swaits
5728ee14e2
NSGA-III's value over NSGA-II shows up at 3+ objectives, where crowding distance loses its diversity signal. Adds a third comparison section to `examples/compare.rs`: DTLZ2 (3-objective, 12-D, the textbook benchmark for many-objective algorithms): unit-sphere-octant Pareto front. Compares RandomSearch, NSGA-II, SPEA2, and NSGA-III on: - mean distance from front points to the unit sphere (closed-form: |1 - sqrt(f1² + f2² + f3²)|), - spacing, - front size, - wall-clock ms. NSGA-III config: H=12 reference divisions (91 reference points, matching the canonical setup from Deb & Jain 2014). Also wires NSGA-III into the existing ZDT1 (2-objective) section even though it's not its sweet spot — useful as a regression check that the algorithm at least keeps up with NSGA-II on bi-objective problems.
590 lines
19 KiB
Rust
590 lines
19 KiB
Rust
//! Multi-seed algorithm comparison harness.
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//!
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//! Runs every applicable optimizer on each test problem across N seeds and
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//! prints aggregate quality metrics. Adding a new algorithm to the
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//! comparison is a single-line edit to the runner table — see the bottom
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//! of this file.
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//!
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//! ```bash
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//! cargo run --release --example compare
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//! ```
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use std::f64::consts::PI;
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use std::time::Instant;
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use heuropt::metrics::{hypervolume::hypervolume_2d, spacing::spacing};
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use heuropt::prelude::*;
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const SEEDS: u64 = 10;
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const ZDT1_DIM: usize = 30;
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const ZDT1_BUDGET: usize = 25_000;
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// Standard ZDT1 reference point. Using [11, 11] (rather than the
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// near-front [1.1, 1.1]) so under-converged algorithms with large `g`
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// values still register a meaningful — if poor — hypervolume.
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const ZDT1_REFERENCE: [f64; 2] = [11.0, 11.0];
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const RASTRIGIN_DIM: usize = 5;
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const RASTRIGIN_BUDGET: usize = 50_000;
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const DTLZ2_OBJECTIVES: usize = 3;
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const DTLZ2_K: usize = 10;
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const DTLZ2_DIM: usize = DTLZ2_OBJECTIVES + DTLZ2_K - 1; // 12
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const DTLZ2_BUDGET: usize = 30_000;
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// -----------------------------------------------------------------------------
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// Test problems
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// -----------------------------------------------------------------------------
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struct Zdt1 {
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dim: usize,
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}
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impl Problem for Zdt1 {
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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 f1 = x[0];
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let tail_sum: f64 = x[1..].iter().sum();
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let g = 1.0 + 9.0 * tail_sum / (self.dim as f64 - 1.0);
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let f2 = g * (1.0 - (f1 / g).sqrt());
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Evaluation::new(vec![f1, f2])
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}
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}
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struct Dtlz2 {
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num_objectives: usize,
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dim: usize,
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}
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impl Problem for Dtlz2 {
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type Decision = Vec<f64>;
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fn objectives(&self) -> ObjectiveSpace {
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ObjectiveSpace::new(
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(0..self.num_objectives)
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.map(|i| Objective::minimize(format!("f{}", i + 1)))
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.collect(),
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)
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}
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fn evaluate(&self, x: &Vec<f64>) -> Evaluation {
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let m = self.num_objectives;
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let g: f64 = x[(m - 1)..self.dim].iter().map(|v| (v - 0.5).powi(2)).sum();
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let scale = 1.0 + g;
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let mut f = vec![0.0_f64; m];
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for i in 0..m {
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let mut prod = scale;
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for j in 0..(m - i - 1) {
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prod *= (x[j] * std::f64::consts::FRAC_PI_2).cos();
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}
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if i > 0 {
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prod *= (x[m - i - 1] * std::f64::consts::FRAC_PI_2).sin();
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}
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f[i] = prod;
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}
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Evaluation::new(f)
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}
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}
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struct Rastrigin {
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dim: usize,
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}
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impl Problem for Rastrigin {
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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("f")])
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}
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fn evaluate(&self, x: &Vec<f64>) -> Evaluation {
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let n = self.dim as f64;
