swaitsandClaude Opus 4.7
398c82326a
Adds a many-objective section to the comparison harness, exercising the regime where Pareto dominance stops discriminating: with enough objectives almost every pair of solutions is mutually non-dominated. - DTLZ2 4-objective: the entry point to many-objective. - DTLZ2 10-objective: the curse of dimensionality in full. - DTLZ1 8-objective: dominance collapse stacked on DTLZ1's deceptive multimodal g-term. Implemented generically: the existing Dtlz1/Dtlz2 structs and distance metrics are already objective-count agnostic, so a single `ManySpec` + nine generic runners (RandomSearch, NSGA-II, NSGA-III, MOEA/D, RVEA, GrEA, IBEA, HypE, AGE-MOEA) cover all three tables -- and any future M. The results are a clean teaching story: - NSGA-II collapses -- on DTLZ2-10 it finishes dead last, *worse than random search* (2.01 vs 0.63); its crowding distance actively misleads in 10-D. - HypE / MOEA/D / GrEA / IBEA barely notice the 4 -> 10 jump. - GrEA wins DTLZ1-8, consistent with the 3-objective DTLZ1 table. - HypE reverses: #1 on both DTLZ2 tables, #6 on the deceptive DTLZ1-8. Regenerated examples/compare-results.md with the three new sections. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
3238 lines
103 KiB
Rust
3238 lines
103 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 rand::Rng as _;
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use heuropt::core::rng::Rng;
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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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const ROSENBROCK_DIM: usize = 5;
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const ROSENBROCK_BUDGET: usize = 30_000;
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const ACKLEY_DIM: usize = 5;
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const ACKLEY_BUDGET: usize = 30_000;
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const ZDT3_DIM: usize = 30;
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const ZDT3_BUDGET: usize = 25_000;
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const ZDT3_REFERENCE: [f64; 2] = [11.0, 11.0];
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const DTLZ1_OBJECTIVES: usize = 3;
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const DTLZ1_K: usize = 5;
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const DTLZ1_DIM: usize = DTLZ1_OBJECTIVES + DTLZ1_K - 1;
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const DTLZ1_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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#[allow(clippy::needless_range_loop)] // Body indexes `x[j]`.
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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 Rosenbrock {
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dim: usize,
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}
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impl Problem for Rosenbrock {
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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 f: f64 = (0..self.dim - 1)
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.map(|i| {
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let a = 1.0 - x[i];
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let b = x[i + 1] - x[i] * x[i];
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a * a + 100.0 * b * b
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})
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.sum();
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Evaluation::new(vec![f])
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}
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}
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struct Ackley {
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dim: usize,
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}
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impl Problem for Ackley {
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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 sum_sq: f64 = x.iter().map(|v| v * v).sum();
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let sum_cos: f64 = x.iter().map(|v| (2.0 * PI * v).cos()).sum();
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let f = -20.0 * (-0.2 * (sum_sq / n).sqrt()).exp() - (sum_cos / n).exp()
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+ 20.0
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+ std::f64::consts::E;
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Evaluation::new(vec![f])
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}
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}
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struct Zdt3 {
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dim: usize,
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}
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impl Problem for Zdt3 {
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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 r = f1 / g;
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let f2 = g * (1.0 - r.sqrt() - r * (10.0 * PI * f1).sin());
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Evaluation::new(vec![f1, f2])
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}
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}
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struct Dtlz1 {
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num_objectives: usize,
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dim: usize,
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}
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impl Problem for Dtlz1 {
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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 k = self.dim - (m - 1);
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let g_term: f64 = x[(m - 1)..self.dim]
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.iter()
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.map(|v| (v - 0.5).powi(2) - (20.0 * PI * (v - 0.5)).cos())
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.sum();
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let g = 100.0 * (k as f64 + g_term);
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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 = 0.5 * (1.0 + g);
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#[allow(clippy::needless_range_loop)] // body indexes x[j].
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for j in 0..(m - i - 1) {
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prod *= x[j];
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}
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if i > 0 {
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prod *= 1.0 - x[m - i - 1];
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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()
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.map(|v| v * v - 10.0 * (2.0 * PI * v).cos())
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.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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/// Print an aligned text table: column 0 left-justified, the rest
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/// right-justified. Column widths are derived from the actual cell
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/// contents (header *and* every row), so the separator and all rows line
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/// up no matter how the value magnitudes vary.
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///
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/// All cells must be ASCII — width is measured with `str::len`, so a
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/// multi-byte character (e.g. `±`, `ε`) would silently break alignment on
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/// terminals that render it at a different column width. Callers format
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/// `mean +/- std` rather than `mean ± std` for exactly this reason.
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fn print_table(header: &[&str], rows: &[Vec<String>]) {
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let ncols = header.len();
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let mut widths: Vec<usize> = header.iter().map(|h| h.len()).collect();
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for row in rows {
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for c in 0..ncols {
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widths[c] = widths[c].max(row[c].len());
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}
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}
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let fmt_row = |cells: &[String]| -> String {
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let mut out = String::new();
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for c in 0..ncols {
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if c > 0 {
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out.push_str(" ");
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}
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let w = widths[c];
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if c == 0 {
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out.push_str(&format!("{:<w$}", cells[c]));
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} else {
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out.push_str(&format!("{:>w$}", cells[c]));
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}
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}
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out
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};
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let header_owned: Vec<String> = header.iter().map(|s| s.to_string()).collect();
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let header_line = fmt_row(&header_owned);
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println!("{header_line}");
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println!("{}", "-".repeat(header_line.len()));
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for row in rows {
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println!("{}", fmt_row(row));
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}
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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 {
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front: result.pareto_front,
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wall_ms: t0.elapsed().as_millis(),
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}
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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 {
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front: result.pareto_front,
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wall_ms: t0.elapsed().as_millis(),
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}
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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 {
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front: result.pareto_front,
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wall_ms: t0.elapsed().as_millis(),
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}
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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 {
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population_size: pop,
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generations: gens,
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seed,
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};
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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 {
|
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front: result.pareto_front,
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wall_ms: t0.elapsed().as_millis(),
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}
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}
|
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fn zdt1_sms_emoa(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());
|
||
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),
|
||
};
|
||
// SMS-EMOA is steady-state and computes O(N²) hypervolumes per
|
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// iteration, so we run it on a smaller population for a smaller
|
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// total budget to keep wall time tractable.
|
||
let config = SmsEmoaConfig {
|
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population_size: 40,
|
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generations: 4_000,
|
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reference_point: vec![11.0, 11.0],
|
||
seed,
|
||
};
|
||
let mut opt = SmsEmoa::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn zdt1_hype(seed: u64) -> MoRun {
|
||
let problem = Zdt1 { dim: ZDT1_DIM };
|
||
let bounds = vec![(0.0, 1.0); ZDT1_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / ZDT1_DIM as f64),
|
||
};
|
||
let pop = 80;
|
||
// Each generation does multiple HV-estimation passes (parent selection +
|
||
// survival truncation), each with mc_samples × N work. Keep budget
|
||
// smaller than NSGA-II's so wall time is tractable.
|
||
let gens = 80;
|
||
let config = HypeConfig {
|
||
population_size: pop,
|
||
generations: gens,
|
||
reference_point: vec![11.0, 11.0],
|
||
mc_samples: 1_000,
|
||
seed,
|
||
};
|
||
let mut opt = Hype::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn zdt1_rvea(seed: u64) -> MoRun {
|
||
let problem = Zdt1 { dim: ZDT1_DIM };
|
||
let bounds = vec![(0.0, 1.0); ZDT1_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / ZDT1_DIM as f64),
|
||
};
|
||
let pop = 100;
|
||
let gens = ZDT1_BUDGET / pop;
|
||
let config = RveaConfig {
|
||
population_size: pop,
|
||
generations: gens,
|
||
reference_divisions: 99,
|
||
alpha: 2.0,
|
||
seed,
|
||
};
|
||
let mut opt = Rvea::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn zdt1_pesa2(seed: u64) -> MoRun {
|
||
let problem = Zdt1 { dim: ZDT1_DIM };
|
||
let bounds = vec![(0.0, 1.0); ZDT1_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / ZDT1_DIM as f64),
|
||
};
|
||
let pop = 50;
|
||
let gens = (ZDT1_BUDGET - pop) / pop;
|
||
let config = PesaIIConfig {
|
||
population_size: pop,
|
||
archive_size: 100,
|
||
generations: gens,
|
||
grid_divisions: 20,
|
||
seed,
|
||
};
|
||
let mut opt = PesaII::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn zdt1_epsilon_moea(seed: u64) -> MoRun {
|
||
let problem = Zdt1 { dim: ZDT1_DIM };
|
||
let bounds = vec![(0.0, 1.0); ZDT1_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / ZDT1_DIM as f64),
|
||
};
|
||
let config = EpsilonMoeaConfig {
|
||
population_size: 50,
|
||
evaluations: ZDT1_BUDGET,
|
||
epsilon: vec![0.01, 0.01],
|
||
seed,
|
||
};
|
||
let mut opt = EpsilonMoea::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn zdt1_mopso(seed: u64) -> MoRun {
|
||
let problem = Zdt1 { dim: ZDT1_DIM };
|
||
let bounds = RealBounds::new(vec![(0.0, 1.0); ZDT1_DIM]);
|
||
let swarm = 100;
|
||
let gens = (ZDT1_BUDGET - 2 * swarm) / swarm;
|
||
let config = MopsoConfig {
|
||
swarm_size: swarm,
|
||
generations: gens,
|
||
archive_size: 100,
|
||
inertia: 0.7,
|
||
cognitive: 1.5,
|
||
social: 1.5,
|
||
seed,
|
||
};
|
||
let mut opt = Mopso::new(config, bounds);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn zdt1_ibea(seed: u64) -> MoRun {
|
||
let problem = Zdt1 { dim: ZDT1_DIM };
|
||
let bounds = vec![(0.0, 1.0); ZDT1_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / ZDT1_DIM as f64),
|
||
};
|
||
let pop = 100;
|
||
let gens = ZDT1_BUDGET / pop;
|
||
let config = IbeaConfig {
|
||
population_size: pop,
|
||
generations: gens,
|
||
kappa: 0.05,
|
||
seed,
|
||
};
|
||
let mut opt = Ibea::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn zdt1_moead(seed: u64) -> MoRun {
|
||
let problem = Zdt1 { dim: ZDT1_DIM };
|
||
let bounds = vec![(0.0, 1.0); ZDT1_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / ZDT1_DIM as f64),
|
||
};
|
||
// 99 divisions → 100 weights for 2 obj. Each generation evaluates one
|
||
// child per weight (so `n_weights` evals/gen).
|
||
let pop = 100;
|
||
let gens = (ZDT1_BUDGET - pop) / pop;
|
||
let config = MoeadConfig {
|
||
generations: gens,
|
||
reference_divisions: 99,
|
||
neighborhood_size: 20,
|
||
seed,
|
||
};
|
||
let mut opt = Moead::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn zdt1_nsga3(seed: u64) -> MoRun {
|
||
let problem = Zdt1 { dim: ZDT1_DIM };
|
||
let bounds = vec![(0.0, 1.0); ZDT1_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / ZDT1_DIM as f64),
|
||
};
|
||
let pop = 100;
|
||
let gens = ZDT1_BUDGET / pop;
|
||
let config = Nsga3Config {
|
||
population_size: pop,
|
||
generations: gens,
|
||
// 99 ref points for 2 objectives — same density as the population.
