feat: shift and rotation wrappers and seventeen CEC- and BBOB-style functions, each with its own example

[tachsinatalay-code]

Batch 10b of #260: the shift and rotation wrappers, and 17 CEC- and BBOB-style functions, each with its own example.

The wrappers

problems::Shifted<P> and problems::Rotated<P>, generic over any Problem on Real genomes and generated from a seed, so the same seed gives the same instance on every platform:

• Shifted moves the wrapped optimum's first solution to a point uniform in the middle 80% of each range: CEC's [−80, 80] in [−100, 100], BBOB's [−4, 4] in [−5, 5].
• Rotated draws a matrix of standard normal numbers from the seed and orthonormalizes its rows by Gram-Schmidt, applied twice, which is BBOB's method. It turns the function about that solution, as CEC 2005's (x − o) M and BBOB's R (x − xᵒᵖᵗ) do.
• Both keep the optimum's value, take their name and reference from the wrapped problem, and draw from separate streams of the seed, so a problem shifted and rotated with one seed gets independent ones. They aren't in the registry, since they're instances of other problems. The shifted and rotated Rastrigin of CEC 2005 and BBOB are these wrappers around Rastrigin.

The functions

Sum of different powers, step, quartic (without noise, or with noise seeded from the genome), Yao, Liu and Lin's penalized 1 and 2, the high-conditioned elliptic, bent cigar, discus, BBOB's different powers, Büche-Rastrigin, non-continuous Rastrigin, Weierstrass, Katsuura, HappyCat, HGBat, Schaffer F7 and the rotated hyper-ellipsoid. They're in problems::all() and gx.problems.

Sources read:

• the BBOB definitions (RR-6829, version 2 of 2019, with its errata)
• the CEC 2005, 2014 and 2017 reports
• Yao, Liu and Lin (1999)
• Liang, Qin, Suganthan and Baskar (2006)
• Molga and Smutnicki (2005)

Not reachable: Beyer and Finck (2012), Katsuura (1991), Schaffer et al. (1989), Levy and Montalvo (1985), and De Jong's thesis for F4's noise.

Choices:

• Form: the functions are the plain basic functions, z = x, as the CEC 2014 and 2017 reports define them; BBOB composes its own with T_osz, T_asy and conditioning matrices. The exception is Büche-Rastrigin, which exists only in BBOB's form and keeps T_osz and its penalty.
• Bounds: each follows its plain form's source: CEC's [−100, 100] for the elliptic, bent cigar and discus; BBOB's [−5, 5] for different powers, Büche-Rastrigin and Katsuura; CEC 2014's scaled [−5, 5] for HappyCat and HGBat; Schaffer F6's [−100, 100] for F7.

Corrections to the sources:

• Molga and Smutnicki's "rotated" hyper-ellipsoid is axis-parallel: Σⱼ (n − j + 1) xⱼ².
• Yao, Liu and Lin's appendix gives f12's minimizer as (1, …, 1); it's (−1, …, −1). Their table I also drops the square of f13's last (xₙ − 1).
• The CEC 2017 report prints Schaffer F7 with sin, for BBOB's sin².

Other findings:

• Katsuura's minima include the bounds ±5, where a PSO that stops particles at the bounds lands.
• At G06's minimum, shifted, rounding in x − o leaves an active constraint violated by 6e-14; the docs say so.

The minima are proven from the formulas, every term being at least 0, except the noisy quartic's, which isn't known. The plan has the details in section 1.1's "Checked in batch 10b".

I checked by hand the bent cigar, discus, high-conditioned elliptic (with its guard for n = 1), HappyCat and Weierstrass (a = 0.5, b = 3, 21 terms, with the offset that makes the minimum exactly 0) against the CEC 2014 definitions.

Examples

One per function, with their rows in examples/README.md and contours on the site, including those of rotated functions (problem.rotation). To fit them among the continuous functions, 111 existing examples' orders move up by 10 or 20, ending at 198. That's below the marine design (229) and the newer method pages (280 on), and no new orders collide.

Rebased on today's main

Three conflicts:

• src/problems.rs: the new mod gradients; and mod transform;, both kept.
• ContourPlot.jsx: both comment additions kept (Nelder-Mead's simplex and the rotation).
• docs/features.md: this keeps main's new method entries, its sentence on the constraints' values, and its gradients clause. The clause now says which problems have gradients: the smooth ones up to Kowalik and Powell.

Follow-up, not in this PR: the new functions don't provide analytic gradients yet, and Shifted/Rotated don't pass a wrapped problem's gradient through (chain rule through the shift and the rotation). Both are worth doing now that main has gradients for the other smooth problems.

Tests

Locally, rebased on main:

• Lint: all four steps pass with Rust 1.99 (WSL): fmt, clippy with and without features, and the docs.
• Rust: cargo test --all-features passes (24 suites).
• Python: mypy --strict genoxide reports no issues, and pytest passes (974 passed, 1 skipped).
• Examples: all 17 print their output.txt identically in Rust and Python.