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let value = 10.0 * n
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+ x.iter().map(|v| v * v - 10.0 * (2.0 * PI * v).cos()).sum::<f64>();
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Evaluation::new(vec![value])
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}
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}
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// -----------------------------------------------------------------------------
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// Run results + metrics aggregation
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// -----------------------------------------------------------------------------
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#[derive(Clone)]
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struct MoRun {
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front: Vec<Candidate<Vec<f64>>>,
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wall_ms: u128,
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}
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#[derive(Clone)]
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struct SoRun {
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best_value: f64,
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wall_ms: u128,
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}
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fn mean_l2_to_zdt1_front(front: &[Candidate<Vec<f64>>]) -> f64 {
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if front.is_empty() {
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return f64::INFINITY;
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}
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let samples: Vec<(f64, f64)> = (0..=1000)
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.map(|i| {
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let f1 = i as f64 / 1000.0;
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(f1, 1.0 - f1.sqrt())
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})
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.collect();
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let mut total = 0.0;
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for c in front {
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let f1 = c.evaluation.objectives[0];
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let f2 = c.evaluation.objectives[1];
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let mut best = f64::INFINITY;
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for &(rf1, rf2) in &samples {
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let d = ((rf1 - f1).powi(2) + (rf2 - f2).powi(2)).sqrt();
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if d < best {
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best = d;
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}
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}
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total += best;
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}
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total / front.len() as f64
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}
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fn mean_std(values: &[f64]) -> (f64, f64) {
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let n = values.len() as f64;
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let mean = values.iter().sum::<f64>() / n;
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let var = values.iter().map(|v| (v - mean).powi(2)).sum::<f64>() / n;
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(mean, var.sqrt())
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}
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// -----------------------------------------------------------------------------
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// ZDT1 algorithm runners
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// -----------------------------------------------------------------------------
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fn zdt1_random(seed: u64) -> MoRun {
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let problem = Zdt1 { dim: ZDT1_DIM };
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let initializer = RealBounds::new(vec![(0.0, 1.0); ZDT1_DIM]);
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let config = RandomSearchConfig {
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iterations: ZDT1_BUDGET,
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batch_size: 1,
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seed,
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};
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let mut opt = RandomSearch::new(config, initializer);
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let t0 = Instant::now();
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let result = opt.run(&problem);
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MoRun { front: result.pareto_front, wall_ms: t0.elapsed().as_millis() }
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}
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fn zdt1_paes(seed: u64) -> MoRun {
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let problem = Zdt1 { dim: ZDT1_DIM };
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let initializer = RealBounds::new(vec![(0.0, 1.0); ZDT1_DIM]);
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let variation = BoundedGaussianMutation::new(0.05, vec![(0.0, 1.0); ZDT1_DIM]);
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let config = PaesConfig {
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iterations: ZDT1_BUDGET,
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archive_size: 100,
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seed,
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};
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let mut opt = Paes::new(config, initializer, variation);
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let t0 = Instant::now();
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let result = opt.run(&problem);
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MoRun { front: result.pareto_front, wall_ms: t0.elapsed().as_millis() }
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}
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fn zdt1_spea2(seed: u64) -> MoRun {
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let problem = Zdt1 { dim: ZDT1_DIM };
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let bounds = vec![(0.0, 1.0); ZDT1_DIM];
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let initializer = RealBounds::new(bounds.clone());
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let variation = CompositeVariation {
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crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
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mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / ZDT1_DIM as f64),
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};
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let pop = 100;
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let arc = 100;
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// SPEA2 evaluates `pop_size` per generation after the initial population.