|
||
reference_divisions: 99,
|
||
seed,
|
||
};
|
||
let mut opt = Nsga3::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
// -----------------------------------------------------------------------------
|
||
// DTLZ2 algorithm runners (3-objective)
|
||
// -----------------------------------------------------------------------------
|
||
|
||
fn dtlz2_problem() -> Dtlz2 {
|
||
Dtlz2 {
|
||
num_objectives: DTLZ2_OBJECTIVES,
|
||
dim: DTLZ2_DIM,
|
||
}
|
||
}
|
||
|
||
fn dtlz2_random(seed: u64) -> MoRun {
|
||
let problem = dtlz2_problem();
|
||
let initializer = RealBounds::new(vec![(0.0, 1.0); DTLZ2_DIM]);
|
||
let config = RandomSearchConfig {
|
||
iterations: DTLZ2_BUDGET,
|
||
batch_size: 1,
|
||
seed,
|
||
};
|
||
let mut opt = RandomSearch::new(config, initializer);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn dtlz2_nsga2(seed: u64) -> MoRun {
|
||
let problem = dtlz2_problem();
|
||
let bounds = vec![(0.0, 1.0); DTLZ2_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ2_DIM as f64),
|
||
};
|
||
let pop = 92; // close to the 91-ref-point NSGA-III pop, for fairness
|
||
let gens = DTLZ2_BUDGET / pop;
|
||
let config = Nsga2Config {
|
||
population_size: pop,
|
||
generations: gens,
|
||
seed,
|
||
};
|
||
let mut opt = Nsga2::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn dtlz2_spea2(seed: u64) -> MoRun {
|
||
let problem = dtlz2_problem();
|
||
let bounds = vec![(0.0, 1.0); DTLZ2_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ2_DIM as f64),
|
||
};
|
||
let pop = 92;
|
||
let arc = 92;
|
||
let gens = (DTLZ2_BUDGET - pop) / pop;
|
||
let config = Spea2Config {
|
||
population_size: pop,
|
||
archive_size: arc,
|
||
generations: gens,
|
||
seed,
|
||
};
|
||
let mut opt = Spea2::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn dtlz2_sms_emoa(seed: u64) -> MoRun {
|
||
let problem = dtlz2_problem();
|
||
let bounds = vec![(0.0, 1.0); DTLZ2_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ2_DIM as f64),
|
||
};
|
||
// 3-D HV-by-slicing is significantly more expensive than 2-D; smaller
|
||
// pop and gen budget here to keep the comparison tractable.
|
||
let pop = 40;
|
||
let gens = 4_000;
|
||
let config = SmsEmoaConfig {
|
||
population_size: pop,
|
||
generations: gens,
|
||
reference_point: vec![3.0, 3.0, 3.0],
|
||
seed,
|
||
};
|
||
let mut opt = SmsEmoa::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn dtlz2_hype(seed: u64) -> MoRun {
|
||
let problem = dtlz2_problem();
|
||
let bounds = vec![(0.0, 1.0); DTLZ2_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ2_DIM as f64),
|
||
};
|
||
let pop = 80;
|
||
let gens = 80;
|
||
let config = HypeConfig {
|
||
population_size: pop,
|
||
generations: gens,
|
||
reference_point: vec![3.0, 3.0, 3.0],
|
||
mc_samples: 1_000,
|
||
seed,
|
||
};
|
||
let mut opt = Hype::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn dtlz2_rvea(seed: u64) -> MoRun {
|
||
let problem = dtlz2_problem();
|
||
let bounds = vec![(0.0, 1.0); DTLZ2_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ2_DIM as f64),
|
||
};
|
||
let pop = 92;
|
||
let gens = DTLZ2_BUDGET / pop;
|
||
let config = RveaConfig {
|
||
population_size: pop,
|
||
generations: gens,
|
||
reference_divisions: 12,
|
||
alpha: 2.0,
|
||
seed,
|
||
};
|
||
let mut opt = Rvea::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn dtlz2_pesa2(seed: u64) -> MoRun {
|
||
let problem = dtlz2_problem();
|
||
let bounds = vec![(0.0, 1.0); DTLZ2_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ2_DIM as f64),
|
||
};
|
||
let pop = 50;
|
||
let gens = (DTLZ2_BUDGET - pop) / pop;
|
||
let config = PesaIIConfig {
|
||
population_size: pop,
|
||
archive_size: 100,
|
||
generations: gens,
|
||
grid_divisions: 12,
|
||
seed,
|
||
};
|
||
let mut opt = PesaII::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn dtlz2_epsilon_moea(seed: u64) -> MoRun {
|
||
let problem = dtlz2_problem();
|
||
let bounds = vec![(0.0, 1.0); DTLZ2_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ2_DIM as f64),
|
||
};
|
||
let config = EpsilonMoeaConfig {
|
||
population_size: 50,
|
||
evaluations: DTLZ2_BUDGET,
|
||
epsilon: vec![0.05, 0.05, 0.05],
|
||
seed,
|
||
};
|
||
let mut opt = EpsilonMoea::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn dtlz2_mopso(seed: u64) -> MoRun {
|
||
let problem = dtlz2_problem();
|
||
let bounds = RealBounds::new(vec![(0.0, 1.0); DTLZ2_DIM]);
|
||
let swarm = 92;
|
||
let gens = (DTLZ2_BUDGET - 2 * swarm) / swarm;
|
||
let config = MopsoConfig {
|
||
swarm_size: swarm,
|
||
generations: gens,
|
||
archive_size: 100,
|
||
inertia: 0.7,
|
||
cognitive: 1.5,
|
||
social: 1.5,
|
||
seed,
|
||
};
|
||
let mut opt = Mopso::new(config, bounds);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn dtlz2_ibea(seed: u64) -> MoRun {
|
||
let problem = dtlz2_problem();
|
||
let bounds = vec![(0.0, 1.0); DTLZ2_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ2_DIM as f64),
|
||
};
|
||
let pop = 92;
|
||
let gens = DTLZ2_BUDGET / pop;
|
||
let config = IbeaConfig {
|
||
population_size: pop,
|
||
generations: gens,
|
||
kappa: 0.05,
|
||
seed,
|
||
};
|
||
let mut opt = Ibea::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn dtlz2_moead(seed: u64) -> MoRun {
|
||
let problem = dtlz2_problem();
|
||
let bounds = vec![(0.0, 1.0); DTLZ2_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ2_DIM as f64),
|
||
};
|
||
// 12 divisions for 3 objectives = 91 weights — same density as NSGA-III.
|
||
let pop = 91;
|
||
let gens = (DTLZ2_BUDGET - pop) / pop;
|
||
let config = MoeadConfig {
|
||
generations: gens,
|
||
reference_divisions: 12,
|
||
neighborhood_size: 20,
|
||
seed,
|
||
};
|
||
let mut opt = Moead::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn dtlz2_nsga3(seed: u64) -> MoRun {
|
||
let problem = dtlz2_problem();
|
||
let bounds = vec![(0.0, 1.0); DTLZ2_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ2_DIM as f64),
|
||
};
|
||
// H=12 → 91 reference points (the canonical NSGA-III 3-objective set).
|
||
// Population is sized to match: the spec recommends pop ≈ #refs.
|
||
let pop = 92;
|
||
let gens = DTLZ2_BUDGET / pop;
|
||
let config = Nsga3Config {
|
||
population_size: pop,
|
||
generations: gens,
|
||
reference_divisions: 12,
|
||
seed,
|
||
};
|
||
let mut opt = Nsga3::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
/// DTLZ2's analytical Pareto front is the unit sphere octant in objective
|
||
/// space (`Σ f_i² = 1`, all `f_i ≥ 0`). The closest-point distance from
|
||
/// `f` to that surface is `|‖f‖ - 1|`.
|
||
fn mean_distance_to_dtlz2_front(front: &[Candidate<Vec<f64>>]) -> f64 {
|
||
if front.is_empty() {
|
||
return f64::INFINITY;
|
||
}
|
||
let total: f64 = front
|
||
.iter()
|
||
.map(|c| {
|
||
let norm: f64 = c
|
||
.evaluation
|
||
.objectives
|
||
.iter()
|
||
.map(|v| v * v)
|
||
.sum::<f64>()
|
||
.sqrt();
|
||
(norm - 1.0).abs()
|
||
})
|
||
.sum();
|
||
total / front.len() as f64
|
||
}
|
||
|
||
// -----------------------------------------------------------------------------
|
||
// Rastrigin algorithm runners
|
||
// -----------------------------------------------------------------------------
|
||
|
||
fn rastrigin_random(seed: u64) -> SoRun {
|
||
let problem = Rastrigin { dim: RASTRIGIN_DIM };
|
||
let initializer = RealBounds::new(vec![(-5.12, 5.12); RASTRIGIN_DIM]);
|
||
let config = RandomSearchConfig {
|
||
iterations: RASTRIGIN_BUDGET,
|
||
batch_size: 1,
|
||
seed,
|
||
};
|
||
let mut opt = RandomSearch::new(config, initializer);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn rastrigin_paes(seed: u64) -> SoRun {
|
||
let problem = Rastrigin { dim: RASTRIGIN_DIM };
|
||
let initializer = RealBounds::new(vec![(-5.12, 5.12); RASTRIGIN_DIM]);
|
||
let variation = BoundedGaussianMutation::new(0.3, vec![(-5.12, 5.12); RASTRIGIN_DIM]);
|
||
let config = PaesConfig {
|
||
iterations: RASTRIGIN_BUDGET,
|
||
archive_size: 32,
|
||
seed,
|
||
};
|
||
let mut opt = Paes::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn rastrigin_nsga2(seed: u64) -> SoRun {
|
||
let problem = Rastrigin { dim: RASTRIGIN_DIM };
|
||
let bounds = vec![(-5.12, 5.12); RASTRIGIN_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / RASTRIGIN_DIM as f64),
|
||
};
|
||
let pop = 50;
|
||
let gens = RASTRIGIN_BUDGET / pop;
|
||
let config = Nsga2Config {
|
||
population_size: pop,
|
||
generations: gens,
|
||
seed,
|
||
};
|
||
let mut opt = Nsga2::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn rastrigin_de(seed: u64) -> SoRun {
|
||
let problem = Rastrigin { dim: RASTRIGIN_DIM };
|
||
let bounds = RealBounds::new(vec![(-5.12, 5.12); RASTRIGIN_DIM]);
|
||
let pop = 50;
|
||
let gens = (RASTRIGIN_BUDGET - pop) / pop; // initial pop also evaluates
|
||
let config = DifferentialEvolutionConfig {
|
||
population_size: pop,
|
||
generations: gens,
|
||
differential_weight: 0.5,
|
||
crossover_probability: 0.9,
|
||
seed,
|
||
};
|
||
let mut opt = DifferentialEvolution::new(config, bounds);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn rastrigin_hill_climber(seed: u64) -> SoRun {
|
||
let problem = Rastrigin { dim: RASTRIGIN_DIM };
|
||
let initializer = RealBounds::new(vec![(-5.12, 5.12); RASTRIGIN_DIM]);
|
||
let variation = BoundedGaussianMutation::new(0.3, vec![(-5.12, 5.12); RASTRIGIN_DIM]);
|
||
let config = HillClimberConfig {
|
||
iterations: RASTRIGIN_BUDGET,
|
||
seed,
|
||
};
|
||
let mut opt = HillClimber::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn rastrigin_simulated_annealing(seed: u64) -> SoRun {
|
||
let problem = Rastrigin { dim: RASTRIGIN_DIM };
|
||
let initializer = RealBounds::new(vec![(-5.12, 5.12); RASTRIGIN_DIM]);
|
||
let variation = BoundedGaussianMutation::new(0.5, vec![(-5.12, 5.12); RASTRIGIN_DIM]);
|
||
let config = SimulatedAnnealingConfig {
|
||
iterations: RASTRIGIN_BUDGET,
|
||
initial_temperature: 5.0,
|
||
final_temperature: 1e-3,
|
||
seed,
|
||
};
|
||
let mut opt = SimulatedAnnealing::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn rastrigin_genetic_algorithm(seed: u64) -> SoRun {
|
||
let problem = Rastrigin { dim: RASTRIGIN_DIM };
|
||
let bounds = vec![(-5.12, 5.12); RASTRIGIN_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / RASTRIGIN_DIM as f64),
|
||
};
|
||
let pop = 50;
|
||
let gens = (RASTRIGIN_BUDGET - pop) / pop;
|
||
let config = GeneticAlgorithmConfig {
|
||
population_size: pop,
|
||
generations: gens,
|
||
tournament_size: 2,
|
||
elitism: 2,
|
||
seed,
|
||
};
|
||
let mut opt = GeneticAlgorithm::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn rastrigin_particle_swarm(seed: u64) -> SoRun {
|
||
let problem = Rastrigin { dim: RASTRIGIN_DIM };
|
||
let bounds = RealBounds::new(vec![(-5.12, 5.12); RASTRIGIN_DIM]);
|
||
let swarm = 40;
|
||
// PSO does swarm + swarm·gens + final evaluations. Approximate budget.
