docs(examples): add toy_nsga2, random_search, and custom_optimizer
The three runnable examples called out in spec §18.5 / §19. All open with `use heuropt::prelude::*;` so they double as a check that the prelude is sufficient on its own: - toy_nsga2.rs: Schaffer N.1 solved with NSGA-II. - random_search.rs: 2D sphere solved with RandomSearch. - custom_optimizer.rs: a minimal hill-climber implementing `Optimizer<P>` directly, demonstrating spec §2.3.
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//! Solve the Schaffer N.1 two-objective problem with NSGA-II.
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//!
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//! Run with:
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//!
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//! ```bash
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//! cargo run --example toy_nsga2
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//! ```
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use heuropt::prelude::*;
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struct SchafferN1;
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impl Problem for SchafferN1 {
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type Decision = Vec<f64>;
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fn objectives(&self) -> ObjectiveSpace {
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ObjectiveSpace::new(vec![Objective::minimize("f1"), Objective::minimize("f2")])
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}
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fn evaluate(&self, x: &Vec<f64>) -> Evaluation {
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let v = x[0];
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Evaluation::new(vec![v * v, (v - 2.0).powi(2)])
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}
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}
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fn main() {
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let initializer = RealBounds::new(vec![(-5.0, 5.0)]);
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let variation = GaussianMutation { sigma: 0.2 };
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let config = Nsga2Config { population_size: 60, generations: 80, seed: 42 };
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let mut optimizer = Nsga2::new(config, initializer, variation);
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let result = optimizer.run(&SchafferN1);
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println!("Final population: {}", result.population.len());
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println!("Pareto front size: {}", result.pareto_front.len());
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println!("Total evaluations: {}", result.evaluations);
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println!("First few front points (f1, f2):");
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for c in result.pareto_front.iter().take(8) {
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let o = &c.evaluation.objectives;
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println!(" ({:.4}, {:.4})", o[0], o[1]);
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}
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}
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