swaitsandClaude Opus 4.7
2b453464e7
The terminal output was misaligned: headers and data were right-aligned with hardcoded column widths and separator lengths, and the mean ± std cells contained the non-ASCII `±` (plus `ε`, `↑`, `↓`) -- on any terminal that renders those at a non-1 column width the columns drift, and the hardcoded `-`.repeat(n) separators didn't match the real table width anyway. Changes: - New `print_table` helper: column widths derived from the actual cell contents (header + every row), separator length computed to match. - All table cells are now ASCII: `+/-` instead of `±`, `eps-MOEA` instead of `ε-MOEA`, arrows dropped from headers. - Every table is sorted best-first by its primary quality metric. - Added three combinatorial / sequencing problems with their own (permutation- / bitstring-native) algorithm rosters: a convex-position ring TSP (known optimum), FT06 job-shop makespan (known optimum 55), and a bi-objective 0/1 knapsack scored by hypervolume. - Expanded every problem's preamble: what it is, why it's hard, and the best-known / optimal result. - Regenerated examples/compare-results.md to match. Continuous-problem quality metrics are unchanged (bit-identical to prior snapshots); only ms columns and row order move. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
235 lines
11 KiB
Markdown
235 lines
11 KiB
Markdown
# `compare` example — reference output
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Snapshot from `cargo run --release --example compare`, refreshed 2026-05-14
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for heuropt v0.10.0. 10 seeds per algorithm per problem.
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Each table is **sorted best-first** by its primary quality metric. The
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live terminal output uses ASCII `+/-` for the mean ± std cells (so column
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alignment can't be broken by a terminal that renders `±` at an odd
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width); this doc uses `±` since markdown renders it fine.
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The **continuous-problem quality metrics** are bit-identical to the
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v0.3.0–v0.4.0 snapshots — every optimization pass so far (including the
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Phase B CPU work) has been verified bit-identical by the `run()` snapshot
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tests. The **ms columns** are the post-Phase-B numbers; SMS-EMOA on DTLZ2
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in particular fell ~2.7× from the `hypervolume_nd` rework.
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This refresh also adds three **combinatorial / sequencing** problems —
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TSP, job-shop scheduling, and a bi-objective knapsack — which exercise the
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permutation and bitstring operators and a different algorithm roster (the
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real-vector methods can't run them).
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Wall-clock numbers are from the development machine and will vary; the
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*relative* numbers across algorithms are the interesting part.
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---
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## ZDT1 (dim=30, 25000 evals/run × 10 seeds)
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Zitzler-Deb-Thiele 2-objective benchmark: 30 real variables, one smooth
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convex Pareto front `f₂ = 1 − √f₁`. Hard because 29 of 30 variables must
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collapse to 0 before the front is even reachable, and only then can the
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population spread along it. Optimum: mean L2 → 0 (the front is known
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exactly). Sorted by hypervolume (reference `[11, 11]`).
