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232dbc0172
CHANGELOG entry consolidates the unreleased work since v0.3.0: testing-infrastructure expansion (proptest suites, cargo-fuzz harness, stability tests, gungraun benches, CI), two real bug fixes the testing surfaced (NaN-cycle non_dominated_sort, simplex projection magnitude precision), the README decision-tree update against the v0.3.0 comparison data, and the v0.4.0 perf pass (cumulative compare harness 18.6 s → 5.7 s, 3.27×). `examples/compare-results.md` refreshed with the post-perf-pass ms numbers; quality metrics are bit-identical to the v0.3.0 snapshot (the perf pass was strictly CPU time, never algorithmic).
6.2 KiB
compare example — reference output
Snapshot from cargo run --release --example compare after the v0.4.0
perf pass landed (2026-05-05). 10 seeds per algorithm per problem.
The quality metrics (hypervolume / spacing / mean L2 / mean dist / front size) are bit-identical to the v0.3.0 snapshot — the v0.4.0 optimization work was strictly CPU-time, never algorithmic. The ms columns reflect the v0.4.0 numbers; total compare-harness wall-clock dropped from ~18.6 s to ~5.7 s (3.27× faster).
Wall-clock numbers are from the development machine and will vary; the relative numbers across algorithms are the interesting part.
ZDT1 (dim=30, 25000 evals/run × 10 seeds)
Two-objective benchmark with a smooth Pareto front along
f₂ = 1 − √f₁. Hypervolume reference point: [11, 11].
| algorithm | hypervolume ↑ | spacing ↓ | mean L2 ↓ | front | ms |
|---|---|---|---|---|---|
| RandomSearch | 99.5691 ± 0.94 | 0.0937 ± 0.03 | 2.3621 ± 0.14 | 28 | 94 |
| PAES | 104.1887 ± 0.90 | 0.0351 ± 0.01 | 1.3195 ± 0.06 | 33 | 30 |
| MOPSO | 120.6149 ± 0.05 | 0.0125 ± 0.00 | 0.0005 ± 0.00 | 100 | 89 |
| SPEA2 | 118.0823 ± 0.60 | 0.0111 ± 0.00 | 0.2408 ± 0.05 | 97 | 234 |
| PESA-II | 119.3670 ± 0.33 | 0.0095 ± 0.00 | 0.0802 ± 0.04 | 100 | 73 |
| ε-MOEA | 118.8742 ± 0.68 | 0.0167 ± 0.01 | 0.0493 ± 0.02 | 45 | 50 |
| IBEA | 120.0167 ± 0.31 | 0.0130 ± 0.00 | 0.0448 ± 0.02 | 73 | 138 |
| HypE | 105.6489 ± 0.98 | 0.0266 ± 0.01 | 1.4820 ± 0.10 | 72 | 38 |
| SMS-EMOA | 102.8871 ± 1.05 | 0.0263 ± 0.00 | 1.4937 ± 0.12 | 40 | 67 |
| RVEA | 111.7151 ± 1.82 | 0.0308 ± 0.01 | 0.8399 ± 0.16 | 47 | 65 |
| NSGA-II | 118.3336 ± 0.78 | 0.0112 ± 0.00 | 0.1891 ± 0.06 | 96 | 67 |
| NSGA-III | 115.1612 ± 0.47 | 0.0139 ± 0.00 | 0.4314 ± 0.06 | 86 | 70 |
| MOEA/D | 119.9450 ± 0.50 | 0.0118 ± 0.00 | 0.0065 ± 0.00 | 96 | 28 |
MOPSO and MOEA/D dominate convergence (mean L2 to true front ≤ 0.01). PESA-II edges spacing.
ZDT3 (dim=30, 25000 evals × 10 seeds)
Disconnected Pareto front; tests an algorithm's ability to maintain spread across gaps.
| algorithm | hypervolume ↑ | spacing ↓ | front | ms |
|---|---|---|---|---|
| NSGA-II | 123.1826 ± 1.58 | 0.0092 ± 0.00 | 98 | 68 |
| MOEA/D | 125.2413 ± 2.16 | 0.0198 ± 0.00 | 92 | 28 |
| IBEA | 126.2072 ± 1.23 | 0.0164 ± 0.00 | 48 | 135 |
| AGE-MOEA | 119.5132 ± 1.27 | 0.0136 ± 0.00 | 90 | 199 |
DTLZ2 (3-obj, dim=12, 30000 evals × 10 seeds)
Spherical Pareto front. Mean dist = |‖f‖ − 1|.
