feat(algorithms): add HillClimber single-objective greedy local search

The simplest possible local search: start from one initializer-sampled
decision, repeatedly mutate it via the variation operator, and keep the
child only when it is strictly better than the current incumbent (with
the standard feasible-beats-infeasible / lower-violation tiebreaks
when relevant).

Single-objective only — panics with a clear message if the problem
exposes more than one objective. Deterministic under a seed. Returns
a population/front of size one (the current incumbent) so it slots
into the comparison harness like any other optimizer.

src/algorithms/hill_climber.rs

@@ -0,0 +1,151 @@
+//! `HillClimber` — single-objective greedy local search.
+
+use crate::core::candidate::Candidate;
+use crate::core::objective::Direction;
+use crate::core::population::Population;
+use crate::core::problem::Problem;
+use crate::core::result::OptimizationResult;
+use crate::core::rng::rng_from_seed;
+use crate::traits::{Initializer, Optimizer, Variation};
+
+/// Configuration for [`HillClimber`].
+#[derive(Debug, Clone)]
+pub struct HillClimberConfig {
+    /// Number of mutation iterations.
+    pub iterations: usize,
+    /// Seed for the deterministic RNG.
+    pub seed: u64,
+}
+
+impl Default for HillClimberConfig {
+    fn default() -> Self {
+        Self { iterations: 1000, seed: 42 }
+    }
+}
+
+/// Single-objective greedy hill climber.
+///
+/// Starts from one initializer-sampled decision, repeatedly mutates it via
+/// the variation operator, and keeps the child only when it is strictly
+/// better than the current incumbent. Standard feasibility tiebreaks apply:
+/// feasible beats infeasible, smaller violation wins among infeasibles.
+///
+/// Single-objective only.
+#[derive(Debug, Clone)]
+pub struct HillClimber<I, V> {
+    /// Algorithm configuration.
+    pub config: HillClimberConfig,
+    /// Initial-decision sampler.
+    pub initializer: I,
+    /// Mutation operator.
+    pub variation: V,
+}
+
+impl<I, V> HillClimber<I, V> {
+    /// Construct a `HillClimber`.
+    pub fn new(config: HillClimberConfig, initializer: I, variation: V) -> Self {
+        Self { config, initializer, variation }
+    }
+}
+
+impl<P, I, V> Optimizer<P> for HillClimber<I, V>
+where
+    P: Problem + Sync,
+    P::Decision: Send,
+    I: Initializer<P::Decision>,
+    V: Variation<P::Decision>,
+{
+    fn run(&mut self, problem: &P) -> OptimizationResult<P::Decision> {
+        let objectives = problem.objectives();
+        assert!(
+            objectives.is_single_objective(),
+            "HillClimber requires exactly one objective",
+        );
+        let direction = objectives.objectives[0].direction;
+        let mut rng = rng_from_seed(self.config.seed);
+
+        let mut initial = self.initializer.initialize(1, &mut rng);
+        assert!(!initial.is_empty(), "HillClimber initializer returned no decisions");
+        let mut current_decision = initial.remove(0);
+        let mut current_eval = problem.evaluate(&current_decision);
+        let mut evaluations = 1usize;
+
+        for _ in 0..self.config.iterations {
+            let parents = vec![current_decision.clone()];
+            let children = self.variation.vary(&parents, &mut rng);
+            assert!(!children.is_empty(), "HillClimber variation returned no children");
+            let child_decision = children.into_iter().next().unwrap();
+            let child_eval = problem.evaluate(&child_decision);
+            evaluations += 1;
+
+            let child_better = match (child_eval.is_feasible(), current_eval.is_feasible()) {
+                (true, false) => true,
+                (false, true) => false,
+                (false, false) => {
+                    child_eval.constraint_violation < current_eval.constraint_violation
+                }
+                (true, true) => match direction {
+                    Direction::Minimize => child_eval.objectives[0] < current_eval.objectives[0],
+                    Direction::Maximize => child_eval.objectives[0] > current_eval.objectives[0],
+                },
+            };
+            if child_better {
+                current_decision = child_decision;
+                current_eval = child_eval;
+            }
+        }
+
+        let best = Candidate::new(current_decision, current_eval);
+        let population = Population::new(vec![best.clone()]);
+        let front = vec![best.clone()];
+        OptimizationResult::new(
+            population,
+            front,
+            Some(best),
+            evaluations,
+            self.config.iterations,
+        )
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::operators::{GaussianMutation, RealBounds};
+    use crate::tests_support::{SchafferN1, Sphere1D};
+
+    fn make_optimizer(seed: u64) -> HillClimber<RealBounds, GaussianMutation> {
+        HillClimber::new(
+            HillClimberConfig { iterations: 500, seed },
+            RealBounds::new(vec![(-5.0, 5.0)]),
+            GaussianMutation { sigma: 0.3 },
+        )
+    }
+
+    #[test]
+    fn finds_minimum_of_sphere() {
+        let mut opt = make_optimizer(1);
+        let r = opt.run(&Sphere1D);
+        let best = r.best.unwrap();
+        assert!(best.evaluation.objectives[0] < 1e-2, "got f = {}", best.evaluation.objectives[0]);
+    }
+
+    #[test]
+    fn deterministic_with_same_seed() {
+        let mut a = make_optimizer(99);
+        let mut b = make_optimizer(99);
+        let ra = a.run(&Sphere1D);
+        let rb = b.run(&Sphere1D);
+        assert_eq!(
+            ra.best.unwrap().evaluation.objectives,
+            rb.best.unwrap().evaluation.objectives,
+        );
+    }
+
+    #[test]
+    #[should_panic(expected = "exactly one objective")]
+    fn multi_objective_panics() {
+        let mut opt = make_optimizer(0);
+        let _ = opt.run(&SchafferN1);
+    }
+}

src/algorithms/mod.rs

@@ -1,6 +1,7 @@
 //! Built-in reference optimizers.
 
 pub mod differential_evolution;
+pub mod hill_climber;
 pub mod moead;
 pub mod nsga2;
 pub mod nsga3;
@@ -10,6 +11,7 @@ pub mod random_search;
 pub mod spea2;
 
 pub use differential_evolution::*;
+pub use hill_climber::*;
 pub use moead::*;
 pub use nsga2::*;
 pub use nsga3::*;

src/prelude.rs

@@ -22,7 +22,7 @@ pub use crate::operators::{
 };
 
 pub use crate::algorithms::{
-    DifferentialEvolution, DifferentialEvolutionConfig, Moead, MoeadConfig, Nsga2,
-    Nsga2Config, Nsga3, Nsga3Config, Paes, PaesConfig, RandomSearch, RandomSearchConfig,
-    Spea2, Spea2Config,
+    DifferentialEvolution, DifferentialEvolutionConfig, HillClimber, HillClimberConfig,
+    Moead, MoeadConfig, Nsga2, Nsga2Config, Nsga3, Nsga3Config, Paes, PaesConfig,
+    RandomSearch, RandomSearchConfig, Spea2, Spea2Config,
 };