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| algorithm | hypervolume ↑ | spacing ↓ | mean L2 ↓ | front | ms |
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|---|---|---|---|---|---|
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| MOPSO | **120.6149 ± 0.0529** | 0.0125 ± 0.0025 | **0.0005 ± 0.0001** | 100 | 80 |
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| IBEA | 120.0167 ± 0.3112 | 0.0130 ± 0.0027 | 0.0448 ± 0.0168 | 73 | 130 |
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| MOEA/D | 119.9450 ± 0.4953 | 0.0118 ± 0.0013 | 0.0065 ± 0.0020 | 96 | 27 |
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| PESA-II | 119.3670 ± 0.3261 | **0.0095 ± 0.0011** | 0.0802 ± 0.0354 | 100 | 67 |
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| eps-MOEA | 118.8742 ± 0.6835 | 0.0167 ± 0.0058 | 0.0493 ± 0.0227 | 45 | 46 |
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| NSGA-II | 118.3336 ± 0.7750 | 0.0112 ± 0.0022 | 0.1891 ± 0.0599 | 96 | 40 |
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| SPEA2 | 118.0823 ± 0.5973 | 0.0111 ± 0.0023 | 0.2408 ± 0.0509 | 97 | 226 |
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| NSGA-III | 115.1612 ± 0.4745 | 0.0139 ± 0.0029 | 0.4314 ± 0.0582 | 86 | 47 |
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| RVEA | 111.7151 ± 1.8195 | 0.0308 ± 0.0099 | 0.8399 ± 0.1569 | 47 | 62 |
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| HypE | 105.6489 ± 0.9789 | 0.0266 ± 0.0053 | 1.4820 ± 0.1003 | 72 | 30 |
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| PAES | 104.1887 ± 0.8953 | 0.0351 ± 0.0067 | 1.3195 ± 0.0558 | 33 | 27 |
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| SMS-EMOA | 102.8871 ± 1.0543 | 0.0263 ± 0.0039 | 1.4937 ± 0.1192 | 40 | 54 |
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| RandomSearch | 99.5691 ± 0.9383 | 0.0937 ± 0.0347 | 2.3621 ± 0.1428 | 28 | 88 |
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**MOPSO and MOEA/D dominate** convergence (mean L2 to true front ≤ 0.01).
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PESA-II edges spacing.
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## ZDT3 (dim=30, 25000 evals × 10 seeds)
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Zitzler-Deb-Thiele 2-objective with a **disconnected** front: five
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separate arcs rather than one curve. Hard because an algorithm has to
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discover and populate every arc while not stranding solutions in the
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dominated gaps between them.
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| algorithm | hypervolume ↑ | spacing ↓ | front | ms |
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|---|---|---|---|---|
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| **IBEA** | **126.2072 ± 1.2280** | 0.0164 ± 0.0036 | 48 | 131 |
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| MOEA/D | 125.2413 ± 2.1647 | 0.0198 ± 0.0043 | 92 | 27 |
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| NSGA-II | 123.1826 ± 1.5829 | **0.0092 ± 0.0020** | 98 | 40 |
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| AGE-MOEA | 119.5132 ± 1.2732 | 0.0136 ± 0.0023 | 90 | 171 |
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## DTLZ2 (3-obj, dim=12, 30000 evals/run × 10 seeds)
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Deb-Thiele-Laumanns-Zitzler 3-objective; the Pareto front is the
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unit-sphere octant (`Σf² = 1, all f ≥ 0`) — a curved 2-D surface embedded
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in 3-D objective space. `mean dist = |‖f‖ − 1|`, so 0 means perfectly on
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the sphere (the known optimum).
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| algorithm | mean dist ↓ | spacing ↓ | front | ms |
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| **IBEA** | **0.0014 ± 0.0002** | 0.0607 ± 0.0047 | 87 | 148 |
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| MOEA/D | 0.0037 ± 0.0003 | 0.0886 ± 0.0024 | 78 | 23 |
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| HypE | 0.0113 ± 0.0033 | **0.0269 ± 0.0172** | 80 | 41 |
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| NSGA-III | 0.0197 ± 0.0015 | 0.0735 ± 0.0052 | 92 | 91 |
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| eps-MOEA | 0.0325 ± 0.0104 | 0.0572 ± 0.0170 | 136 | 88 |
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| NSGA-II | 0.0332 ± 0.0068 | 0.0577 ± 0.0109 | 92 | 60 |
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| SPEA2 | 0.0368 ± 0.0021 | 0.0288 ± 0.0038 | 92 | 530 |
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| PESA-II | 0.0395 ± 0.0033 | 0.0616 ± 0.0051 | 100 | 372 |
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| SMS-EMOA | 0.0484 ± 0.0134 | 0.0764 ± 0.0081 | 40 | 483 |
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| RVEA | 0.0510 ± 0.0044 | 0.0631 ± 0.0024 | 68 | 66 |
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| MOPSO | 0.0566 ± 0.0048 | 0.0687 ± 0.0084 | 100 | 66 |
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| RandomSearch | 0.3949 ± 0.0152 | 0.0797 ± 0.0083 | 239 | 530 |
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**IBEA wins decisively** (14× closer to the true front than NSGA-III).