|
||
let gens = (RASTRIGIN_BUDGET - 2 * swarm) / swarm;
|
||
let config = ParticleSwarmConfig {
|
||
swarm_size: swarm,
|
||
generations: gens,
|
||
inertia: 0.7,
|
||
cognitive: 1.5,
|
||
social: 1.5,
|
||
seed,
|
||
};
|
||
let mut opt = ParticleSwarm::new(config, bounds);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn rastrigin_cma_es(seed: u64) -> SoRun {
|
||
let problem = Rastrigin { dim: RASTRIGIN_DIM };
|
||
let bounds = RealBounds::new(vec![(-5.12, 5.12); RASTRIGIN_DIM]);
|
||
let pop = 16;
|
||
let gens = RASTRIGIN_BUDGET / pop;
|
||
let config = CmaEsConfig {
|
||
population_size: pop,
|
||
generations: gens,
|
||
initial_sigma: 1.0,
|
||
eigen_decomposition_period: 1,
|
||
initial_mean: None,
|
||
seed,
|
||
};
|
||
let mut opt = CmaEs::new(config, bounds);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn rastrigin_ipop_cma_es(seed: u64) -> SoRun {
|
||
let problem = Rastrigin { dim: RASTRIGIN_DIM };
|
||
let bounds = RealBounds::new(vec![(-5.12, 5.12); RASTRIGIN_DIM]);
|
||
let pop = 16;
|
||
let config = IpopCmaEsConfig {
|
||
initial_population_size: pop,
|
||
total_generations: RASTRIGIN_BUDGET / pop,
|
||
initial_sigma: 1.0,
|
||
eigen_decomposition_period: 1,
|
||
stall_generations: None,
|
||
seed,
|
||
};
|
||
let mut opt = IpopCmaEs::new(config, bounds);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn rastrigin_one_plus_one_es(seed: u64) -> SoRun {
|
||
let problem = Rastrigin { dim: RASTRIGIN_DIM };
|
||
let bounds = RealBounds::new(vec![(-5.12, 5.12); RASTRIGIN_DIM]);
|
||
let config = OnePlusOneEsConfig {
|
||
iterations: RASTRIGIN_BUDGET,
|
||
initial_sigma: 1.0,
|
||
adaptation_period: 50,
|
||
step_increase: 1.22,
|
||
seed,
|
||
};
|
||
let mut opt = OnePlusOneEs::new(config, bounds);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn rosenbrock_nelder_mead(_seed: u64) -> SoRun {
|
||
let problem = rosenbrock_problem();
|
||
let bounds = RealBounds::new(vec![(-5.0, 10.0); ROSENBROCK_DIM]);
|
||
let config = NelderMeadConfig {
|
||
iterations: ROSENBROCK_BUDGET / 4,
|
||
..NelderMeadConfig::default()
|
||
};
|
||
let mut opt = NelderMead::new(config, bounds);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn rosenbrock_one_plus_one_es(seed: u64) -> SoRun {
|
||
let problem = rosenbrock_problem();
|
||
let bounds = RealBounds::new(vec![(-5.0, 10.0); ROSENBROCK_DIM]);
|
||
let config = OnePlusOneEsConfig {
|
||
iterations: ROSENBROCK_BUDGET,
|
||
initial_sigma: 1.0,
|
||
adaptation_period: 30,
|
||
step_increase: 1.22,
|
||
seed,
|
||
};
|
||
let mut opt = OnePlusOneEs::new(config, bounds);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn rosenbrock_bo(seed: u64) -> SoRun {
|
||
let problem = rosenbrock_problem();
|
||
let bounds = RealBounds::new(vec![(-5.0, 10.0); ROSENBROCK_DIM]);
|
||
let config = BayesianOptConfig {
|
||
initial_samples: 10,
|
||
iterations: 50,
|
||
length_scales: None,
|
||
signal_variance: 1.0,
|
||
noise_variance: 1e-6,
|
||
acquisition_samples: 1_000,
|
||
seed,
|
||
};
|
||
let mut opt = BayesianOpt::new(config, bounds);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn ackley_bo(seed: u64) -> SoRun {
|
||
let problem = ackley_problem();
|
||
let bounds = RealBounds::new(vec![(-32.768, 32.768); ACKLEY_DIM]);
|
||
let config = BayesianOptConfig {
|
||
initial_samples: 10,
|
||
iterations: 50,
|
||
length_scales: None,
|
||
signal_variance: 1.0,
|
||
noise_variance: 1e-6,
|
||
acquisition_samples: 1_000,
|
||
seed,
|
||
};
|
||
let mut opt = BayesianOpt::new(config, bounds);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
// -----------------------------------------------------------------------------
|
||
// Rosenbrock + Ackley runners (a curated SO subset on each)
|
||
// -----------------------------------------------------------------------------
|
||
|
||
fn rosenbrock_problem() -> Rosenbrock {
|
||
Rosenbrock {
|
||
dim: ROSENBROCK_DIM,
|
||
}
|
||
}
|
||
fn ackley_problem() -> Ackley {
|
||
Ackley { dim: ACKLEY_DIM }
|
||
}
|
||
|
||
macro_rules! so_run_de {
|
||
($problem_expr:expr, $dim:expr, $bounds_lo:expr, $bounds_hi:expr, $budget:expr, $seed:expr) => {{
|
||
let problem = $problem_expr;
|
||
let bounds = RealBounds::new(vec![($bounds_lo, $bounds_hi); $dim]);
|
||
let pop = 50;
|
||
let gens = ($budget - pop) / pop;
|
||
let config = DifferentialEvolutionConfig {
|
||
population_size: pop,
|
||
generations: gens,
|
||
differential_weight: 0.5,
|
||
crossover_probability: 0.9,
|
||
seed: $seed,
|
||
};
|
||
let mut opt = DifferentialEvolution::new(config, bounds);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}};
|
||
}
|
||
|
||
macro_rules! so_run_cma {
|
||
($problem_expr:expr, $dim:expr, $bounds_lo:expr, $bounds_hi:expr, $budget:expr, $seed:expr) => {{
|
||
let problem = $problem_expr;
|
||
let bounds = RealBounds::new(vec![($bounds_lo, $bounds_hi); $dim]);
|
||
let pop = 16;
|
||
let config = CmaEsConfig {
|
||
population_size: pop,
|
||
generations: $budget / pop,
|
||
initial_sigma: 1.0,
|
||
eigen_decomposition_period: 1,
|
||
initial_mean: None,
|
||
seed: $seed,
|
||
};
|
||
let mut opt = CmaEs::new(config, bounds);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}};
|
||
}
|
||
|
||
macro_rules! so_run_pso {
|
||
($problem_expr:expr, $dim:expr, $bounds_lo:expr, $bounds_hi:expr, $budget:expr, $seed:expr) => {{
|
||
let problem = $problem_expr;
|
||
let bounds = RealBounds::new(vec![($bounds_lo, $bounds_hi); $dim]);
|
||
let swarm = 40;
|
||
let config = ParticleSwarmConfig {
|
||
swarm_size: swarm,
|
||
generations: ($budget - 2 * swarm) / swarm,
|
||
inertia: 0.7,
|
||
cognitive: 1.5,
|
||
social: 1.5,
|
||
seed: $seed,
|
||
};
|
||
let mut opt = ParticleSwarm::new(config, bounds);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}};
|
||
}
|
||
|
||
macro_rules! so_run_tlbo {
|
||
($problem_expr:expr, $dim:expr, $bounds_lo:expr, $bounds_hi:expr, $budget:expr, $seed:expr) => {{
|
||
let problem = $problem_expr;
|
||
let bounds = RealBounds::new(vec![($bounds_lo, $bounds_hi); $dim]);
|
||
let pop = 30;
|
||
// TLBO does ~2N evaluations per generation.
|
||
let gens = ($budget - pop) / (2 * pop);
|
||
let config = TlboConfig {
|
||
population_size: pop,
|
||
generations: gens,
|
||
seed: $seed,
|
||
};
|
||
let mut opt = Tlbo::new(config, bounds);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}};
|
||
}
|
||
|
||
fn rosenbrock_de(seed: u64) -> SoRun {
|
||
so_run_de!(
|
||
rosenbrock_problem(),
|
||
ROSENBROCK_DIM,
|
||
-5.0,
|
||
10.0,
|
||
ROSENBROCK_BUDGET,
|
||
seed
|
||
)
|
||
}
|
||
fn rosenbrock_cma(seed: u64) -> SoRun {
|
||
so_run_cma!(
|
||
rosenbrock_problem(),
|
||
ROSENBROCK_DIM,
|
||
-5.0,
|
||
10.0,
|
||
ROSENBROCK_BUDGET,
|
||
seed
|
||
)
|
||
}
|
||
fn rosenbrock_pso(seed: u64) -> SoRun {
|
||
so_run_pso!(
|
||
rosenbrock_problem(),
|
||
ROSENBROCK_DIM,
|
||
-5.0,
|
||
10.0,
|
||
ROSENBROCK_BUDGET,
|
||
seed
|
||
)
|
||
}
|
||
fn rosenbrock_tlbo(seed: u64) -> SoRun {
|
||
so_run_tlbo!(
|
||
rosenbrock_problem(),
|
||
ROSENBROCK_DIM,
|
||
-5.0,
|
||
10.0,
|
||
ROSENBROCK_BUDGET,
|
||
seed
|
||
)
|
||
}
|
||
|
||
fn ackley_de(seed: u64) -> SoRun {
|
||
so_run_de!(
|
||
ackley_problem(),
|
||
ACKLEY_DIM,
|
||
-32.768,
|
||
32.768,
|
||
ACKLEY_BUDGET,
|
||
seed
|
||
)
|
||
}
|
||
fn ackley_cma(seed: u64) -> SoRun {
|
||
so_run_cma!(
|
||
ackley_problem(),
|
||
ACKLEY_DIM,
|
||
-32.768,
|
||
32.768,
|
||
ACKLEY_BUDGET,
|
||
seed
|
||
)
|
||
}
|
||
fn ackley_pso(seed: u64) -> SoRun {
|
||
so_run_pso!(
|
||
ackley_problem(),
|
||
ACKLEY_DIM,
|
||
-32.768,
|
||
32.768,
|
||
ACKLEY_BUDGET,
|
||
seed
|
||
)
|
||
}
|
||
fn ackley_tlbo(seed: u64) -> SoRun {
|
||
so_run_tlbo!(
|
||
ackley_problem(),
|
||
ACKLEY_DIM,
|
||
-32.768,
|
||
32.768,
|
||
ACKLEY_BUDGET,
|
||
seed
|
||
)
|
||
}
|
||
|
||
// -----------------------------------------------------------------------------
|
||
// ZDT3 runners (curated MO subset)
|
||
// -----------------------------------------------------------------------------
|
||
|
||
fn zdt3_problem() -> Zdt3 {
|
||
Zdt3 { dim: ZDT3_DIM }
|
||
}
|
||
|
||
fn zdt3_nsga2(seed: u64) -> MoRun {
|
||
let problem = zdt3_problem();
|
||
let bounds = vec![(0.0, 1.0); ZDT3_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / ZDT3_DIM as f64),
|
||
};
|
||
let pop = 100;
|
||
let config = Nsga2Config {
|
||
population_size: pop,
|
||
generations: ZDT3_BUDGET / pop,
|
||
seed,
|
||
};
|
||
let mut opt = Nsga2::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn zdt3_moead(seed: u64) -> MoRun {
|
||
let problem = zdt3_problem();
|
||
let bounds = vec![(0.0, 1.0); ZDT3_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / ZDT3_DIM as f64),
|
||
};
|
||
let pop = 100;
|
||
let config = MoeadConfig {
|
||
generations: (ZDT3_BUDGET - pop) / pop,
|
||
reference_divisions: 99,
|
||
neighborhood_size: 20,
|
||
seed,
|
||
};
|
||
let mut opt = Moead::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn zdt3_ibea(seed: u64) -> MoRun {
|
||
let problem = zdt3_problem();
|
||
let bounds = vec![(0.0, 1.0); ZDT3_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / ZDT3_DIM as f64),
|
||
};
|
||
let pop = 100;
|
||
let config = IbeaConfig {
|
||
population_size: pop,
|
||
generations: ZDT3_BUDGET / pop,
|
||
kappa: 0.05,
|
||
seed,
|
||
};
|
||
let mut opt = Ibea::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn zdt3_age_moea(seed: u64) -> MoRun {
|
||
let problem = zdt3_problem();
|
||
let bounds = vec![(0.0, 1.0); ZDT3_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / ZDT3_DIM as f64),
|
||
};
|
||
let pop = 100;
|
||
let config = AgeMoeaConfig {
|
||
population_size: pop,
|
||
generations: ZDT3_BUDGET / pop,
|
||
seed,
|
||
};
|
||
let mut opt = AgeMoea::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn zdt3_knea(seed: u64) -> MoRun {
|
||
let problem = zdt3_problem();
|
||
let bounds = vec![(0.0, 1.0); ZDT3_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 15.0, 0.5),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / ZDT3_DIM as f64),
|
||
};
|
||
let pop = 100;
|
||
let config = KneaConfig {
|
||
population_size: pop,
|
||
generations: ZDT3_BUDGET / pop,
|
||
seed,
|
||
};
|
||
let mut opt = Knea::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
// -----------------------------------------------------------------------------
|
||
// DTLZ1 runners (curated many-obj subset)
|
||
// -----------------------------------------------------------------------------
|
||
|
||
fn dtlz1_problem() -> Dtlz1 {
|
||
Dtlz1 {
|
||
num_objectives: DTLZ1_OBJECTIVES,
|
||
dim: DTLZ1_DIM,
|
||
}
|
||
}
|
||
|
||
fn dtlz1_nsga3(seed: u64) -> MoRun {
|
||
let problem = dtlz1_problem();
|
||
let bounds = vec![(0.0, 1.0); DTLZ1_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ1_DIM as f64),
|
||
};
|
||
let pop = 92;
|
||
let config = Nsga3Config {
|
||
population_size: pop,
|
||
generations: DTLZ1_BUDGET / pop,
|
||
reference_divisions: 12,
|
||
seed,
|
||
};
|
||
let mut opt = Nsga3::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn dtlz1_moead(seed: u64) -> MoRun {
|
||
let problem = dtlz1_problem();
|
||
let bounds = vec![(0.0, 1.0); DTLZ1_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ1_DIM as f64),
|
||
};
|
||
let pop = 91;
|
||
let config = MoeadConfig {
|
||
generations: (DTLZ1_BUDGET - pop) / pop,
|
||
reference_divisions: 12,
|
||
neighborhood_size: 20,
|
||
seed,
|
||
};
|
||
let mut opt = Moead::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn dtlz1_age_moea(seed: u64) -> MoRun {
|
||
let problem = dtlz1_problem();
|
||
let bounds = vec![(0.0, 1.0); DTLZ1_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ1_DIM as f64),
|
||
};
|
||
let pop = 92;
|
||
let config = AgeMoeaConfig {
|
||
population_size: pop,
|
||
generations: DTLZ1_BUDGET / pop,
|
||
seed,
|
||
};
|
||
let mut opt = AgeMoea::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn dtlz1_grea(seed: u64) -> MoRun {
|
||
let problem = dtlz1_problem();
|
||
let bounds = vec![(0.0, 1.0); DTLZ1_DIM];
|
||
let initializer = RealBounds::new(bounds.clone());
|
||
let variation = CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(bounds.clone(), 30.0, 1.0),
|
||
mutation: PolynomialMutation::new(bounds, 20.0, 1.0 / DTLZ1_DIM as f64),
|
||
};
|
||
let pop = 92;
|
||
let config = GreaConfig {
|
||
population_size: pop,
|
||
generations: DTLZ1_BUDGET / pop,
|
||
grid_divisions: 8,
|
||
seed,
|
||
};
|
||
let mut opt = Grea::new(config, initializer, variation);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
/// Mean L2 distance from each front point to the analytical DTLZ1 front
|
||
/// (`Σf_i = 0.5`, all `f_i ≥ 0`). Closed-form: signed distance from the
|
||
/// hyperplane projected to non-negative.
