Module pareto 

Multi-objective comparison: dominance, fronts, crowding, constraints and hypervolume.

This is the arithmetic multi-objective optimization rests on, kept free of any sampler, study or storage state so every piece can be pinned by an exact golden computed by hand. Nsga2 is its first consumer; StudyView::pareto_front is the second.

Piece	Answers
dominates	is a at least as good in every objective and better in one?
constrained_dominates	the same question, feasibility first
fast_non_dominated_sort	which front does each point belong to?
crowding_distance	how isolated is a point inside its front?
hypervolume	how much objective space does a front cover?
worst_constraints	what does a multi-seed fan’s feasibility collapse to?

Multi-objective is not a bolt-on

The seams were built for this from M1: a trial’s values is a Vec<f64>, Scheduler::on_report takes a values slice so pruning is multi-objective-aware, and StudyView::best deliberately returns None for a multi-objective study because there is no total order on a Pareto front. This module is the answer that replaces it.

Two decisions that run through everything

A NaN objective never wins. A vector that carries a NaN — or that has the wrong number of objectives — is incomparable rubbish: it dominates nothing and is dominated by every well-formed vector, so it sinks to the last front instead of silently colonising the Pareto set. This matches Direction::is_better (where NaN is never better than anything) and the multi-seed aggregates (where NaN propagates and simply cannot win). ±∞ is an ordinary float here and compares normally.

Constraints are feasibility-first (Constraints): a feasible solution beats an infeasible one whatever their objectives say, and two infeasible ones are ranked by total violation. The sign convention is Optuna’s — ≤ 0 is satisfied, > 0 is violated — and a constraint value is recorded as typed state on the trial (constraint, TrialCtx::record_constraints), never as an extra objective column. A trial that is a multi-seed fan records one vector per replicate and carries their componentwise worst (worst_constraints), because feasibility has to hold on every seed.

Re-exports

pub use constraint::CONSTRAINT_BLOB_KIND;

pub use constraint::CONSTRAINT_BLOB_VERSION;

pub use constraint::TrialConstraints;

pub use constraint::constraint_scope;

pub use constraint::is_feasible;

pub use constraint::total_violation;

pub use constraint::worst_constraints;

Modules

constraint

Typed constraints: the sign convention, the arithmetic, and where a trial’s constraint values live.

Structs

Point

One solution as the comparison layer sees it: its objectives and, if it declared any, its constraint values.

Constants

MAX_EXACT_HYPERVOLUME_DIM

The highest objective count hypervolume computes exactly.

Functions

constrained_dominates

Feasibility-first dominance (Deb 2000), the relation a constrained multi-objective study ranks by.

crowding_distance

The crowding distance of every member of one front (Deb et al. 2002).

dominates

Direction-aware Pareto dominance: a dominates b iff it is no worse in every objective and strictly better in at least one.

fast_non_dominated_sort

Deb’s fast non-dominated sort: partitions points into fronts, front 0 being the non-dominated (Pareto) set.

hypervolume

The hypervolume indicator: the volume of objective space that points dominate, bounded by reference.

nadir_point

The nadir point of a set of objective vectors: the componentwise worst value observed, in the study’s own orientation.

non_domination_ranks

The non-domination rank of every point: 0 for the Pareto front, 1 for what is left once it is removed, and so on.

pareto_front_indices

The indices of the non-dominated (Pareto) set — front 0 of fast_non_dominated_sort, ascending.