
+        let v_lo = Evaluation::constrained(vec![0.0], 0.2);
+        let v_hi = Evaluation::constrained(vec![0.0], 0.8);
+        assert!(better_than(&v_lo, &v_hi, Direction::Minimize));
+    }
 }
diff --git a/src/algorithms/tlbo.rs b/src/algorithms/tlbo.rs
index 04fdea8..daeef4b 100644
--- a/src/algorithms/tlbo.rs
+++ b/src/algorithms/tlbo.rs
@@ -383,4 +383,40 @@ mod tests {
         let mut opt = make_optimizer(0);
         let _ = opt.run(&SchafferN1);
     }
+
+    // ---- Mutation-test pinned helpers --------------------------------------
+
+    use crate::core::evaluation::Evaluation;
+    use crate::core::objective::Direction;
+
+    #[test]
+    fn better_feasibility_first_and_direction() {
+        let feasible = Evaluation::new(vec![100.0]);
+        let infeasible = Evaluation::constrained(vec![0.0], 1.0);
+        assert!(better(&feasible, &infeasible, Direction::Minimize));
+        assert!(!better(&infeasible, &feasible, Direction::Minimize));
+        let lo = Evaluation::new(vec![1.0]);
+        let hi = Evaluation::new(vec![2.0]);
+        assert!(better(&lo, &hi, Direction::Minimize));
+        assert!(better(&hi, &lo, Direction::Maximize));
+        let eq = Evaluation::new(vec![1.0]);
+        assert!(!better(&lo, &eq, Direction::Minimize));
+        let v_lo = Evaluation::constrained(vec![0.0], 0.2);
+        let v_hi = Evaluation::constrained(vec![0.0], 0.8);
+        assert!(better(&v_lo, &v_hi, Direction::Minimize));
+    }
+
+    #[test]
+    fn best_index_finds_min_and_max() {
+        let evals = [
+            Evaluation::new(vec![3.0]),
+            Evaluation::new(vec![1.0]),
+            Evaluation::new(vec![4.0]),
+        ];
+        assert_eq!(best_index(&evals, Direction::Minimize), 1);
+        assert_eq!(best_index(&evals, Direction::Maximize), 2);
+        // tie keeps the first.
+        let flat = [Evaluation::new(vec![1.0]), Evaluation::new(vec![1.0])];
+        assert_eq!(best_index(&flat, Direction::Minimize), 0);
+    }
 }
diff --git a/src/algorithms/tpe.rs b/src/algorithms/tpe.rs
index 9a7a805..b02646a 100644
--- a/src/algorithms/tpe.rs
+++ b/src/algorithms/tpe.rs
@@ -552,4 +552,56 @@ mod tests {
         let mut opt = make_optimizer(0);
         let _ = opt.run(&SchafferN1);
     }
+
+    // ---- Mutation-test pinned helpers --------------------------------------
+
+    use crate::core::evaluation::Evaluation;
+    use crate::core::objective::Direction;
+
+    #[test]
+    fn oriented_target_flips_sign_and_penalizes() {
+        let e = Evaluation::new(vec![3.0]);
+        assert!((oriented_target(&e, Direction::Minimize) - 3.0).abs() < 1e-12);
+        assert!((oriented_target(&e, Direction::Maximize) + 3.0).abs() < 1e-12);
+        let mut bad = Evaluation::new(vec![1.0]);
+        bad.constraint_violation = 0.5;
+        assert!((oriented_target(&bad, Direction::Minimize) - 500_001.0).abs() < 1e-9);
+    }
+
+    #[test]
+    fn better_feasibility_first_and_direction() {
+        let feasible = Evaluation::new(vec![100.0]);
+        let infeasible = Evaluation::constrained(vec![0.0], 1.0);
+        assert!(better(&feasible, &infeasible, Direction::Minimize));
+        let lo = Evaluation::new(vec![1.0]);
+        let hi = Evaluation::new(vec![2.0]);
+        assert!(better(&lo, &hi, Direction::Minimize));
+        assert!(better(&hi, &lo, Direction::Maximize));
+    }
+
+    #[test]
+    fn split_good_bad_partitions_by_target_rank() {
+        // targets 5, 1, 3, 9, 7 → ranked 1<3<5<7<9 → indices 1,2,0,4,3.
+        let targets = [5.0, 1.0, 3.0, 9.0, 7.0];
+        let (good, bad) = split_good_bad(&targets, 0.4);
+        // 40% of 5 = 2 good.
+        assert_eq!(good.len(), 2);
+        assert_eq!(bad.len(), 3);
+        // The two smallest targets (1.0 at idx 1, 3.0 at idx 2) are "good".
+        assert!(good.contains(&1));
+        assert!(good.contains(&2));
+    }
+
+    #[test]
+    fn split_good_bad_clamps_to_at_least_one_each() {
+        let targets = [5.0, 1.0, 3.0];
+        // good_fraction 0.0 would round to 0 — must clamp to >= 1.
+        let (good, bad) = split_good_bad(&targets, 0.0);
+        assert!(!good.is_empty());
+        assert!(!bad.is_empty());
+        // good_fraction 1.0 would take everything — must leave >= 1 bad.
+        let (good2, bad2) = split_good_bad(&targets, 1.0);
+        assert!(!good2.is_empty());
+        assert!(!bad2.is_empty());
+    }
 }
diff --git a/src/algorithms/umda.rs b/src/algorithms/umda.rs
index 23f5e1f..520da3e 100644
--- a/src/algorithms/umda.rs
+++ b/src/algorithms/umda.rs
@@ -449,4 +449,30 @@ mod tests {
         });
         let _ = opt.run(&DummyMo);
     }
+
+    // ---- Mutation-test pinned helpers --------------------------------------
+
+    #[test]
+    fn compare_so_feasibility_first_and_direction() {
+        let feasible = Evaluation::new(vec![100.0]);
+        let infeasible = Evaluation::constrained(vec![0.0], 1.0);
+        assert_eq!(compare_so(&feasible, &infeasible, Direction::Minimize), std::cmp::Ordering::Less);
+        let lo = Evaluation::new(vec![1.0]);
+        let hi = Evaluation::new(vec![2.0]);
+        assert_eq!(compare_so(&lo, &hi, Direction::Minimize), std::cmp::Ordering::Less);
+        assert_eq!(compare_so(&lo, &hi, Direction::Maximize), std::cmp::Ordering::Greater);
+        let v_lo = Evaluation::constrained(vec![0.0], 0.2);
+        let v_hi = Evaluation::constrained(vec![0.0], 0.8);
+        assert_eq!(compare_so(&v_lo, &v_hi, Direction::Minimize), std::cmp::Ordering::Less);
+    }
+
+    #[test]
+    fn better_than_so_is_strict_less() {
+        let lo = Evaluation::new(vec![1.0]);
+        let hi = Evaluation::new(vec![2.0]);
+        assert!(better_than_so(&lo, &hi, Direction::Minimize));
+        assert!(!better_than_so(&hi, &lo, Direction::Minimize));
+        let eq = Evaluation::new(vec![1.0]);
+        assert!(!better_than_so(&lo, &eq, Direction::Minimize));
+    }
 }