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docs(examples): capture full comparison run output as compare-results.md

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Snapshot of `cargo run --release --example compare` after the v0.3.0
algorithm cohort. The harness runs 7 benchmark problems × ~20
algorithms × 10 seeds each (≈3 minutes wall-clock); this file is the
reference output so readers can scan results without running it
themselves.

Highlights worth reading even if you're skipping the file:
- ZDT1: MOPSO and MOEA/D dominate convergence; (1+1)-ES and DE tie
  at f = 0 on Rastrigin
- IPOP-CMA-ES drops vanilla CMA-ES from f=2.35 to f=0.13 on
  Rastrigin (the multimodal failure-mode it was added to fix)
- IBEA wins DTLZ2 (15× closer to true front than NSGA-III)
- GrEA wins DTLZ1 (linear simplex front matches grid-based niching)
- Nelder-Mead = 0 exactly on Rosenbrock; CMA-ES at machine epsilon
- Bayesian optimization at 60 evals is honestly bad on 5-D problems
  with the default kernel — flagged so readers don't conclude BO is
  weak in general; it just needs more evals or hyperparameter tuning
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# `compare` example — reference output
Snapshot from `cargo run --release --example compare` after the v0.3.0
algorithm cohort landed (2026-05-05). 10 seeds per algorithm per problem.
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 | 111 |
| PAES | 104.1887 ± 0.90 | 0.0351 ± 0.01 | 1.3195 ± 0.06 | 33 | 16 |
| MOPSO | **120.6149 ± 0.05** | 0.0125 ± 0.00 | **0.0005 ± 0.00** | 100 | 106 |
| SPEA2 | 118.0823 ± 0.60 | 0.0111 ± 0.00 | 0.2408 ± 0.05 | 97 | 461 |
| PESA-II | 119.3670 ± 0.33 | **0.0095 ± 0.00** | 0.0802 ± 0.04 | 100 | 86 |
| ε-MOEA | 118.8742 ± 0.68 | 0.0167 ± 0.01 | 0.0493 ± 0.02 | 45 | 55 |
| IBEA | 120.0167 ± 0.31 | 0.0130 ± 0.00 | 0.0448 ± 0.02 | 73 | 141 |
| HypE | 105.6489 ± 0.98 | 0.0266 ± 0.01 | 1.4820 ± 0.10 | 72 | 66 |
| SMS-EMOA | 102.8871 ± 1.05 | 0.0263 ± 0.00 | 1.4937 ± 0.12 | 40 | 181 |
| RVEA | 111.7151 ± 1.82 | 0.0308 ± 0.01 | 0.8399 ± 0.16 | 47 | 60 |
| NSGA-II | 118.3336 ± 0.78 | 0.0112 ± 0.00 | 0.1891 ± 0.06 | 96 | 287 |
| NSGA-III | 115.1612 ± 0.47 | 0.0139 ± 0.00 | 0.4314 ± 0.06 | 86 | 244 |
| MOEA/D | 119.9450 ± 0.50 | 0.0118 ± 0.00 | 0.0065 ± 0.00 | 96 | 30 |
**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 | 284 |
| MOEA/D | 125.2413 ± 2.16 | 0.0198 ± 0.00 | 92 | 31 |
| **IBEA** | **126.2072 ± 1.23** | 0.0164 ± 0.00 | 48 | 140 |
| AGE-MOEA | 119.5132 ± 1.27 | 0.0136 ± 0.00 | 90 | 1028 |
## 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 | 621 |
| MOPSO | 0.0566 ± 0.00 | 0.0687 ± 0.01 | 100 | 48 |
| NSGA-II | 0.0332 ± 0.01 | 0.0577 ± 0.01 | 92 | 380 |
| SPEA2 | 0.0368 ± 0.00 | **0.0288 ± 0.00** | 92 | 4723 |
| PESA-II | 0.0395 ± 0.00 | 0.0616 ± 0.01 | 100 | 530 |
| ε-MOEA | 0.0325 ± 0.01 | 0.0572 ± 0.02 | 136 | 104 |
| **IBEA** | **0.0014 ± 0.00** | 0.0607 ± 0.00 | 87 | 158 |
| HypE | 0.0113 ± 0.00 | 0.0269 ± 0.02 | 80 | 82 |
| SMS-EMOA | 0.0484 ± 0.01 | 0.0764 ± 0.01 | 40 | 6002 |
| RVEA | 0.0510 ± 0.00 | 0.0631 ± 0.00 | 68 | 68 |
| NSGA-III | 0.0197 ± 0.00 | 0.0735 ± 0.01 | 92 | 325 |
| MOEA/D | 0.0037 ± 0.00 | 0.0886 ± 0.00 | 78 | 25 |
**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 | 310 |
| MOEA/D | 2.8022 ± 1.78 | 0.2279 ± 0.22 | 78 | 21 |
| AGE-MOEA | 4.5395 ± 2.21 | 0.3930 ± 0.29 | 90 | 2327 |
| **GrEA** | **1.7725 ± 0.99** | **0.0719 ± 0.04** | 72 | 286 |
**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 | 16 |
| HillClimber | 1.5966e1 ± 6.25 | 7 |
| **(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 | 269 |
| **DE** | **0.0000e0 ± 0.00** | 6 |
| CMA-ES | 2.3453e0 ± 1.49 | 12 |
| **IPOP-CMA-ES** | 1.3423e-1 ± 2.71e-1 | 69 |
(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 | 3 |
| PSO | 8.2124e-1 ± 1.58e0 | 2 |
| **CMA-ES** | **3.6207e-29 ± 2.35e-29** | 6 |
| 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 | 3 |
| PSO | 1.5099e-15 ± 1.63e-15 | 3 |
| CMA-ES | 1.5099e-15 ± 1.63e-15 | 7 |
| 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.