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let gens = (ZDT1_BUDGET - pop) / pop;
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let config = Spea2Config {
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population_size: pop,
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archive_size: arc,
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generations: gens,
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seed,
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};
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let mut opt = Spea2::new(config, initializer, variation);
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let t0 = Instant::now();
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let result = opt.run(&problem);
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MoRun { front: result.pareto_front, wall_ms: t0.elapsed().as_millis() }
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}
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fn zdt1_nsga2(seed: u64) -> MoRun {
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let problem = Zdt1 { dim: ZDT1_DIM };
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let bounds = vec![(0.0, 1.0); ZDT1_DIM];
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let initializer = RealBounds::new(bounds.clone());
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let variation = CompositeVariation {
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crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
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mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / ZDT1_DIM as f64),
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};
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let pop = 100;
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let gens = ZDT1_BUDGET / pop;
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let config = Nsga2Config { population_size: pop, generations: gens, seed };
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let mut opt = Nsga2::new(config, initializer, variation);
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let t0 = Instant::now();
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let result = opt.run(&problem);
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MoRun { front: result.pareto_front, wall_ms: t0.elapsed().as_millis() }
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}
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fn zdt1_nsga3(seed: u64) -> MoRun {
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let problem = Zdt1 { dim: ZDT1_DIM };
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let bounds = vec![(0.0, 1.0); ZDT1_DIM];
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let initializer = RealBounds::new(bounds.clone());
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let variation = CompositeVariation {
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crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
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mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / ZDT1_DIM as f64),
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};
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let pop = 100;
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let gens = ZDT1_BUDGET / pop;
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let config = Nsga3Config {
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population_size: pop,
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generations: gens,
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// 99 ref points for 2 objectives — same density as the population.
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reference_divisions: 99,
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seed,
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};
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let mut opt = Nsga3::new(config, initializer, variation);
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let t0 = Instant::now();
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let result = opt.run(&problem);
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MoRun { front: result.pareto_front, wall_ms: t0.elapsed().as_millis() }
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}
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// -----------------------------------------------------------------------------
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// DTLZ2 algorithm runners (3-objective)
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// -----------------------------------------------------------------------------
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fn dtlz2_problem() -> Dtlz2 {
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Dtlz2 { num_objectives: DTLZ2_OBJECTIVES, dim: DTLZ2_DIM }
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}
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fn dtlz2_random(seed: u64) -> MoRun {
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let problem = dtlz2_problem();
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let initializer = RealBounds::new(vec![(0.0, 1.0); DTLZ2_DIM]);
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let config = RandomSearchConfig {
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iterations: DTLZ2_BUDGET,
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batch_size: 1,
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seed,
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};
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let mut opt = RandomSearch::new(config, initializer);
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let t0 = Instant::now();
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let result = opt.run(&problem);
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MoRun { front: result.pareto_front, wall_ms: t0.elapsed().as_millis() }
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}
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fn dtlz2_nsga2(seed: u64) -> MoRun {
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let problem = dtlz2_problem();
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let bounds = vec![(0.0, 1.0); DTLZ2_DIM];
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let initializer = RealBounds::new(bounds.clone());
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let variation = CompositeVariation {
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crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
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mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ2_DIM as f64),
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};
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let pop = 92; // close to the 91-ref-point NSGA-III pop, for fairness
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let gens = DTLZ2_BUDGET / pop;
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let config = Nsga2Config { population_size: pop, generations: gens, seed };
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let mut opt = Nsga2::new(config, initializer, variation);
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let t0 = Instant::now();
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let result = opt.run(&problem);
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MoRun { front: result.pareto_front, wall_ms: t0.elapsed().as_millis() }
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}
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fn dtlz2_spea2(seed: u64) -> MoRun {
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let problem = dtlz2_problem();
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let bounds = vec![(0.0, 1.0); DTLZ2_DIM];
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let initializer = RealBounds::new(bounds.clone());
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let variation = CompositeVariation {
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crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
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mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ2_DIM as f64),
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};
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let pop = 92;
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let arc = 92;
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let gens = (DTLZ2_BUDGET - pop) / pop;
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let config = Spea2Config {
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population_size: pop,
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archive_size: arc,
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generations: gens,
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seed,
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};
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let mut opt = Spea2::new(config, initializer, variation);
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let t0 = Instant::now();
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let result = opt.run(&problem);
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MoRun { front: result.pareto_front, wall_ms: t0.elapsed().as_millis() }
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}
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fn dtlz2_nsga3(seed: u64) -> MoRun {
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let problem = dtlz2_problem();
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let bounds = vec![(0.0, 1.0); DTLZ2_DIM];
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let initializer = RealBounds::new(bounds.clone());
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let variation = CompositeVariation {
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crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
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mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ2_DIM as f64),
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};
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// H=12 → 91 reference points (the canonical NSGA-III 3-objective set).
