feat: add Study::summary() and Display impl

Add a human-readable summary method and Display trait for Study<V>
where V: Display. The summary shows optimization direction, trial
counts (with complete/pruned breakdown), best value, and best
parameters with their labels.

Also derive PartialOrd + Ord on ParamId for deterministic parameter
ordering in summary output.

src/parameter.rs

@@ -37,7 +37,7 @@ static NEXT_PARAM_ID: AtomicU64 = AtomicU64::new(0);
 ///
 /// Each parameter is assigned a unique `ParamId` at creation time. Cloning a parameter
 /// copies its `ParamId`, so clones refer to the same logical parameter.
-#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash)]
+#[derive(Clone, Copy, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)]
 pub struct ParamId(u64);
 
 impl ParamId {

src/study.rs

@@ -1,6 +1,7 @@
 //! Study implementation for managing optimization trials.
 
 use core::any::Any;
+use core::fmt;
 #[cfg(feature = "async")]
 use core::future::Future;
 use core::ops::ControlFlow;
@@ -1465,6 +1466,86 @@ where
     }
 }
 
+impl<V> Study<V>
+where
+    V: PartialOrd + Clone + fmt::Display,
+{
+    /// Returns a human-readable summary of the study.
+    ///
+    /// The summary includes:
+    /// - Optimization direction and total trial count
+    /// - Breakdown by state (complete, pruned) when applicable
+    /// - Best trial value and parameters (if any completed trials exist)
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use optimizer::parameter::{FloatParam, Parameter};
+    /// use optimizer::{Direction, Study};
+    ///
+    /// let study: Study<f64> = Study::new(Direction::Minimize);
+    /// let x = FloatParam::new(0.0, 10.0).name("x");
+    ///
+    /// let mut trial = study.create_trial();
+    /// let _ = x.suggest(&mut trial).unwrap();
+    /// study.complete_trial(trial, 0.42);
+    ///
+    /// let summary = study.summary();
+    /// assert!(summary.contains("Minimize"));
+    /// assert!(summary.contains("0.42"));
+    /// ```
+    #[must_use]
+    pub fn summary(&self) -> String {
+        use fmt::Write;
+
+        let trials = self.completed_trials.read();
+        let n_complete = trials
+            .iter()
+            .filter(|t| t.state == TrialState::Complete)
+            .count();
+        let n_pruned = trials
+            .iter()
+            .filter(|t| t.state == TrialState::Pruned)
+            .count();
+
+        let direction_str = match self.direction {
+            Direction::Minimize => "Minimize",
+            Direction::Maximize => "Maximize",
+        };
+
+        let mut s = format!("Study: {direction_str} | {n} trials", n = trials.len());
+        if n_pruned > 0 {
+            let _ = write!(s, " ({n_complete} complete, {n_pruned} pruned)");
+        }
+
+        drop(trials);
+
+        if let Ok(best) = self.best_trial() {
+            let _ = write!(s, "\nBest value: {} (trial #{})", best.value, best.id);
+            if !best.params.is_empty() {
+                s.push_str("\nBest parameters:");
+                let mut params: Vec<_> = best.params.iter().collect();
+                params.sort_by_key(|(id, _)| *id);
+                for (id, value) in params {
+                    let label = best.param_labels.get(id).map_or("?", String::as_str);
+                    let _ = write!(s, "\n  {label} = {value}");
+                }
+            }
+        }
+
+        s
+    }
+}
+
+impl<V> fmt::Display for Study<V>
+where
+    V: PartialOrd + Clone + fmt::Display,
+{
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(&self.summary())
+    }
+}
+
 // Specialized implementation for Study<f64> that provides deprecated `_with_sampler` aliases.
 //
 // For Study<f64>, the generic methods from `impl<V> Study<V>` (like `optimize()`,

tests/integration.rs

@@ -1892,3 +1892,75 @@ fn test_enqueue_counted_in_n_trials() {
     // All 5 trials count, including the 2 enqueued ones
     assert_eq!(study.n_trials(), 5);
 }
+
+// =============================================================================
+// Test: Study summary and Display
+// =============================================================================
+
+#[test]
+fn test_summary_with_completed_trials() {
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, RandomSampler::with_seed(1));
+    let x = FloatParam::new(0.0, 10.0).name("x");
+
+    study
+        .optimize(5, |trial| {
+            let val = x.suggest(trial)?;
+            Ok::<_, Error>(val * val)
+        })
+        .unwrap();
+
+    let summary = study.summary();
+    assert!(summary.contains("Minimize"));
+    assert!(summary.contains("5 trials"));
+    assert!(summary.contains("Best value:"));
+    assert!(summary.contains("x = "));
+}
+
+#[test]
+fn test_summary_no_completed_trials() {
+    let study: Study<f64> = Study::new(Direction::Maximize);
+    let summary = study.summary();
+    assert!(summary.contains("Maximize"));
+    assert!(summary.contains("0 trials"));
+    assert!(!summary.contains("Best value:"));
+}
+
+#[test]
+fn test_summary_with_pruned_trials() {
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, RandomSampler::with_seed(1));
+    let x = FloatParam::new(0.0, 10.0).name("x");
+
+    // Manually create some complete and pruned trials
+    for _ in 0..3 {
+        let mut trial = study.create_trial();
+        let val = x.suggest(&mut trial).unwrap();
+        study.complete_trial(trial, val);
+    }
+    for _ in 0..2 {
+        let mut trial = study.create_trial();
+        let _ = x.suggest(&mut trial).unwrap();
+        study.prune_trial(trial);
+    }
+
+    let summary = study.summary();
+    // Should show breakdown when there are pruned trials
+    if study.n_pruned_trials() > 0 {
+        assert!(summary.contains("complete"));
+        assert!(summary.contains("pruned"));
+    }
+}
+
+#[test]
+fn test_display_matches_summary() {
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, RandomSampler::with_seed(1));
+    let x = FloatParam::new(0.0, 10.0).name("x");
+
+    study
+        .optimize(3, |trial| {
+            let val = x.suggest(trial)?;
+            Ok::<_, Error>(val)
+        })
+        .unwrap();
+
+    assert_eq!(format!("{study}"), study.summary());
+}