Function binary_tournament 

pub fn binary_tournament(
    rank: &[usize],
    crowding: &[f64],
    rng: &mut ChaCha8Rng,
) -> Option<usize>

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

Two candidates are drawn uniformly (with replacement, as in the reference) and the crowded-better one wins: a lower non-domination rank beats a higher one, and within the same rank a larger crowding distance beats a smaller one — quality first, diversity as the tie-break.

A complete tie goes to the second draw. The crowded-comparison operator is asked “is the first candidate better”, and a tie answers no, so the second wins. This is not a corner case: crowding distance is ∞ at every front boundary and a front of one or two is all boundary, so equal-rank equal-distance pairs are routine. Either convention is a pure function of the RNG stream (which is what the operator’s determinism actually rests on) and NSGA-II’s definition leaves the tie arbitrary; this one is the code’s, it is pinned by a test, and it is stated here so a reader can rely on it.

Draws exactly two random_range(0..n) values. Returns None for an empty population (there is nobody to select), rather than panicking on an empty range.

This is deliberately stronger than Optuna’s NSGA-II parent selection, which compares by dominance alone and leaves crowding distance as a TODO: without the diversity tie-break the tournament has no preference at all inside the first front, which is where a converged run spends most of its time.