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// Population is sized to match: the spec recommends pop ≈ #refs.
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let pop = 92;
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let gens = DTLZ2_BUDGET / pop;
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let config = Nsga3Config {
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population_size: pop,
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generations: gens,
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reference_divisions: 12,
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seed,
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};
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let mut opt = Nsga3::new(config, initializer, variation);
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let t0 = Instant::now();
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let result = opt.run(&problem);
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MoRun { front: result.pareto_front, wall_ms: t0.elapsed().as_millis() }
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}
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/// DTLZ2's analytical Pareto front is the unit sphere octant in objective
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/// space (`Σ f_i² = 1`, all `f_i ≥ 0`). The closest-point distance from
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/// `f` to that surface is `|‖f‖ - 1|`.
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fn mean_distance_to_dtlz2_front(front: &[Candidate<Vec<f64>>]) -> f64 {
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if front.is_empty() {
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return f64::INFINITY;
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}
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let total: f64 = front
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.iter()
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.map(|c| {
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let norm: f64 = c.evaluation.objectives.iter().map(|v| v * v).sum::<f64>().sqrt();
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(norm - 1.0).abs()
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})
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.sum();
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total / front.len() as f64
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}
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// -----------------------------------------------------------------------------
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// Rastrigin algorithm runners
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// -----------------------------------------------------------------------------
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fn rastrigin_random(seed: u64) -> SoRun {
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let problem = Rastrigin { dim: RASTRIGIN_DIM };
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let initializer = RealBounds::new(vec![(-5.12, 5.12); RASTRIGIN_DIM]);
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let config = RandomSearchConfig {
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iterations: RASTRIGIN_BUDGET,
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batch_size: 1,
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seed,
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};
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let mut opt = RandomSearch::new(config, initializer);
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let t0 = Instant::now();
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let result = opt.run(&problem);
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SoRun {
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best_value: result.best.unwrap().evaluation.objectives[0],
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wall_ms: t0.elapsed().as_millis(),
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}
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}
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fn rastrigin_paes(seed: u64) -> SoRun {
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let problem = Rastrigin { dim: RASTRIGIN_DIM };
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let initializer = RealBounds::new(vec![(-5.12, 5.12); RASTRIGIN_DIM]);
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let variation = BoundedGaussianMutation::new(0.3, vec![(-5.12, 5.12); RASTRIGIN_DIM]);
