Module indicators 

Auditable quality indicators for minimized multi-objective fronts.

Every function rejects empty, non-finite, or dimensionally inconsistent input. Hypervolume additionally requires an explicit reference point that is weakly worse than every approximation point. Exact and sampled results are different enum variants so an approximation cannot be reported as an exact value accidentally.

Structs

HypervolumeReport

Hypervolume value plus deterministic front-cleanup accounting.

ReferencePoint

Explicit, validated hypervolume reference point for minimized objectives.

Enums

HypervolumeEstimate

Exact or explicitly sampled hypervolume estimate.

IndicatorError

Validation failures returned by quality indicators.

OutsidePolicy

Policy for hypervolume points outside the minimized reference box.

Functions

additive_epsilon

Unary additive epsilon indicator Iε+(front, reference_set) for minimized objectives. Smaller values are better and negative values indicate strict improvement over the complete reference set.

crowding_distance

Compute normalized NSGA-II crowding distances for one supplied front.

gd

Generational distance: mean nearest Euclidean distance from each approximation point to the reference set.

gd_plus

GD+ using only approximation coordinates that are worse than a reference point under minimization.

hypervolume

Compute exact hypervolume through four objectives and deterministic Monte Carlo hypervolume above four objectives.

hypervolume_monte_carlo

Estimate hypervolume uniformly inside the front/reference bounding box.

hypervolume_with

Compute hypervolume with an explicit outside-reference policy.

igd

Inverted generational distance: mean nearest Euclidean distance from each reference point to the approximation front.

igd_plus

IGD+ using only approximation coordinates that are worse than a reference point under minimization.

nondominated_sort

Partition minimized objective vectors into successive non-dominated fronts.

spacing

Standard spacing of nearest-neighbor Manhattan distances within a front. A single-point front has zero spacing.

spread

Generalized Deb spread using nearest-neighbor Euclidean distances and explicit extreme points. Zero is perfectly even; larger is less uniform.