|
||
fn mean_distance_to_dtlz1_front(front: &[Candidate<Vec<f64>>]) -> f64 {
|
||
if front.is_empty() {
|
||
return f64::INFINITY;
|
||
}
|
||
let total: f64 = front
|
||
.iter()
|
||
.map(|c| {
|
||
let s: f64 = c.evaluation.objectives.iter().sum();
|
||
(s - 0.5).abs()
|
||
})
|
||
.sum();
|
||
total / front.len() as f64
|
||
}
|
||
|
||
// -----------------------------------------------------------------------------
|
||
// Main
|
||
// -----------------------------------------------------------------------------
|
||
|
||
fn run_zdt1_comparison() {
|
||
println!("== ZDT1 (dim={ZDT1_DIM}, {ZDT1_BUDGET} evals/run × {SEEDS} seeds) ==");
|
||
println!("Zitzler-Deb-Thiele 2-objective benchmark: {ZDT1_DIM} real variables, one smooth");
|
||
println!("convex Pareto front f2 = 1 - sqrt(f1). Hard because 29 of 30 variables must");
|
||
println!("collapse to 0 before the front is even reachable, and only then can the");
|
||
println!("population spread along it. Optimum: mean L2 -> 0 (the front is known exactly).");
|
||
println!("sorted best-first by hypervolume (higher better; spacing / mean L2 lower better)");
|
||
println!();
|
||
|
||
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),
|
||
("MOPSO", zdt1_mopso),
|
||
("SPEA2", zdt1_spea2),
|
||
("PESA-II", zdt1_pesa2),
|
||
("eps-MOEA", zdt1_epsilon_moea),
|
||
("IBEA", zdt1_ibea),
|
||
("HypE", zdt1_hype),
|
||
("SMS-EMOA", zdt1_sms_emoa),
|
||
("RVEA", zdt1_rvea),
|
||
("NSGA-II", zdt1_nsga2),
|
||
("NSGA-III", zdt1_nsga3),
|
||
("MOEA/D", zdt1_moead),
|
||
];
|
||
|
||
let mut rows: Vec<(f64, Vec<String>)> = Vec::new();
|
||
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);
|
||
|
||
rows.push((
|
||
hv_m,
|
||
vec![
|
||
name.to_string(),
|
||
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}"),
|
||
],
|
||
));
|
||
}
|
||
// Higher hypervolume is better.
|
||
rows.sort_by(|a, b| b.0.partial_cmp(&a.0).unwrap_or(std::cmp::Ordering::Equal));
|
||
let table: Vec<Vec<String>> = rows.into_iter().map(|(_, r)| r).collect();
|
||
print_table(
|
||
&[
|
||
"algorithm",
|
||
"hypervolume",
|
||
"spacing",
|
||
"mean L2",
|
||
"front",
|
||
"ms",
|
||
],
|
||
&table,
|
||
);
|
||
}
|
||
|
||
fn run_dtlz2_comparison() {
|
||
println!();
|
||
println!("== DTLZ2 (3-obj, dim={DTLZ2_DIM}, {DTLZ2_BUDGET} evals/run × {SEEDS} seeds) ==");
|
||
println!("Deb-Thiele-Laumanns-Zitzler 3-objective; the Pareto front is the unit-sphere");
|
||
println!("octant (Σf² = 1, all f >= 0) -- a curved 2-D surface embedded in 3-D objective");
|
||
println!("space. Hard because crowding/spacing must work in a higher dimension.");
|
||
println!("'mean dist' = |‖f‖ - 1|, so 0 means perfectly on the sphere (the known optimum).");
|
||
println!("sorted best-first by mean dist (lower is better)");
|
||
println!();
|
||
|
||
let dtlz2 = dtlz2_problem();
|
||
let dtlz2_objs = dtlz2.objectives();
|
||
|
||
type Runner = fn(u64) -> MoRun;
|
||
let runners: &[(&str, Runner)] = &[
|
||
("RandomSearch", dtlz2_random),
|
||
("MOPSO", dtlz2_mopso),
|
||
("NSGA-II", dtlz2_nsga2),
|
||
("SPEA2", dtlz2_spea2),
|
||
("PESA-II", dtlz2_pesa2),
|
||
("eps-MOEA", dtlz2_epsilon_moea),
|
||
("IBEA", dtlz2_ibea),
|
||
("HypE", dtlz2_hype),
|
||
("SMS-EMOA", dtlz2_sms_emoa),
|
||
("RVEA", dtlz2_rvea),
|
||
("NSGA-III", dtlz2_nsga3),
|
||
("MOEA/D", dtlz2_moead),
|
||
];
|
||
|
||
let mut rows: Vec<(f64, Vec<String>)> = Vec::new();
|
||
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);
|
||
|
||
rows.push((
|
||
d_m,
|
||
vec![
|
||
name.to_string(),
|
||
format!("{d_m:.4}+/-{d_s:.4}"),
|
||
format!("{sp_m:.4}+/-{sp_s:.4}"),
|
||
format!("{fs_m:.0}"),
|
||
format!("{ms_m:.0}"),
|
||
],
|
||
));
|
||
}
|
||
// Lower mean distance to the true front is better.
|
||
rows.sort_by(|a, b| a.0.partial_cmp(&b.0).unwrap_or(std::cmp::Ordering::Equal));
|
||
let table: Vec<Vec<String>> = rows.into_iter().map(|(_, r)| r).collect();
|
||
print_table(
|
||
&["algorithm", "mean dist", "spacing", "front", "ms"],
|
||
&table,
|
||
);
|
||
}
|
||
|
||
fn run_rastrigin_comparison() {
|
||
println!();
|
||
println!("== Rastrigin (dim={RASTRIGIN_DIM}, {RASTRIGIN_BUDGET} evals/run × {SEEDS} seeds) ==");
|
||
println!(
|
||
"Highly multimodal trap: f = 10n + Σ(x_i² - 10·cos(2π·x_i)), {RASTRIGIN_DIM} dimensions."
|
||
);
|
||
println!(
|
||
"Hard because a near-quadratic global bowl is overlaid with ~10^{RASTRIGIN_DIM} regularly"
|
||
);
|
||
println!("spaced local minima -- any greedy step lands in the nearest dimple.");
|
||
println!("Global optimum: f = 0 at the origin.");
|
||
println!("sorted best-first (lower is better)");
|
||
println!();
|
||
|
||
type Runner = fn(u64) -> SoRun;
|
||
let runners: &[(&str, Runner)] = &[
|
||
("RandomSearch", rastrigin_random),
|
||
("HillClimber", rastrigin_hill_climber),
|
||
("(1+1)-ES", rastrigin_one_plus_one_es),
|
||
("SimulatedAnneal", rastrigin_simulated_annealing),
|
||
("PAES", rastrigin_paes),
|
||
("GA", rastrigin_genetic_algorithm),
|
||
("PSO", rastrigin_particle_swarm),
|
||
("NSGA-II", rastrigin_nsga2),
|
||
("DE", rastrigin_de),
|
||
("CMA-ES", rastrigin_cma_es),
|
||
("IPOP-CMA-ES", rastrigin_ipop_cma_es),
|
||
];
|
||
|
||
let mut rows: Vec<(f64, Vec<String>)> = Vec::new();
|
||
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);
|
||
|
||
rows.push((
|
||
b_m,
|
||
vec![
|
||
name.to_string(),
|
||
format!("{b_m:.4e} +/- {b_s:.2e}"),
|
||
format!("{ms_m:.0}"),
|
||
],
|
||
));
|
||
}
|
||
// Lower best f is better.
|
||
rows.sort_by(|a, b| a.0.partial_cmp(&b.0).unwrap_or(std::cmp::Ordering::Equal));
|
||
let table: Vec<Vec<String>> = rows.into_iter().map(|(_, r)| r).collect();
|
||
print_table(&["algorithm", "best f", "ms"], &table);
|
||
}
|
||
|
||
fn run_rosenbrock_comparison() {
|
||
println!();
|
||
println!("== Rosenbrock (dim={ROSENBROCK_DIM}, {ROSENBROCK_BUDGET} evals × {SEEDS} seeds) ==");
|
||
println!(
|
||
"Rosenbrock's banana valley: f = Σ(100·(x_{{i+1}} - x_i²)² + (1 - x_i)²), {ROSENBROCK_DIM} dims."
