refactor(docs): Documentation Overhaul

examples/basic_optimization.rs

@@ -0,0 +1,32 @@
+//! Basic optimization example — the "hello world" of the optimizer crate.
+//!
+//! Minimizes a simple quadratic function f(x) = (x - 3)² using the default
+//! random sampler. No feature flags are required.
+//!
+//! Run with: `cargo run --example basic_optimization`
+
+use optimizer::prelude::*;
+
+fn main() {
+    // Create a study that minimizes the objective function.
+    // The default sampler is random; for smarter sampling, pass a TpeSampler.
+    let study: Study<f64> = Study::new(Direction::Minimize);
+
+    // Search for x in [-10, 10]. The optimizer will suggest values from this range.
+    let x = FloatParam::new(-10.0, 10.0).name("x");
+
+    // Run 50 trials, each evaluating f(x) = (x - 3)²
+    study
+        .optimize(50, |trial| {
+            let x_val = x.suggest(trial)?;
+            let value = (x_val - 3.0).powi(2);
+            Ok::<_, Error>(value)
+        })
+        .unwrap();
+
+    // Retrieve and display the best result
+    let best = study.best_trial().unwrap();
+    println!("Best trial #{}", best.id);
+    println!("  x     = {:.4}", best.get(&x).unwrap());
+    println!("  f(x)  = {:.4}", best.value);
+}