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let config = PaesConfig {
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iterations: RASTRIGIN_BUDGET,
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archive_size: 32,
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seed,
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};
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let mut opt = Paes::new(config, initializer, variation);
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let t0 = Instant::now();
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let result = opt.run(&problem);
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SoRun {
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best_value: result.best.unwrap().evaluation.objectives[0],
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wall_ms: t0.elapsed().as_millis(),
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}
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}
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fn rastrigin_nsga2(seed: u64) -> SoRun {
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let problem = Rastrigin { dim: RASTRIGIN_DIM };
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let bounds = vec![(-5.12, 5.12); RASTRIGIN_DIM];
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let initializer = RealBounds::new(bounds.clone());
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let variation = CompositeVariation {
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crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
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mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / RASTRIGIN_DIM as f64),
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};
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let pop = 50;
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let gens = RASTRIGIN_BUDGET / pop;
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let config = Nsga2Config { population_size: pop, generations: gens, seed };
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let mut opt = Nsga2::new(config, initializer, variation);
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let t0 = Instant::now();
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let result = opt.run(&problem);
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SoRun {
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best_value: result.best.unwrap().evaluation.objectives[0],
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wall_ms: t0.elapsed().as_millis(),
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}
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}
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fn rastrigin_de(seed: u64) -> SoRun {
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let problem = Rastrigin { dim: RASTRIGIN_DIM };
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let bounds = RealBounds::new(vec![(-5.12, 5.12); RASTRIGIN_DIM]);
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let pop = 50;
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let gens = (RASTRIGIN_BUDGET - pop) / pop; // initial pop also evaluates
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let config = DifferentialEvolutionConfig {
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population_size: pop,
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generations: gens,
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differential_weight: 0.5,
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crossover_probability: 0.9,
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seed,
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};
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let mut opt = DifferentialEvolution::new(config, bounds);
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let t0 = Instant::now();
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let result = opt.run(&problem);
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SoRun {
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best_value: result.best.unwrap().evaluation.objectives[0],
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wall_ms: t0.elapsed().as_millis(),
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}
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}
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// -----------------------------------------------------------------------------
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// Main
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// -----------------------------------------------------------------------------
