Module variation 

The pure NSGA-II variation operators, in the transform-layer unit hypercube.

The arithmetic core of Nsga2, kept free of any sampler or study state so every operator can be pinned by an exact golden computed by hand from the published formulas.

Everything works on the unit representation of a configuration — one coordinate in [0, 1] per declared parameter — so a single implementation covers every Distribution kind; mapping back to the declared support is Distribution::from_unit’s job, done once when the child is finally assigned.

A categorical is not an interval, and this module says so

Simulated binary crossover and polynomial mutation are real-parameter operators: they assume that the numbers between two parents are meaningful intermediates. That is true for a Float and (after rounding) for an Int — the unit coordinate of a log-scaled or stepped numeric is still a position on a monotone axis. It is false for a Cat or a Bool: “halfway between adam and rmsprop” is not a thing, and blending their unit coordinates would invent an ordering that the study never declared.

So the two kinds get different operators, and the split is GeneKind-driven rather than hidden:

Gene	Crossover	Mutation
Numeric	SBX, η_c	polynomial, η_m
Categorical	uniform: take one parent’s value whole	uniform re-choice over the support

The RNG stream is a function of the dimension alone

Both operators draw a fixed number of f64s per dimension, whatever the rates are and whichever branch a coin takes: crossover draws exactly one per dimension, mutate exactly two (a rate coin and a magnitude, even when the coin does not fire). That costs a few wasted draws and buys the property a resumed study rests on — the stream position after an operator depends only on d. Short-circuiting either loop would make the sequence depend on the coins, which is precisely the defect crossover_bin documents having been fixed.

Enums

GeneKind

Which family of operators a declared parameter belongs to.

Functions

binary_tournament

NSGA-II’s binary tournament on the crowded-comparison operator.

crossover

Breeds one child from two parents, gene by gene.

mutate

Mutates a child in place, gene by gene, at per-gene probability rate.

polynomial_delta

The perturbation of polynomial mutation (Deb & Goyal 1996).

random_unit_vector

A fresh uniform-random unit vector in [0, 1]^d — the initial population’s generator, drawing exactly one f64 per dimension.

sbx_child

One child coordinate of simulated binary crossover (Deb & Agrawal 1995).