| algorithm | mean dist ↓ | spacing ↓ | front | ms |
|---|---|---|---|---|
| RandomSearch | 0.3949 ± 0.02 | 0.0797 ± 0.01 | 239 | 520 |
| MOPSO | 0.0566 ± 0.00 | 0.0687 ± 0.01 | 100 | 71 |
| NSGA-II | 0.0332 ± 0.01 | 0.0577 ± 0.01 | 92 | 104 |
| SPEA2 | 0.0368 ± 0.00 | 0.0288 ± 0.00 | 92 | 534 |
| PESA-II | 0.0395 ± 0.00 | 0.0616 ± 0.01 | 100 | 396 |
| ε-MOEA | 0.0325 ± 0.01 | 0.0572 ± 0.02 | 136 | 89 |
| IBEA | 0.0014 ± 0.00 | 0.0607 ± 0.00 | 87 | 156 |
| HypE | 0.0113 ± 0.00 | 0.0269 ± 0.02 | 80 | 53 |
| SMS-EMOA | 0.0484 ± 0.01 | 0.0764 ± 0.01 | 40 | 1218 |
| RVEA | 0.0510 ± 0.00 | 0.0631 ± 0.00 | 68 | 73 |
| NSGA-III | 0.0197 ± 0.00 | 0.0735 ± 0.01 | 92 | 137 |
| MOEA/D | 0.0037 ± 0.00 | 0.0886 ± 0.00 | 78 | 24 |
IBEA wins decisively (15× closer to the true front than NSGA-III).
DTLZ1 (3-obj, dim=7, 30000 evals × 10 seeds)
Linear simplex Pareto front (Σf = 0.5).
| algorithm | mean dist ↓ | spacing ↓ | front | ms |
|---|---|---|---|---|
| NSGA-III | 5.9130 ± 2.82 | 0.4375 ± 0.22 | 92 | 133 |
| MOEA/D | 2.8022 ± 1.78 | 0.2279 ± 0.22 | 78 | 21 |
| AGE-MOEA | 4.5395 ± 2.21 | 0.3930 ± 0.29 | 90 | 247 |
| GrEA | 1.7725 ± 0.99 | 0.0719 ± 0.04 | 72 | 104 |
GrEA shines on linear fronts — the grid-based niching matches the geometry better than reference points.
Rastrigin (dim=5, 50000 evals/run × 10 seeds)
Multimodal trap. Global minimum f = 0 at the origin.
| algorithm | best f | ms |
|---|---|---|
| RandomSearch | 1.1064e1 ± 2.54 | 14 |
| HillClimber | 1.5966e1 ± 6.25 | 6 |
| (1+1)-ES | 0.0000e0 ± 0.00 | 4 |
| SimulatedAnneal | 3.8540e0 ± 1.48 | 7 |
| PAES | 1.5966e1 ± 6.25 | 10 |
| GA | 7.0913e-8 ± 5.50e-8 | 16 |
| PSO | 7.9598e-1 ± 8.67e-1 | 5 |
| NSGA-II | 4.9270e-5 ± 5.04e-5 | 83 |
| DE | 0.0000e0 ± 0.00 | 6 |
| CMA-ES | 2.3453e0 ± 1.49 | 11 |
| IPOP-CMA-ES | 1.3423e-1 ± 2.71e-1 | 66 |
(1+1)-ES and DE tie for f = 0. IPOP-CMA-ES drops vanilla CMA-ES from 2.35 → 0.13 — the restart logic does what it should.
Rosenbrock (dim=5, 30000 evals × 10 seeds)
Smooth non-convex valley.
| algorithm | best f | ms |
|---|---|---|
| DE | 3.3345e-1 ± 3.01e-1 | 2 |
| PSO | 8.2124e-1 ± 1.58e0 | 2 |
| CMA-ES | 3.6207e-29 ± 2.35e-29 | 5 |
| TLBO | 1.8458e-3 ± 1.91e-3 | 1 |
| (1+1)-ES | 2.2115e0 ± 2.70e0 | 1 |
| Nelder-Mead | 0.0000e0 ± 0.00 | 1 |
| BO (60 evals) | 3.1725e3 ± 2.92e3 | 40 |
Nelder-Mead = 0 exactly, CMA-ES at machine epsilon. BO at only 60 evaluations is honestly bad on 5-D Rosenbrock (no kernel hyperparameter tuning) — included as a reminder that BO needs more evaluations than a smooth problem actually requires for these other methods.
Ackley (dim=5, 30000 evals × 10 seeds)
Smoother multimodal landscape than Rastrigin.
| algorithm | best f | ms |
|---|---|---|
| DE | 4.4409e-16 ± 0.00 | 4 |
| PSO | 1.5099e-15 ± 1.63e-15 | 3 |
| CMA-ES | 1.5099e-15 ± 1.63e-15 | 6 |
| TLBO | 2.2204e-15 ± 1.78e-15 | 2 |
| BO (60 evals) | 1.9622e1 ± 1.23 | 40 |
All conventional methods reach machine precision. BO at 60 evals struggles — same caveat as Rosenbrock.