|
||
);
|
||
println!("Hard because the minimum sits in a long, bent, near-flat valley -- easy to enter,");
|
||
println!("very slow to crawl along to the tip. Global optimum: f = 0 at the all-ones point.");
|
||
println!("sorted best-first (lower is better)");
|
||
println!();
|
||
type Runner = fn(u64) -> SoRun;
|
||
let runners: &[(&str, Runner)] = &[
|
||
("DE", rosenbrock_de),
|
||
("PSO", rosenbrock_pso),
|
||
("CMA-ES", rosenbrock_cma),
|
||
("TLBO", rosenbrock_tlbo),
|
||
("(1+1)-ES", rosenbrock_one_plus_one_es),
|
||
("Nelder-Mead", rosenbrock_nelder_mead),
|
||
("BO (60 evals)", rosenbrock_bo),
|
||
];
|
||
let mut rows: Vec<(f64, Vec<String>)> = Vec::new();
|
||
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);
|
||
rows.push((
|
||
b_m,
|
||
vec![
|
||
name.to_string(),
|
||
format!("{b_m:.4e} +/- {b_s:.2e}"),
|
||
format!("{ms_m:.0}"),
|
||
],
|
||
));
|
||
}
|
||
rows.sort_by(|a, b| a.0.partial_cmp(&b.0).unwrap_or(std::cmp::Ordering::Equal));
|
||
let table: Vec<Vec<String>> = rows.into_iter().map(|(_, r)| r).collect();
|
||
print_table(&["algorithm", "best f", "ms"], &table);
|
||
}
|
||
|
||
fn run_ackley_comparison() {
|
||
println!();
|
||
println!("== Ackley (dim={ACKLEY_DIM}, {ACKLEY_BUDGET} evals × {SEEDS} seeds) ==");
|
||
println!("Ackley's function: a near-flat outer plateau with shallow ripples surrounding a");
|
||
println!(
|
||
"single deep, narrow global basin, {ACKLEY_DIM} dimensions. Hard because the gradient is"
|
||
);
|
||
println!("almost zero far from the optimum, giving local search little to follow.");
|
||
println!("Global optimum: f = 0 at the origin.");
|
||
println!("sorted best-first (lower is better)");
|
||
println!();
|
||
type Runner = fn(u64) -> SoRun;
|
||
let runners: &[(&str, Runner)] = &[
|
||
("DE", ackley_de),
|
||
("PSO", ackley_pso),
|
||
("CMA-ES", ackley_cma),
|
||
("TLBO", ackley_tlbo),
|
||
("BO (60 evals)", ackley_bo),
|
||
];
|
||
let mut rows: Vec<(f64, Vec<String>)> = Vec::new();
|
||
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);
|
||
rows.push((
|
||
b_m,
|
||
vec![
|
||
name.to_string(),
|
||
format!("{b_m:.4e} +/- {b_s:.2e}"),
|
||
format!("{ms_m:.0}"),
|
||
],
|
||
));
|
||
}
|
||
rows.sort_by(|a, b| a.0.partial_cmp(&b.0).unwrap_or(std::cmp::Ordering::Equal));
|
||
let table: Vec<Vec<String>> = rows.into_iter().map(|(_, r)| r).collect();
|
||
print_table(&["algorithm", "best f", "ms"], &table);
|
||
}
|
||
|
||
fn run_zdt3_comparison() {
|
||
println!();
|
||
println!("== ZDT3 (dim={ZDT3_DIM}, {ZDT3_BUDGET} evals × {SEEDS} seeds) ==");
|
||
println!("Zitzler-Deb-Thiele 2-objective with a DISCONNECTED front: five separate arcs");
|
||
println!("rather than one curve. Hard because an algorithm has to discover and populate");
|
||
println!("every arc while not stranding solutions in the dominated gaps between them.");
|
||
println!("Optimum: cover all five arcs; scored by hypervolume vs [11, 11].");
|
||
println!("sorted best-first by hypervolume (higher better; spacing lower better)");
|
||
println!();
|
||
let problem = zdt3_problem();
|
||
let objs = problem.objectives();
|
||
type Runner = fn(u64) -> MoRun;
|
||
let runners: &[(&str, Runner)] = &[
|
||
("NSGA-II", zdt3_nsga2),
|
||
("MOEA/D", zdt3_moead),
|
||
("IBEA", zdt3_ibea),
|
||
("AGE-MOEA", zdt3_age_moea),
|
||
("KnEA", zdt3_knea),
|
||
];
|
||
let mut rows: Vec<(f64, Vec<String>)> = Vec::new();
|
||
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, &objs, ZDT3_REFERENCE))
|
||
.collect();
|
||
let sp: Vec<f64> = runs.iter().map(|r| spacing(&r.front, &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 (hv_m, hv_s) = mean_std(&hv);
|
||
let (sp_m, sp_s) = mean_std(&sp);
|
||
let (fs_m, _) = mean_std(&fs);
|
||
let (ms_m, _) = mean_std(&ms);
|
||
rows.push((
|
||
hv_m,
|
||
vec![
|
||
name.to_string(),
|
||
format!("{hv_m:.4}+/-{hv_s:.4}"),
|
||
format!("{sp_m:.4}+/-{sp_s:.4}"),
|
||
format!("{fs_m:.0}"),
|
||
format!("{ms_m:.0}"),
|
||
],
|
||
));
|
||
}
|
||
rows.sort_by(|a, b| b.0.partial_cmp(&a.0).unwrap_or(std::cmp::Ordering::Equal));
|
||
let table: Vec<Vec<String>> = rows.into_iter().map(|(_, r)| r).collect();
|
||
print_table(
|
||
&["algorithm", "hypervolume", "spacing", "front", "ms"],
|
||
&table,
|
||
);
|
||
}
|
||
|
||
fn run_dtlz1_comparison() {
|
||
println!();
|
||
println!("== DTLZ1 (3-obj, dim={DTLZ1_DIM}, {DTLZ1_BUDGET} evals × {SEEDS} seeds) ==");
|
||
println!("Deb-Thiele-Laumanns-Zitzler 3-objective; the Pareto front is the linear simplex");
|
||
println!("Σf = 0.5 in the positive octant. Hard because a deceptive multimodal 'g' term");
|
||
println!("riddles the approach with a huge number of local fronts -- only fully-converged");
|
||
println!("runs land on the simplex. Optimum: mean dist -> 0.");
|
||
println!("sorted best-first by mean dist (lower is better)");
|
||
println!();
|
||
let problem = dtlz1_problem();
|
||
let objs = problem.objectives();
|
||
type Runner = fn(u64) -> MoRun;
|
||
let runners: &[(&str, Runner)] = &[
|
||
("NSGA-III", dtlz1_nsga3),
|
||
("MOEA/D", dtlz1_moead),
|
||
("AGE-MOEA", dtlz1_age_moea),
|
||
("GrEA", dtlz1_grea),
|
||
];
|
||
let mut rows: Vec<(f64, Vec<String>)> = Vec::new();
|
||
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_dtlz1_front(&r.front))
|
||
.collect();
|
||
let sp: Vec<f64> = runs.iter().map(|r| spacing(&r.front, &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);
|
||
rows.push((
|
||
d_m,
|
||
vec![
|
||
name.to_string(),
|
||
format!("{d_m:.4}+/-{d_s:.4}"),
|
||
format!("{sp_m:.4}+/-{sp_s:.4}"),
|
||
format!("{fs_m:.0}"),
|
||
format!("{ms_m:.0}"),
|
||
],
|
||
));
|
||
}
|
||
rows.sort_by(|a, b| a.0.partial_cmp(&b.0).unwrap_or(std::cmp::Ordering::Equal));
|
||
let table: Vec<Vec<String>> = rows.into_iter().map(|(_, r)| r).collect();
|
||
print_table(
|
||
&["algorithm", "mean dist", "spacing", "front", "ms"],
|
||
&table,
|
||
);
|
||
}
|
||
|
||
// =============================================================================
|
||
// Combinatorial / sequencing problems
|
||
//
|
||
// These use a different decision encoding — `Vec<usize>` permutations and
|
||
// `Vec<bool>` bitstrings — than the continuous problems above, so the
|
||
// applicable-algorithm roster differs: the real-vector methods (CMA-ES, DE,
|
||
// PSO, …) cannot run here, while permutation-native methods (Ant Colony,
|
||
// Tabu Search) and the EDA-style ones can.
|
||
// =============================================================================
|
||
|
||
const TSP_CITIES: usize = 15;
|
||
const TSP_BUDGET: usize = 8_000;
|
||
const JSS_BUDGET: usize = 8_000;
|
||
const KNAPSACK_BUDGET: usize = 20_000;
|
||
|
||
// ---- Single-objective TSP: a regular polygon on the unit circle -------------
|
||
|
||
/// `TSP_CITIES` points equally spaced on the unit circle. The optimal tour
|
||
/// just visits them in angular order; its length is the regular-polygon
|
||
/// perimeter `2·n·sin(π/n)`, which gives an exact known-best baseline.
|
||
struct RingTsp {
|
||
distances: Vec<Vec<f64>>,
|
||
}
|
||
impl RingTsp {
|
||
fn new() -> Self {
|
||
let pts: Vec<(f64, f64)> = (0..TSP_CITIES)
|
||
.map(|i| {
|
||
let a = 2.0 * PI * (i as f64) / (TSP_CITIES as f64);
|
||
(a.cos(), a.sin())
|
||
})
|
||
.collect();
|
||
let distances = (0..TSP_CITIES)
|
||
.map(|i| {
|
||
(0..TSP_CITIES)
|
||
.map(|j| {
|
||
let (xi, yi) = pts[i];
|
||
let (xj, yj) = pts[j];
|
||
((xi - xj).powi(2) + (yi - yj).powi(2)).sqrt()
|
||
})
|
||
.collect()
|
||
})
|
||
.collect();
|
||
Self { distances }
|
||
}
|
||
/// Known optimal tour length — the regular-polygon perimeter.
|
||
fn optimal_length() -> f64 {
|
||
2.0 * TSP_CITIES as f64 * (PI / TSP_CITIES as f64).sin()
|
||
}
|
||
}
|
||
impl Problem for RingTsp {
|
||
type Decision = Vec<usize>;
|
||
fn objectives(&self) -> ObjectiveSpace {
|
||
ObjectiveSpace::new(vec![Objective::minimize("tour_length")])
|
||
}
|
||
fn evaluate(&self, tour: &Vec<usize>) -> Evaluation {
|
||
let n = tour.len();
|
||
let mut total = 0.0;
|
||
for i in 0..n {
|
||
total += self.distances[tour[i]][tour[(i + 1) % n]];
|
||
}
|
||
Evaluation::new(vec![total])
|
||
}
|
||
}
|
||
|
||
fn tsp_random(seed: u64) -> SoRun {
|
||
let problem = RingTsp::new();
|
||
let mut opt = RandomSearch::new(
|
||
RandomSearchConfig {
|
||
iterations: TSP_BUDGET,
|
||
batch_size: 1,
|
||
seed,
|
||
},
|
||
ShuffledPermutation { n: TSP_CITIES },
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn tsp_hill_climber(seed: u64) -> SoRun {
|
||
let problem = RingTsp::new();
|
||
let mut opt = HillClimber::new(
|
||
HillClimberConfig {
|
||
iterations: TSP_BUDGET,
|
||
seed,
|
||
},
|
||
ShuffledPermutation { n: TSP_CITIES },
|
||
InversionMutation,
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn tsp_simulated_annealing(seed: u64) -> SoRun {
|
||
let problem = RingTsp::new();
|
||
let mut opt = SimulatedAnnealing::new(
|
||
SimulatedAnnealingConfig {
|
||
iterations: TSP_BUDGET,
|
||
initial_temperature: 1.0,
|
||
final_temperature: 1e-3,
|
||
seed,
|
||
},
|
||
ShuffledPermutation { n: TSP_CITIES },
|
||
InversionMutation,
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn tsp_tabu_search(seed: u64) -> SoRun {
|
||
let problem = RingTsp::new();
|
||
// Each step considers 16 inversion (2-opt-style) neighbours.