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SMS-EMOA's wall-clock fell ~2.7× from the v0.4.0 snapshot — the
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`hypervolume_nd` rework.
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## DTLZ1 (3-obj, dim=7, 30000 evals × 10 seeds)
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Deb-Thiele-Laumanns-Zitzler 3-objective; the Pareto front is the linear
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simplex `Σf = 0.5` in the positive octant. Hard because a deceptive
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multimodal `g` term riddles the approach with a huge number of local
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fronts — only fully-converged runs land on the simplex.
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| algorithm | mean dist ↓ | spacing ↓ | front | ms |
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| **GrEA** | **1.7725 ± 0.9897** | **0.0719 ± 0.0438** | 72 | 62 |
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| MOEA/D | 2.8022 ± 1.7807 | 0.2279 ± 0.2247 | 78 | 22 |
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| AGE-MOEA | 4.5395 ± 2.2114 | 0.3930 ± 0.2864 | 90 | 193 |
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| NSGA-III | 5.9130 ± 2.8212 | 0.4375 ± 0.2212 | 92 | 81 |
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**GrEA shines on linear fronts** — the grid-based niching matches the
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geometry better than reference points.
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## Rastrigin (dim=5, 50000 evals/run × 10 seeds)
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Highly multimodal trap: `f = 10n + Σ(xᵢ² − 10·cos(2π·xᵢ))`. Hard because a
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near-quadratic global bowl is overlaid with ~10⁵ regularly spaced local
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minima — any greedy step lands in the nearest dimple. Global optimum
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`f = 0` at the origin.
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| algorithm | best f | ms |
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| **(1+1)-ES** | **0.0000e0 ± 0.00e0** | 4 |
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| **DE** | **0.0000e0 ± 0.00e0** | 6 |
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| GA | 7.0913e-8 ± 5.50e-8 | 15 |
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| NSGA-II | 4.9270e-5 ± 5.04e-5 | 60 |
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| IPOP-CMA-ES | 1.3423e-1 ± 2.71e-1 | 61 |
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| PSO | 7.9598e-1 ± 8.67e-1 | 5 |
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| CMA-ES | 2.3453e0 ± 1.49e0 | 10 |
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| SimulatedAnneal | 3.8540e0 ± 1.48e0 | 7 |
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| RandomSearch | 1.1064e1 ± 2.54e0 | 14 |
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| HillClimber | 1.5966e1 ± 6.25e0 | 6 |
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| PAES | 1.5966e1 ± 6.25e0 | 10 |
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(1+1)-ES and DE tie for `f = 0`. **IPOP-CMA-ES drops vanilla CMA-ES from
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2.35 → 0.13** — the restart logic does what it should.
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## Rosenbrock (dim=5, 30000 evals × 10 seeds)
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Rosenbrock's banana valley: `f = Σ(100·(xᵢ₊₁ − xᵢ²)² + (1 − xᵢ)²)`. Hard
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because the minimum sits in a long, bent, near-flat valley — easy to
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enter, very slow to crawl along to the tip. Global optimum `f = 0` at the
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all-ones point.
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| algorithm | best f | ms |
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| **Nelder-Mead** | **0.0000e0 ± 0.00e0** | 1 |
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| CMA-ES | 3.6207e-29 ± 2.35e-29 | 5 |
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| TLBO | 1.8458e-3 ± 1.91e-3 | 1 |
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| DE | 3.3345e-1 ± 3.01e-1 | 2 |
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| PSO | 8.2124e-1 ± 1.58e0 | 2 |
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| (1+1)-ES | 2.2115e0 ± 2.70e0 | 1 |
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| BO (60 evals) | 3.1725e3 ± 2.92e3 | 39 |
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Nelder-Mead **= 0 exactly**, CMA-ES at machine epsilon. BO at only 60
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evaluations is honestly bad on 5-D Rosenbrock (no kernel hyperparameter
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tuning) — included as a reminder that BO needs more evaluations than a
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smooth problem actually requires for these other methods.