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fn run_zdt1_comparison() {
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||
println!(
|
||
"== ZDT1 (dim={ZDT1_DIM}, {ZDT1_BUDGET} evals/run × {SEEDS} seeds) =="
|
||
);
|
||
println!("metric arrows: hypervolume↑ (higher better), others↓ (lower better)");
|
||
println!();
|
||
println!(
|
||
"{:<14} {:>16} {:>14} {:>14} {:>10} {:>10}",
|
||
"algorithm", "hypervolume", "spacing", "mean L2", "front", "ms",
|
||
);
|
||
println!("{}", "-".repeat(82));
|
||
|
||
let zdt1 = Zdt1 { dim: ZDT1_DIM };
|
||
let zdt1_objs = zdt1.objectives();
|
||
|
||
type Runner = fn(u64) -> MoRun;
|
||
let runners: &[(&str, Runner)] = &[
|
||
("RandomSearch", zdt1_random),
|
||
("PAES", zdt1_paes),
|
||
("SPEA2", zdt1_spea2),
|
||
("NSGA-II", zdt1_nsga2),
|
||
("NSGA-III", zdt1_nsga3),
|
||
];
|
||
|
||
for (name, runner) in runners {
|
||
let runs: Vec<MoRun> = (0..SEEDS).map(runner).collect();
|
||
let hv: Vec<f64> = runs
|
||
.iter()
|
||
.map(|r| hypervolume_2d(&r.front, &zdt1_objs, ZDT1_REFERENCE))
|
||
.collect();
|
||
let sp: Vec<f64> =
|
||
runs.iter().map(|r| spacing(&r.front, &zdt1_objs)).collect();
|
||
let l2: Vec<f64> =
|
||
runs.iter().map(|r| mean_l2_to_zdt1_front(&r.front)).collect();
|
||
let fs: Vec<f64> = runs.iter().map(|r| r.front.len() as f64).collect();
|
||
let ms: Vec<f64> = runs.iter().map(|r| r.wall_ms as f64).collect();
|
||
|
||
let (hv_m, hv_s) = mean_std(&hv);
|
||
let (sp_m, sp_s) = mean_std(&sp);
|
||
let (l2_m, l2_s) = mean_std(&l2);
|
||
let (fs_m, _) = mean_std(&fs);
|
||
let (ms_m, _) = mean_std(&ms);
|
||
|
||
println!(
|
||
"{:<14} {:>16} {:>14} {:>14} {:>10} {:>10}",
|
||
name,
|
||
format!("{hv_m:.4}±{hv_s:.4}"),
|
||
format!("{sp_m:.4}±{sp_s:.4}"),
|
||
format!("{l2_m:.4}±{l2_s:.4}"),
|
||
format!("{fs_m:.0}"),
|
||
format!("{ms_m:.0}"),
|
||
);
|
||
}
|
||
}
|
||
|
||
fn run_dtlz2_comparison() {
|
||
println!();
|
||
println!(
|
||
"== DTLZ2 (3-obj, dim={DTLZ2_DIM}, {DTLZ2_BUDGET} evals/run × {SEEDS} seeds) =="
|
||
);
|
||
println!("Pareto front: unit sphere octant (Σf²=1, all f≥0); 'mean dist' is |‖f‖−1|");
|
||
println!();
|
||
println!(
|
||
"{:<14} {:>16} {:>14} {:>10} {:>10}",
|
||
"algorithm", "mean dist↓", "spacing↓", "front", "ms",
|
||
);
|
||
println!("{}", "-".repeat(70));
|
||
|
||
let dtlz2 = dtlz2_problem();
|
||
let dtlz2_objs = dtlz2.objectives();
|
||
|
||
type Runner = fn(u64) -> MoRun;
|
||
let runners: &[(&str, Runner)] = &[
|
||
("RandomSearch", dtlz2_random),
|
||
("NSGA-II", dtlz2_nsga2),
|
||
("SPEA2", dtlz2_spea2),
|
||
("NSGA-III", dtlz2_nsga3),
|
||
];
|
||
|
||
for (name, runner) in runners {
|
||
let runs: Vec<MoRun> = (0..SEEDS).map(runner).collect();
|
||
let dist: Vec<f64> =
|
||
runs.iter().map(|r| mean_distance_to_dtlz2_front(&r.front)).collect();
|
||
let sp: Vec<f64> =
|
||
runs.iter().map(|r| spacing(&r.front, &dtlz2_objs)).collect();
|
||
let fs: Vec<f64> = runs.iter().map(|r| r.front.len() as f64).collect();
|
||
let ms: Vec<f64> = runs.iter().map(|r| r.wall_ms as f64).collect();
|
||
|
||
let (d_m, d_s) = mean_std(&dist);
|
||
let (sp_m, sp_s) = mean_std(&sp);
|
||
let (fs_m, _) = mean_std(&fs);
|
||
let (ms_m, _) = mean_std(&ms);
|
||
|
||
println!(
|
||
"{:<14} {:>16} {:>14} {:>10} {:>10}",
|
||
name,
|
||
format!("{d_m:.4}±{d_s:.4}"),
|
||
format!("{sp_m:.4}±{sp_s:.4}"),
|
||
format!("{fs_m:.0}"),
|
||
format!("{ms_m:.0}"),
|
||
);
|
||
}
|
||
}
|
||
|
||
fn run_rastrigin_comparison() {
|
||
println!();
|
||
println!(
|
||
"== Rastrigin (dim={RASTRIGIN_DIM}, {RASTRIGIN_BUDGET} evals/run × {SEEDS} seeds) =="
|
||
);
|
||
println!("global minimum: f = 0 (lower is better)");
|
||
println!();
|
||
println!("{:<14} {:>20} {:>10}", "algorithm", "best f", "ms");
|
||
println!("{}", "-".repeat(48));
|
||
|
||
type Runner = fn(u64) -> SoRun;
|
||
let runners: &[(&str, Runner)] = &[
|
||
("RandomSearch", rastrigin_random),
|
||
("PAES", rastrigin_paes),
|
||
("NSGA-II", rastrigin_nsga2),
|
||
("DE", rastrigin_de),
|
||
];
|
||
|
||
for (name, runner) in runners {
|
||
let runs: Vec<SoRun> = (0..SEEDS).map(runner).collect();
|
||
let best: Vec<f64> = runs.iter().map(|r| r.best_value).collect();
|
||
let ms: Vec<f64> = runs.iter().map(|r| r.wall_ms as f64).collect();
|
||
|
||
let (b_m, b_s) = mean_std(&best);
|
||
let (ms_m, _) = mean_std(&ms);
|
||
|
||
println!(
|
||
"{:<14} {:>20} {:>10}",
|
||
name,
|
||
format!("{b_m:.4e} ± {b_s:.2e}"),
|
||
format!("{ms_m:.0}"),
|
||
);
|
||
}
|
||
}
|
||
|
||
fn main() {
|
||
run_zdt1_comparison();
|
||
run_dtlz2_comparison();
|
||
run_rastrigin_comparison();
|
||
}
|