|
||
let neighbors = |tour: &Vec<usize>, rng: &mut Rng| {
|
||
let mut m = InversionMutation;
|
||
(0..16)
|
||
.map(|_| m.vary(std::slice::from_ref(tour), rng).pop().unwrap())
|
||
.collect()
|
||
};
|
||
let mut opt = TabuSearch::new(
|
||
TabuSearchConfig {
|
||
iterations: TSP_BUDGET / 16,
|
||
tabu_tenure: 20,
|
||
seed,
|
||
},
|
||
ShuffledPermutation { n: TSP_CITIES },
|
||
neighbors,
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn tsp_genetic_algorithm(seed: u64) -> SoRun {
|
||
let problem = RingTsp::new();
|
||
let mut opt = GeneticAlgorithm::new(
|
||
GeneticAlgorithmConfig {
|
||
population_size: 80,
|
||
generations: TSP_BUDGET / 80,
|
||
tournament_size: 3,
|
||
elitism: 2,
|
||
seed,
|
||
},
|
||
ShuffledPermutation { n: TSP_CITIES },
|
||
CompositeVariation {
|
||
crossover: OrderCrossover,
|
||
mutation: InversionMutation,
|
||
},
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn tsp_ant_colony(seed: u64) -> SoRun {
|
||
let problem = RingTsp::new();
|
||
let distances = problem.distances.clone();
|
||
let mut opt = AntColonyTsp::new(
|
||
AntColonyTspConfig {
|
||
ants: 20,
|
||
generations: TSP_BUDGET / 20,
|
||
alpha: 1.0,
|
||
beta: 3.0,
|
||
evaporation: 0.5,
|
||
deposit: 1.0,
|
||
initial_pheromone: 1.0,
|
||
seed,
|
||
},
|
||
distances,
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
// ---- Single-objective job-shop scheduling: Fisher & Thompson FT06 -----------
|
||
|
||
const JSS_JOBS: usize = 6;
|
||
const JSS_MACHINES: usize = 6;
|
||
|
||
/// FT06 routing — machine id of the k-th operation of job j.
|
||
const FT06_MACHINE: [[usize; JSS_MACHINES]; JSS_JOBS] = [
|
||
[2, 0, 1, 3, 5, 4],
|
||
[1, 2, 4, 5, 0, 3],
|
||
[2, 3, 5, 0, 1, 4],
|
||
[1, 0, 2, 3, 4, 5],
|
||
[2, 1, 4, 5, 0, 3],
|
||
[1, 3, 5, 0, 4, 2],
|
||
];
|
||
/// FT06 processing times — duration of the k-th operation of job j.
|
||
const FT06_TIME: [[f64; JSS_MACHINES]; JSS_JOBS] = [
|
||
[1.0, 3.0, 6.0, 7.0, 3.0, 6.0],
|
||
[8.0, 5.0, 10.0, 10.0, 10.0, 4.0],
|
||
[5.0, 4.0, 8.0, 9.0, 1.0, 7.0],
|
||
[5.0, 5.0, 5.0, 3.0, 8.0, 9.0],
|
||
[9.0, 3.0, 5.0, 4.0, 3.0, 1.0],
|
||
[3.0, 3.0, 9.0, 10.0, 4.0, 1.0],
|
||
];
|
||
/// FT06's optimal makespan is a long-settled benchmark value.
|
||
const FT06_OPTIMAL_MAKESPAN: f64 = 55.0;
|
||
|
||
/// FT06 job-shop, makespan objective. Operation-string encoding: a length-36
|
||
/// multiset where job id `j` appears `JSS_MACHINES` times; the k-th
|
||
/// occurrence of `j` is its k-th operation.
|
||
struct Ft06Makespan;
|
||
impl Problem for Ft06Makespan {
|
||
type Decision = Vec<usize>;
|
||
fn objectives(&self) -> ObjectiveSpace {
|
||
ObjectiveSpace::new(vec![Objective::minimize("makespan")])
|
||
}
|
||
fn evaluate(&self, schedule: &Vec<usize>) -> Evaluation {
|
||
let mut job_next = [0_usize; JSS_JOBS];
|
||
let mut job_clock = [0.0_f64; JSS_JOBS];
|
||
let mut machine_clock = [0.0_f64; JSS_MACHINES];
|
||
for &job in schedule {
|
||
let k = job_next[job];
|
||
let m = FT06_MACHINE[job][k];
|
||
let t = FT06_TIME[job][k];
|
||
let start = job_clock[job].max(machine_clock[m]);
|
||
let end = start + t;
|
||
job_clock[job] = end;
|
||
machine_clock[m] = end;
|
||
job_next[job] = k + 1;
|
||
}
|
||
let makespan = machine_clock.iter().cloned().fold(0.0_f64, f64::max);
|
||
Evaluation::new(vec![makespan])
|
||
}
|
||
}
|
||
|
||
/// Precedence-Order Crossover — multiset-preserving recombination for the
|
||
/// operation-string encoding (the strict-permutation crossovers would
|
||
/// corrupt the multiset).
|
||
#[derive(Debug, Clone, Copy, Default)]
|
||
struct PrecedenceOrderCrossover;
|
||
impl Variation<Vec<usize>> for PrecedenceOrderCrossover {
|
||
fn vary(&mut self, parents: &[Vec<usize>], rng: &mut Rng) -> Vec<Vec<usize>> {
|
||
assert!(parents.len() >= 2, "POX requires 2 parents");
|
||
let (p1, p2) = (&parents[0], &parents[1]);
|
||
let mut in_j1 = [false; JSS_JOBS];
|
||
loop {
|
||
for slot in &mut in_j1 {
|
||
*slot = rng.random_bool(0.5);
|
||
}
|
||
let c = in_j1.iter().filter(|&&b| b).count();
|
||
if c > 0 && c < JSS_JOBS {
|
||
break;
|
||
}
|
||
}
|
||
vec![pox_child(p1, p2, &in_j1), pox_child(p2, p1, &in_j1)]
|
||
}
|
||
}
|
||
fn pox_child(donor: &[usize], filler: &[usize], in_donor_set: &[bool]) -> Vec<usize> {
|
||
let n = donor.len();
|
||
let mut child = vec![usize::MAX; n];
|
||
for k in 0..n {
|
||
if in_donor_set[donor[k]] {
|
||
child[k] = donor[k];
|
||
}
|
||
}
|
||
let mut fill_idx = 0;
|
||
for &v in filler {
|
||
if !in_donor_set[v] {
|
||
while fill_idx < n && child[fill_idx] != usize::MAX {
|
||
fill_idx += 1;
|
||
}
|
||
child[fill_idx] = v;
|
||
fill_idx += 1;
|
||
}
|
||
}
|
||
child
|
||
}
|
||
|
||
fn jss_initializer() -> ShuffledMultisetPermutation {
|
||
ShuffledMultisetPermutation::new(vec![JSS_MACHINES; JSS_JOBS])
|
||
}
|
||
|
||
fn jss_random(seed: u64) -> SoRun {
|
||
let mut opt = RandomSearch::new(
|
||
RandomSearchConfig {
|
||
iterations: JSS_BUDGET,
|
||
batch_size: 1,
|
||
seed,
|
||
},
|
||
jss_initializer(),
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&Ft06Makespan);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn jss_hill_climber(seed: u64) -> SoRun {
|
||
let mut opt = HillClimber::new(
|
||
HillClimberConfig {
|
||
iterations: JSS_BUDGET,
|
||
seed,
|
||
},
|
||
jss_initializer(),
|
||
InsertionMutation,
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&Ft06Makespan);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn jss_simulated_annealing(seed: u64) -> SoRun {
|
||
let mut opt = SimulatedAnnealing::new(
|
||
SimulatedAnnealingConfig {
|
||
iterations: JSS_BUDGET,
|
||
initial_temperature: 5.0,
|
||
final_temperature: 1e-2,
|
||
seed,
|
||
},
|
||
jss_initializer(),
|
||
InsertionMutation,
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&Ft06Makespan);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn jss_tabu_search(seed: u64) -> SoRun {
|
||
let neighbors = |schedule: &Vec<usize>, rng: &mut Rng| {
|
||
let mut m = InsertionMutation;
|
||
(0..16)
|
||
.map(|_| m.vary(std::slice::from_ref(schedule), rng).pop().unwrap())
|
||
.collect()
|
||
};
|
||
let mut opt = TabuSearch::new(
|
||
TabuSearchConfig {
|
||
iterations: JSS_BUDGET / 16,
|
||
tabu_tenure: 20,
|
||
seed,
|
||
},
|
||
jss_initializer(),
|
||
neighbors,
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&Ft06Makespan);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn jss_genetic_algorithm(seed: u64) -> SoRun {
|
||
let mut opt = GeneticAlgorithm::new(
|
||
GeneticAlgorithmConfig {
|
||
population_size: 80,
|
||
generations: JSS_BUDGET / 80,
|
||
tournament_size: 3,
|
||
elitism: 2,
|
||
seed,
|
||
},
|
||
jss_initializer(),
|
||
CompositeVariation {
|
||
crossover: PrecedenceOrderCrossover,
|
||
mutation: InsertionMutation,
|
||
},
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&Ft06Makespan);
|
||
SoRun {
|
||
best_value: result.best.unwrap().evaluation.objectives[0],
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
// ---- Bi-objective 0/1 knapsack: Zitzler & Thiele style ----------------------
|
||
|
||
const KNAPSACK_N: usize = 30;
|
||
const KP_PROFIT_A: [f64; KNAPSACK_N] = [
|
||
61.0, 17.0, 92.0, 49.0, 73.0, 28.0, 84.0, 36.0, 55.0, 78.0, 23.0, 91.0, 12.0, 67.0, 45.0, 58.0,
|
||
33.0, 71.0, 14.0, 26.0, 87.0, 42.0, 19.0, 65.0, 30.0, 51.0, 79.0, 22.0, 47.0, 88.0,
|
||
];
|
||
const KP_PROFIT_B: [f64; KNAPSACK_N] = [
|
||
24.0, 81.0, 16.0, 67.0, 29.0, 73.0, 41.0, 60.0, 52.0, 19.0, 77.0, 34.0, 95.0, 22.0, 71.0, 88.0,
|
||
56.0, 27.0, 64.0, 90.0, 18.0, 43.0, 79.0, 31.0, 85.0, 25.0, 38.0, 92.0, 70.0, 13.0,
|
||
];
|
||
const KP_WEIGHT: [f64; KNAPSACK_N] = [
|
||
35.0, 58.0, 22.0, 71.0, 14.0, 86.0, 31.0, 53.0, 78.0, 19.0, 44.0, 16.0, 67.0, 88.0, 25.0, 51.0,
|
||
33.0, 74.0, 12.0, 47.0, 63.0, 28.0, 91.0, 36.0, 55.0, 17.0, 82.0, 41.0, 24.0, 68.0,
|
||
];
|
||
/// Hypervolume reference point for the knapsack front. Both objectives are
|
||
/// maximized, so in the minimization-oriented frame any positive profit is
|
||
/// below 0 — `[0, 0]` is dominated by every feasible solution.
|
||
const KNAPSACK_REFERENCE: [f64; 2] = [0.0, 0.0];
|
||
|
||
/// Bi-objective 0/1 knapsack: two profit vectors, one shared capacity.
|
||
/// Weight overruns are penalized in both objectives so the Pareto front is
|
||
/// composed of feasible solutions.
|
||
struct BiKnapsack {
|
||
capacity: f64,
|
||
}
|
||
impl BiKnapsack {
|
||
fn new() -> Self {
|
||
Self {
|
||
capacity: 0.5 * KP_WEIGHT.iter().sum::<f64>(),
|
||
}
|
||
}
|
||
}
|
||
impl Problem for BiKnapsack {
|
||
type Decision = Vec<bool>;
|
||
fn objectives(&self) -> ObjectiveSpace {
|
||
ObjectiveSpace::new(vec![
|
||
Objective::maximize("profit_a"),
|
||
Objective::maximize("profit_b"),
|
||
])
|
||
}
|
||
fn evaluate(&self, take: &Vec<bool>) -> Evaluation {
|
||
let (mut pa, mut pb, mut w) = (0.0, 0.0, 0.0);
|
||
for (i, &t) in take.iter().enumerate() {
|
||
if t {
|
||
pa += KP_PROFIT_A[i];
|
||
pb += KP_PROFIT_B[i];
|
||
w += KP_WEIGHT[i];
|
||
}
|
||
}
|
||
let penalty = 1000.0 * (w - self.capacity).max(0.0);
|
||
Evaluation::new(vec![pa - penalty, pb - penalty])
|
||
}
|
||
}
|
||
|
||
/// Random binary initializer — each bit 50/50 independently.
|
||
#[derive(Debug, Clone, Copy)]
|
||
struct RandomBinary {
|
||
n: usize,
|
||
}
|
||
impl Initializer<Vec<bool>> for RandomBinary {
|
||
fn initialize(&mut self, size: usize, rng: &mut Rng) -> Vec<Vec<bool>> {
|
||
(0..size)
|
||
.map(|_| (0..self.n).map(|_| rng.random_bool(0.5)).collect())
|
||
.collect()
|
||
}
|
||
}
|
||
|
||
/// One-point crossover for binary chromosomes.