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## Ackley (dim=5, 30000 evals × 10 seeds)
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Ackley's function: a near-flat outer plateau with shallow ripples
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surrounding a single deep, narrow global basin. Hard because the gradient
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is almost zero far from the optimum, giving local search little to
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follow. Global optimum `f = 0` at the origin.
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| algorithm | best f | ms |
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| **DE** | **4.4409e-16 ± 0.00e0** | 3 |
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| PSO | 1.5099e-15 ± 1.63e-15 | 3 |
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| CMA-ES | 1.5099e-15 ± 1.63e-15 | 5 |
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| TLBO | 2.2204e-15 ± 1.78e-15 | 2 |
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| BO (60 evals) | 1.9622e1 ± 1.23e0 | 38 |
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All conventional methods reach machine precision. BO at 60 evals
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struggles — same caveat as Rosenbrock.
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---
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## TSP ring-15 (8000 evals/run × 10 seeds)
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15 equally-spaced cities on the unit circle; minimize the closed tour
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length. The space is `(15−1)!/2` distinct tours, but cities in convex
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position have no 2-opt local optima — so this instance cleanly separates
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methods with good neighbourhood moves (inversion = 2-opt) from blind
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recombination / sampling. Known optimum (the polygon perimeter):
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**6.2374**.
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| algorithm | tour length ↓ | ms |
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| **HillClimber** | **6.2374 ± 0.0000** | 0 |
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| **SimulatedAnneal** | **6.2374 ± 0.0000** | 0 |
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| **TabuSearch** | **6.2374 ± 0.0000** | 0 |
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| **AntColony** | **6.2374 ± 0.0000** | 8 |
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| GA | 7.0133 ± 0.6725 | 2 |
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| RandomSearch | 12.1474 ± 0.6797 | 1 |
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Every local-search method (and Ant Colony) hits the exact optimum — as
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theory predicts for convex-position TSP under 2-opt. The GA's order
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crossover drifts off the optimum, and random sampling is hopeless.
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## JSS FT06 (8000 evals/run × 10 seeds)
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Fisher & Thompson 1963 6-job × 6-machine job-shop; minimize makespan.
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Hard because every job has a fixed machine order, so swapping two
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operations can ripple delays across the whole schedule. Known optimum:
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**55**.
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| algorithm | makespan ↓ | ms |
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| **SimulatedAnneal** | **55.2000 ± 0.6000** | 1 |
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| TabuSearch | 55.9000 ± 1.4457 | 1 |
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| GA | 56.0000 ± 1.5492 | 4 |
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| RandomSearch | 58.5000 ± 1.2042 | 4 |
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| HillClimber | 62.5000 ± 4.3186 | 0 |
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Simulated annealing gets within 0.4% of the known optimum on average;
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greedy hill-climbing stalls in operation-order local optima.
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## Knapsack (30 items, bi-objective, 20000 evals/run × 10 seeds)
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Zitzler-Thiele style 0/1 knapsack: two profit vectors, one capacity (half
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the total weight). Hard because the two profit objectives conflict and
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the capacity constraint carves feasible regions out of the `2³⁰`
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bitstrings. No closed-form optimum; scored by hypervolume vs reference
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`[0, 0]` (higher is better).
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| algorithm | hypervolume ↑ | front | ms |
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| **NSGA-II** | **1360468.3 ± 11619.6** | 100 | 39 |
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| SPEA2 | 1355615.5 ± 9266.8 | 100 | 213 |
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| IBEA | 1352595.5 ± 10183.6 | 99 | 101 |
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| NSGA-III | 1346446.0 ± 6922.1 | 100 | 39 |
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| RandomSearch | 1118233.1 ± 34150.3 | 9 | 17 |
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The three Pareto EAs land within ~1% of each other; random search finds a
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front of only ~9 points and trails badly.
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