docs(examples): add Ulysses16 TSP and FT06 bi-objective JSS benchmarks

Two canonical combinatorial optimization benchmarks demonstrating the
new permutation toolkit:

- tsp_ulysses16.rs — single-objective TSP via GeneticAlgorithm using
  OrderCrossover + InversionMutation. Reaches the known TSPLIB
  optimum (6859) for the 16-city Ulysses GEO-distance instance.

- jss_ft06_bi.rs — bi-objective JSS (makespan + total flow time) on
  the Fisher-Thompson 6x6 benchmark via NSGA-II using a local POX
  crossover + SwapMutation. Makespan corner reaches the known
  single-objective optimum (55).

examples/tsp_ulysses16.rs

@@ -0,0 +1,168 @@
+//! Solve the Ulysses16 TSP benchmark from TSPLIB using a Genetic Algorithm
+//! with the new permutation-toolkit operators.
+//!
+//! - **Benchmark**: Ulysses16 (Groetschel/Padberg "Odyssey of Ulysses"),
+//!   16 cities, GEO distance metric (TSPLIB-95).
+//! - **Known optimum**: tour length **6859**.
+//! - **Algorithm**: [`GeneticAlgorithm`] with elitism.
+//! - **Variation**: [`OrderCrossover`] (OX) → [`InversionMutation`], piped
+//!   via [`CompositeVariation`].
+//! - **Initializer**: [`ShuffledPermutation`].
+//!
+//! Source: TSPLIB95
+//! <http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/tsp/>
+//!
+//! Run with:
+//!
+//! ```bash
+//! cargo run --release --example tsp_ulysses16
+//! ```
+//!
+//! The GA reliably converges to within a few percent of the known optimum on
+//! this instance; on most seeds it hits 6859 exactly.
+
+use heuropt::prelude::*;
+
+/// TSPLIB Ulysses16 coordinates as `(lat, lon)` in TSPLIB DD.MM format.
+///
+/// The "decimal" part is *minutes* (out of 60), not a true decimal fraction;
+/// the GEO distance formula handles the conversion.
+const ULYSSES16: [(f64, f64); 16] = [
+    (38.24, 20.42),
+    (39.57, 26.15),
+    (40.56, 25.32),
+    (36.26, 23.12),
+    (33.48, 10.54),
+    (37.56, 12.19),
+    (38.42, 13.11),
+    (37.52, 20.44),
+    (41.23, 9.10),
+    (41.17, 13.05),
+    (36.08, -5.21),
+    (38.47, 15.13),
+    (38.15, 15.35),
+    (37.51, 15.17),
+    (35.49, 14.32),
+    (39.36, 19.56),
+];
+
+const KNOWN_OPTIMUM: f64 = 6859.0;
+
+/// TSPLIB-95 GEO distance metric.
+///
+/// Coordinates are interpreted as latitude/longitude in DD.MM (decimal-degrees
+/// with the fractional part being minutes/100), converted to radians, and the
+/// arc length between the two points on a sphere of radius `RRR = 6378.388`
+/// is rounded to the next integer (`floor(d + 1)`).
+fn geo_distance_matrix(coords: &[(f64, f64)]) -> Vec<Vec<f64>> {
+    const RRR: f64 = 6378.388;
+    let to_radians = |x: f64| {
+        let deg = x.trunc();
+        let min = x - deg;
+        std::f64::consts::PI * (deg + 5.0 * min / 3.0) / 180.0
+    };
+    let radians: Vec<(f64, f64)> = coords
+        .iter()
+        .map(|&(la, lo)| (to_radians(la), to_radians(lo)))
+        .collect();
+    let n = radians.len();
+    let mut d = vec![vec![0.0_f64; n]; n];
+    for i in 0..n {
+        for j in (i + 1)..n {
+            let (la_i, lo_i) = radians[i];
+            let (la_j, lo_j) = radians[j];
+            let q1 = (lo_i - lo_j).cos();
+            let q2 = (la_i - la_j).cos();
+            let q3 = (la_i + la_j).cos();
+            let dij = (RRR * (0.5 * ((1.0 + q1) * q2 - (1.0 - q1) * q3)).acos() + 1.0).trunc();
+            d[i][j] = dij;
+            d[j][i] = dij;
+        }
+    }
+    d
+}
+
+struct Ulysses16Tsp {
+    dist: Vec<Vec<f64>>,
+}
+
+impl Ulysses16Tsp {
+    fn new() -> Self {
+        Self {
+            dist: geo_distance_matrix(&ULYSSES16),
+        }
+    }
+
+    fn tour_length(&self, tour: &[usize]) -> f64 {
+        let n = tour.len();
+        let mut total = 0.0;
+        for i in 0..n {
+            let a = tour[i];
+            let b = tour[(i + 1) % n];
+            total += self.dist[a][b];
+        }
+        total
+    }
+}
+
+impl Problem for Ulysses16Tsp {
+    type Decision = Vec<usize>;
+
+    fn objectives(&self) -> ObjectiveSpace {
+        ObjectiveSpace::new(vec![Objective::minimize("tour_length")])
+    }
+
+    fn evaluate(&self, tour: &Vec<usize>) -> Evaluation {
+        Evaluation::new(vec![self.tour_length(tour)])
+    }
+
+    fn decision_schema(&self) -> Vec<DecisionVariable> {
+        (0..ULYSSES16.len())
+            .map(|k| DecisionVariable::new(format!("tour_position_{k}")))
+            .collect()
+    }
+}
+
+fn main() {
+    let problem = Ulysses16Tsp::new();
+    let n = ULYSSES16.len();
+
+    let mut optimizer = GeneticAlgorithm::new(
+        GeneticAlgorithmConfig {
+            population_size: 150,
+            generations: 1500,
+            tournament_size: 3,
+            elitism: 4,
+            seed: 42,
+        },
+        ShuffledPermutation { n },
+        CompositeVariation {
+            crossover: OrderCrossover,
+            mutation: InversionMutation,
+        },
+    );
+    let result = optimizer.run(&problem);
+
+    let best = result.best.expect("GA always returns a best candidate");
+    let best_len = best.evaluation.objectives[0];
+    let gap_abs = best_len - KNOWN_OPTIMUM;
+    let gap_pct = 100.0 * gap_abs / KNOWN_OPTIMUM;
+
+    println!("TSPLIB Ulysses16 — single-objective TSP via Genetic Algorithm");
+    println!("Source: TSPLIB95 (Groetschel/Padberg)");
+    println!();
+    println!("Known optimum:    {:>8.0}", KNOWN_OPTIMUM);
+    println!("GA best found:    {:>8.0}   (gap {:+.0}, {:+.2}%)", best_len, gap_abs, gap_pct);
+    println!();
+    println!("Total evaluations: {}", result.evaluations);
+    println!("Final population:  {}", result.population.len());
+    println!();
+    println!("Tour (city indices, returning to start):");
+    for (i, c) in best.decision.iter().enumerate() {
+        print!("{:>3}", c);
+        if i + 1 < best.decision.len() {
+            print!(" → ");
+        }
+    }
+    println!(" → {}", best.decision[0]);
+}