|
||
#[derive(Debug, Clone, Copy, Default)]
|
||
struct OnePointCrossoverBool;
|
||
impl Variation<Vec<bool>> for OnePointCrossoverBool {
|
||
fn vary(&mut self, parents: &[Vec<bool>], rng: &mut Rng) -> Vec<Vec<bool>> {
|
||
assert!(
|
||
parents.len() >= 2,
|
||
"OnePointCrossoverBool requires 2 parents"
|
||
);
|
||
let (p1, p2) = (&parents[0], &parents[1]);
|
||
let n = p1.len();
|
||
if n < 2 {
|
||
return vec![p1.clone(), p2.clone()];
|
||
}
|
||
let cut = rng.random_range(1..n);
|
||
let mut c1 = Vec::with_capacity(n);
|
||
let mut c2 = Vec::with_capacity(n);
|
||
c1.extend_from_slice(&p1[..cut]);
|
||
c1.extend_from_slice(&p2[cut..]);
|
||
c2.extend_from_slice(&p2[..cut]);
|
||
c2.extend_from_slice(&p1[cut..]);
|
||
vec![c1, c2]
|
||
}
|
||
}
|
||
|
||
fn knap_binary_variation() -> CompositeVariation<OnePointCrossoverBool, BitFlipMutation> {
|
||
CompositeVariation {
|
||
crossover: OnePointCrossoverBool,
|
||
mutation: BitFlipMutation {
|
||
probability: 1.0 / KNAPSACK_N as f64,
|
||
},
|
||
}
|
||
}
|
||
|
||
/// One run's knapsack metrics. The bi-objective front lives over `Vec<bool>`
|
||
/// decisions, so `MoRun` (which fixes `Vec<f64>`) does not fit — we keep
|
||
/// only the aggregate quality numbers.
|
||
#[derive(Clone)]
|
||
struct KnapRun {
|
||
hypervolume: f64,
|
||
front_size: usize,
|
||
wall_ms: u128,
|
||
}
|
||
|
||
fn knap_run(front: &[Candidate<Vec<bool>>], problem: &BiKnapsack, wall_ms: u128) -> KnapRun {
|
||
KnapRun {
|
||
hypervolume: hypervolume_2d(front, &problem.objectives(), KNAPSACK_REFERENCE),
|
||
front_size: front.len(),
|
||
wall_ms,
|
||
}
|
||
}
|
||
|
||
fn knapsack_random(seed: u64) -> KnapRun {
|
||
let problem = BiKnapsack::new();
|
||
let mut opt = RandomSearch::new(
|
||
RandomSearchConfig {
|
||
iterations: KNAPSACK_BUDGET,
|
||
batch_size: 1,
|
||
seed,
|
||
},
|
||
RandomBinary { n: KNAPSACK_N },
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
let ms = t0.elapsed().as_millis();
|
||
knap_run(&result.pareto_front, &problem, ms)
|
||
}
|
||
|
||
fn knapsack_nsga2(seed: u64) -> KnapRun {
|
||
let problem = BiKnapsack::new();
|
||
let mut opt = Nsga2::new(
|
||
Nsga2Config {
|
||
population_size: 100,
|
||
generations: KNAPSACK_BUDGET / 100,
|
||
seed,
|
||
},
|
||
RandomBinary { n: KNAPSACK_N },
|
||
knap_binary_variation(),
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
let ms = t0.elapsed().as_millis();
|
||
knap_run(&result.pareto_front, &problem, ms)
|
||
}
|
||
|
||
fn knapsack_spea2(seed: u64) -> KnapRun {
|
||
let problem = BiKnapsack::new();
|
||
let mut opt = Spea2::new(
|
||
Spea2Config {
|
||
population_size: 100,
|
||
archive_size: 100,
|
||
generations: KNAPSACK_BUDGET / 100,
|
||
seed,
|
||
},
|
||
RandomBinary { n: KNAPSACK_N },
|
||
knap_binary_variation(),
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
let ms = t0.elapsed().as_millis();
|
||
knap_run(&result.pareto_front, &problem, ms)
|
||
}
|
||
|
||
fn knapsack_nsga3(seed: u64) -> KnapRun {
|
||
let problem = BiKnapsack::new();
|
||
let mut opt = Nsga3::new(
|
||
Nsga3Config {
|
||
population_size: 100,
|
||
generations: KNAPSACK_BUDGET / 100,
|
||
reference_divisions: 20,
|
||
seed,
|
||
},
|
||
RandomBinary { n: KNAPSACK_N },
|
||
knap_binary_variation(),
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
let ms = t0.elapsed().as_millis();
|
||
knap_run(&result.pareto_front, &problem, ms)
|
||
}
|
||
|
||
fn knapsack_ibea(seed: u64) -> KnapRun {
|
||
let problem = BiKnapsack::new();
|
||
let mut opt = Ibea::new(
|
||
IbeaConfig {
|
||
population_size: 100,
|
||
generations: KNAPSACK_BUDGET / 100,
|
||
kappa: 0.05,
|
||
seed,
|
||
},
|
||
RandomBinary { n: KNAPSACK_N },
|
||
knap_binary_variation(),
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
let ms = t0.elapsed().as_millis();
|
||
knap_run(&result.pareto_front, &problem, ms)
|
||
}
|
||
|
||
// ---- Combinatorial comparison runners --------------------------------------
|
||
|
||
fn run_tsp_comparison() {
|
||
println!();
|
||
println!("== TSP ring-{TSP_CITIES} ({TSP_BUDGET} evals/run × {SEEDS} seeds) ==");
|
||
println!(
|
||
"{TSP_CITIES} equally-spaced cities on the unit circle; minimize the closed tour length."
|
||
);
|
||
println!(
|
||
"The space is ({TSP_CITIES}-1)!/2 distinct tours, but cities in convex position have no"
|
||
);
|
||
println!("2-opt local optima -- so this instance cleanly separates methods with good");
|
||
println!("neighbourhood moves (inversion = 2-opt) from blind recombination / sampling.");
|
||
println!(
|
||
"Known optimum (the polygon perimeter): {:.4}",
|
||
RingTsp::optimal_length()
|
||
);
|
||
println!("sorted best-first by tour length (lower is better)");
|
||
println!();
|
||
|
||
type Runner = fn(u64) -> SoRun;
|
||
let runners: &[(&str, Runner)] = &[
|
||
("RandomSearch", tsp_random),
|
||
("HillClimber", tsp_hill_climber),
|
||
("SimulatedAnneal", tsp_simulated_annealing),
|
||
("TabuSearch", tsp_tabu_search),
|
||
("GA", tsp_genetic_algorithm),
|
||
("AntColony", tsp_ant_colony),
|
||
];
|
||
|
||
let mut rows: Vec<(f64, Vec<String>)> = Vec::new();
|
||
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);
|
||
rows.push((
|
||
b_m,
|
||
vec![
|
||
name.to_string(),
|
||
format!("{b_m:.4}+/-{b_s:.4}"),
|
||
format!("{ms_m:.0}"),
|
||
],
|
||
));
|
||
}
|
||
rows.sort_by(|a, b| a.0.partial_cmp(&b.0).unwrap_or(std::cmp::Ordering::Equal));
|
||
let table: Vec<Vec<String>> = rows.into_iter().map(|(_, r)| r).collect();
|
||
print_table(&["algorithm", "tour length", "ms"], &table);
|
||
}
|
||
|
||
fn run_jss_comparison() {
|
||
println!();
|
||
println!("== JSS FT06 ({JSS_BUDGET} evals/run × {SEEDS} seeds) ==");
|
||
println!("Fisher & Thompson 1963 6-job × 6-machine job-shop; minimize makespan.");
|
||
println!("Hard because every job has a fixed machine order, so swapping two");
|
||
println!(
|
||
"operations can ripple delays across the whole schedule. Known optimum: {FT06_OPTIMAL_MAKESPAN:.0}"
|
||
);
|
||
println!("sorted best-first by makespan (lower is better)");
|
||
println!();
|
||
|
||
type Runner = fn(u64) -> SoRun;
|
||
let runners: &[(&str, Runner)] = &[
|
||
("RandomSearch", jss_random),
|
||
("HillClimber", jss_hill_climber),
|
||
("SimulatedAnneal", jss_simulated_annealing),
|
||
("TabuSearch", jss_tabu_search),
|
||
("GA", jss_genetic_algorithm),
|
||
];
|
||
|
||
let mut rows: Vec<(f64, Vec<String>)> = Vec::new();
|
||
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);
|
||
rows.push((
|
||
b_m,
|
||
vec![
|
||
name.to_string(),
|
||
format!("{b_m:.4}+/-{b_s:.4}"),
|
||
format!("{ms_m:.0}"),
|
||
],
|
||
));
|
||
}
|
||
rows.sort_by(|a, b| a.0.partial_cmp(&b.0).unwrap_or(std::cmp::Ordering::Equal));
|
||
let table: Vec<Vec<String>> = rows.into_iter().map(|(_, r)| r).collect();
|
||
print_table(&["algorithm", "makespan", "ms"], &table);
|
||
}
|
||
|
||
fn run_knapsack_comparison() {
|
||
println!();
|
||
println!(
|
||
"== Knapsack ({KNAPSACK_N} items, bi-objective, {KNAPSACK_BUDGET} evals/run × {SEEDS} seeds) =="
|
||
);
|
||
println!("Zitzler-Thiele style 0/1 knapsack: two profit vectors, one capacity");
|
||
println!("(half the total weight). Hard because the two profit objectives");
|
||
println!("conflict and the capacity constraint carves feasible regions out of");
|
||
println!("the 2^{KNAPSACK_N} bitstrings. No closed-form optimum; scored by hypervolume");
|
||
println!("vs reference {KNAPSACK_REFERENCE:?} (higher is better).");
|
||
println!("sorted best-first by hypervolume");
|
||
println!();
|
||
|
||
type Runner = fn(u64) -> KnapRun;
|
||
let runners: &[(&str, Runner)] = &[
|
||
("RandomSearch", knapsack_random),
|
||
("NSGA-II", knapsack_nsga2),
|
||
("SPEA2", knapsack_spea2),
|
||
("NSGA-III", knapsack_nsga3),
|
||
("IBEA", knapsack_ibea),
|
||
];
|
||
|
||
let mut rows: Vec<(f64, Vec<String>)> = Vec::new();
|
||
for (name, runner) in runners {
|
||
let runs: Vec<KnapRun> = (0..SEEDS).map(runner).collect();
|
||
let hv: Vec<f64> = runs.iter().map(|r| r.hypervolume).collect();
|
||
let fs: Vec<f64> = runs.iter().map(|r| r.front_size 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 (fs_m, _) = mean_std(&fs);
|
||
let (ms_m, _) = mean_std(&ms);
|
||
rows.push((
|
||
hv_m,
|
||
vec![
|
||
name.to_string(),
|
||
format!("{hv_m:.1}+/-{hv_s:.1}"),
|
||
format!("{fs_m:.0}"),
|
||
format!("{ms_m:.0}"),
|
||
],
|
||
));
|
||
}
|
||
rows.sort_by(|a, b| b.0.partial_cmp(&a.0).unwrap_or(std::cmp::Ordering::Equal));
|
||
let table: Vec<Vec<String>> = rows.into_iter().map(|(_, r)| r).collect();
|
||
print_table(&["algorithm", "hypervolume", "front", "ms"], &table);
|
||
}
|
||
|
||
// =============================================================================
|
||
// Many-objective problems (4+ objectives)
|
||
//
|
||
// The "curse of dimensionality" for multi-objective optimizers: as the
|
||
// objective count climbs, the fraction of mutually non-dominated solution
|
||
// pairs rushes toward 1, so Pareto rank alone stops discriminating.
|
||
// NSGA-II's whole population collapses into front 0 and only crowding
|
||
// distance is left to steer. Reference-point (NSGA-III), decomposition
|
||
// (MOEA/D), reference-vector (RVEA), grid (GrEA) and indicator (IBEA,
|
||
// HypE) methods are built to survive this regime.
|
||
//
|
||
// Both DTLZ structs above are already parameterised by objective count,
|
||
// and the DTLZ1/DTLZ2 distance metrics generalise to any M, so a single
|
||
// `ManySpec` + generic runners cover every objective count.
|
||
// =============================================================================
|
||
|
||
/// A DTLZ instance at an arbitrary objective count, plus the budget and
|
||
/// the reference-set sizing the many-objective algorithms need.
|
||
#[derive(Clone, Copy)]
|
||
struct ManySpec {
|
||
objectives: usize,
|
||
dim: usize,
|
||
budget: usize,
|
||
/// Population for the fixed-population algorithms; also the
|
||
/// Das-Dennis weight count MOEA/D derives from `reference_divisions`.
|
||
population: usize,
|
||
/// Das-Dennis divisions for NSGA-III / RVEA / MOEA/D reference sets.
|
||
reference_divisions: usize,
|
||
/// `true` = DTLZ1 (deceptive multimodal, linear-simplex front);
|
||
/// `false` = DTLZ2 (unit-hypersphere-octant front).
|
||
is_dtlz1: bool,
|
||
/// Per-axis HypE hypervolume reference coordinate.
|
||
hype_ref: f64,
|
||
}
|
||
|
||
/// One DTLZ problem type so the generic runners have a single `Problem`
|
||
/// to hand to `run` regardless of which front geometry is in play.
|
||
enum ManyDtlz {
|
||
D1(Dtlz1),
|
||
D2(Dtlz2),
|
||
}
|
||
impl Problem for ManyDtlz {
|
||
type Decision = Vec<f64>;
|
||
fn objectives(&self) -> ObjectiveSpace {
|
||
match self {
|
||
ManyDtlz::D1(p) => p.objectives(),
|
||
ManyDtlz::D2(p) => p.objectives(),
|
||
}
|
||
}
|
||
fn evaluate(&self, x: &Vec<f64>) -> Evaluation {
|
||
match self {
|
||
ManyDtlz::D1(p) => p.evaluate(x),
|
||
ManyDtlz::D2(p) => p.evaluate(x),
|
||
}
|
||
}
|
||
}
|
||
|
||
impl ManySpec {
|
||
fn problem(&self) -> ManyDtlz {
|
||
if self.is_dtlz1 {
|
||
ManyDtlz::D1(Dtlz1 {
|
||
num_objectives: self.objectives,
|
||
dim: self.dim,
|
||
})
|
||
} else {
|
||
ManyDtlz::D2(Dtlz2 {
|
||
num_objectives: self.objectives,
|
||
dim: self.dim,
|
||
})
|
||
}
|
||
}
|
||
fn bounds(&self) -> Vec<(f64, f64)> {
|
||
vec![(0.0, 1.0); self.dim]
|
||
}
|
||
fn variation(&self) -> CompositeVariation<SimulatedBinaryCrossover, PolynomialMutation> {
|
||
let b = self.bounds();
|
||
CompositeVariation {
|
||
crossover: SimulatedBinaryCrossover::new(b.clone(), 30.0, 1.0),
|
||
mutation: PolynomialMutation::new(b, 20.0, 1.0 / self.dim as f64),
|
||
}
|
||
}
|
||
fn mean_dist(&self, front: &[Candidate<Vec<f64>>]) -> f64 {
|
||
if self.is_dtlz1 {
|
||
mean_distance_to_dtlz1_front(front)
|
||
} else {
|
||
mean_distance_to_dtlz2_front(front)
|
||
}
|
||
}
|
||
}
|
||
|
||
fn many_random(spec: ManySpec, seed: u64) -> MoRun {
|
||
let problem = spec.problem();
|
||
let mut opt = RandomSearch::new(
|
||
RandomSearchConfig {
|
||
iterations: spec.budget,
|
||
batch_size: 1,
|
||
seed,
|
||
},
|
||
RealBounds::new(spec.bounds()),
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn many_nsga2(spec: ManySpec, seed: u64) -> MoRun {
|
||
let problem = spec.problem();
|
||
let mut opt = Nsga2::new(
|
||
Nsga2Config {
|
||
population_size: spec.population,
|
||
generations: spec.budget / spec.population,
|
||
seed,
|
||
},
|
||
RealBounds::new(spec.bounds()),
|
||
spec.variation(),
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn many_nsga3(spec: ManySpec, seed: u64) -> MoRun {
|
||
let problem = spec.problem();
|
||
let mut opt = Nsga3::new(
|
||
Nsga3Config {
|
||
population_size: spec.population,
|
||
generations: spec.budget / spec.population,
|
||
reference_divisions: spec.reference_divisions,
|
||
seed,
|
||
},
|
||
RealBounds::new(spec.bounds()),
|
||
spec.variation(),
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn many_moead(spec: ManySpec, seed: u64) -> MoRun {
|
||
let problem = spec.problem();
|
||
let mut opt = Moead::new(
|
||
MoeadConfig {
|
||
generations: spec.budget / spec.population,
|
||
reference_divisions: spec.reference_divisions,
|
||
neighborhood_size: 20,
|
||
seed,
|
||
},
|
||
RealBounds::new(spec.bounds()),
|
||
spec.variation(),
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn many_rvea(spec: ManySpec, seed: u64) -> MoRun {
|
||
let problem = spec.problem();
|
||
let mut opt = Rvea::new(
|
||
RveaConfig {
|
||
population_size: spec.population,
|
||
generations: spec.budget / spec.population,
|
||
reference_divisions: spec.reference_divisions,
|
||
alpha: 2.0,
|
||
seed,
|
||
},
|
||
RealBounds::new(spec.bounds()),
|
||
spec.variation(),
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn many_grea(spec: ManySpec, seed: u64) -> MoRun {
|
||
let problem = spec.problem();
|
||
let mut opt = Grea::new(
|
||
GreaConfig {
|
||
population_size: spec.population,
|
||
generations: spec.budget / spec.population,
|
||
grid_divisions: 10,
|
||
seed,
|
||
},
|
||
RealBounds::new(spec.bounds()),
|
||
spec.variation(),
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn many_ibea(spec: ManySpec, seed: u64) -> MoRun {
|
||
let problem = spec.problem();
|
||
let mut opt = Ibea::new(
|
||
IbeaConfig {
|
||
population_size: spec.population,
|
||
generations: spec.budget / spec.population,
|
||
kappa: 0.05,
|
||
seed,
|
||
},
|
||
RealBounds::new(spec.bounds()),
|
||
spec.variation(),
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn many_hype(spec: ManySpec, seed: u64) -> MoRun {
|
||
let problem = spec.problem();
|
||
let mut opt = Hype::new(
|
||
HypeConfig {
|
||
population_size: spec.population,
|
||
generations: spec.budget / spec.population,
|
||
reference_point: vec![spec.hype_ref; spec.objectives],
|
||
mc_samples: 1_000,
|
||
seed,
|
||
},
|
||
RealBounds::new(spec.bounds()),
|
||
spec.variation(),
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn many_age_moea(spec: ManySpec, seed: u64) -> MoRun {
|
||
let problem = spec.problem();
|
||
let mut opt = AgeMoea::new(
|
||
AgeMoeaConfig {
|
||
population_size: spec.population,
|
||
generations: spec.budget / spec.population,
|
||
seed,
|
||
},
|
||
RealBounds::new(spec.bounds()),
|
||
spec.variation(),
|
||
);
|
||
let t0 = Instant::now();
|
||
let result = opt.run(&problem);
|
||
MoRun {
|
||
front: result.pareto_front,
|
||
wall_ms: t0.elapsed().as_millis(),
|
||
}
|
||
}
|
||
|
||
fn run_many_objective_comparison(title: &str, blurb: &[&str], spec: ManySpec) {
|
||
println!();
|
||
println!("== {title} ==");
|
||
for line in blurb {
|
||
println!("{line}");
|
||
}
|
||
println!("sorted best-first by mean dist to the true front (lower is better)");
|
||
println!();
|
||
|
||
type Runner = fn(ManySpec, u64) -> MoRun;
|
||
let runners: &[(&str, Runner)] = &[
|
||
("RandomSearch", many_random),
|
||
("NSGA-II", many_nsga2),
|
||
("NSGA-III", many_nsga3),
|
||
("MOEA/D", many_moead),
|
||
("RVEA", many_rvea),
|
||
("GrEA", many_grea),
|
||
("IBEA", many_ibea),
|
||
("HypE", many_hype),
|
||
("AGE-MOEA", many_age_moea),
|
||
];
|
||
|
||
let mut rows: Vec<(f64, Vec<String>)> = Vec::new();
|
||
for (name, runner) in runners {
|
||
let runs: Vec<MoRun> = (0..SEEDS).map(|s| runner(spec, s)).collect();
|
||
let dist: Vec<f64> = runs.iter().map(|r| spec.mean_dist(&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 (d_m, d_s) = mean_std(&dist);
|
||
let (fs_m, _) = mean_std(&fs);
|
||
let (ms_m, _) = mean_std(&ms);
|
||
rows.push((
|
||
d_m,
|
||
vec![
|
||
name.to_string(),
|
||
format!("{d_m:.4}+/-{d_s:.4}"),
|
||
format!("{fs_m:.0}"),
|
||
format!("{ms_m:.0}"),
|
||
],
|
||
));
|
||
}
|
||
rows.sort_by(|a, b| a.0.partial_cmp(&b.0).unwrap_or(std::cmp::Ordering::Equal));
|
||
let table: Vec<Vec<String>> = rows.into_iter().map(|(_, r)| r).collect();
|
||
print_table(&["algorithm", "mean dist", "front", "ms"], &table);
|
||
}
|
||
|
||
fn main() {
|
||
run_zdt1_comparison();
|
||
run_zdt3_comparison();
|
||
run_dtlz2_comparison();
|
||
run_dtlz1_comparison();
|
||
run_rastrigin_comparison();
|
||
run_rosenbrock_comparison();
|
||
run_ackley_comparison();
|
||
run_tsp_comparison();
|
||
run_jss_comparison();
|
||
run_knapsack_comparison();
|
||
|
||
// ---- Many-objective (4+) ----
|
||
run_many_objective_comparison(
|
||
"DTLZ2 4-objective (dim=13, 40000 evals/run × 10 seeds)",
|
||
&[
|
||
"DTLZ2 scaled to 4 objectives -- the entry point to many-objective.",
|
||
"Front is still the unit-hypersphere octant (Σf² = 1). Already hard:",
|
||
"with 4 objectives most random pairs of solutions are mutually",
|
||
"non-dominated, so Pareto rank alone barely discriminates. Optimum:",
|
||
"mean dist -> 0.",
|
||
],
|
||
ManySpec {
|
||
objectives: 4,
|
||
dim: 13,
|
||
budget: 40_000,
|
||
population: 56,
|
||
reference_divisions: 5,
|
||
is_dtlz1: false,
|
||
hype_ref: 3.0,
|
||
},
|
||
);
|
||
run_many_objective_comparison(
|
||
"DTLZ2 10-objective (dim=19, 40000 evals/run × 10 seeds)",
|
||
&[
|
||
"DTLZ2 scaled to 10 objectives -- the curse of dimensionality in full.",
|
||
"In 10-D objective space almost EVERY pair of solutions is mutually",
|
||
"non-dominated, so NSGA-II's whole population collapses into front 0",
|
||
"and crowding distance is the only signal left. Reference-point,",
|
||
"decomposition and indicator methods are built for exactly this.",
|
||
"Watch the 'front' column: it pins to the population size because",
|
||
"nothing dominates anything. Optimum: mean dist -> 0.",
|
||
],
|
||
ManySpec {
|
||
objectives: 10,
|
||
dim: 19,
|
||
budget: 40_000,
|
||
population: 55,
|
||
reference_divisions: 2,
|
||
is_dtlz1: false,
|
||
hype_ref: 3.0,
|
||
},
|
||
);
|
||
run_many_objective_comparison(
|
||
"DTLZ1 8-objective (dim=12, 40000 evals/run × 10 seeds)",
|
||
&[
|
||
"DTLZ1 scaled to 8 objectives -- the brutal one. Stacks the",
|
||
"many-objective dominance collapse on top of DTLZ1's deceptive",
|
||
"multimodal g-term (a huge number of local fronts). The true front",
|
||
"is the linear simplex Σf = 0.5; reaching it at all is the",
|
||
"achievement. Expect large mean-dist values and wide spreads -- this",
|
||
"is near the edge of what the catalogue does at this budget.",
|
||
],
|
||
ManySpec {
|
||
objectives: 8,
|
||
dim: 12,
|
||
budget: 40_000,
|
||
population: 120,
|
||
reference_divisions: 3,
|
||
is_dtlz1: true,
|
||
hype_ref: 1.0,
|
||
},
|
||
);
|
||
}
|