Table of Contents

Class NSGAIIIElitePopulationSelectionStrategy

Namespace
OptunaSharp.Samplers.Nsgaiii
Assembly
OptunaSharp.dll

The default elite-population selection strategy of NSGAIIISampler. Port of optuna/samplers/_nsgaiii/_elite_population_selection_strategy.py.

Ranks the combined population by (constrained) non-domination (shared RankPopulation(IReadOnlyList<FrozenTrial>, IReadOnlyList<StudyDirection>, bool)), then fills the elite population rank by rank. The rank that overflows population_size — the borderline front — is truncated by reference-point niching rather than crowding distance: objective values are normalized onto a hyperplane (ideal point + achievement-scalarizing extreme points), each individual is associated with its closest reference point, and survivors are drawn to keep the reference points as evenly populated (sparse) as possible.

Bit-exact. The whole pipeline matches Optuna bit-for-bit: _filter_inf, the ideal-point subtraction, the ASF einsum/argmin extreme-point pick, the reference-point association (numpy's 4-operand einsum replicated term-by-term, verified bit-identical over 2000 cases; its two np.linalg.norm(axis=...) calls and the axis argmin/min run through NumSharp, so the row sums take NumPy's pairwise order from eight objectives on — before 2026-11-11 they were left-to-right sums, exact only up to seven objectives), the niching, and — since 2.15 — the hyperplane fit itself: the degeneracy MatrixRank(double[,]) branch and the Solve(double[,], double[]) route through NumSharp's np.linalg.matrix_rank/solve over the OpenBLAS LAPACK backend, which is byte-identical to NumPy (the earlier managed reciprocal-multiplier LU drifted ~1 ULP on a few percent of the extreme-point systems; the LAPACK route removes even that). Every RNG draw (rng.shuffle) stays in lock-step. Confirmed byte-for-byte over a 400-config differential (5 crossovers × {2,3,4} objectives × 25 seeds + 25 constrained); the many-objective regime (8 and 10 objectives) is pinned by the live NsgaiiiSamplerParityTests.ManyObjectives_FullState_IsBitIdentical.

public class NSGAIIIElitePopulationSelectionStrategy
Inheritance
NSGAIIIElitePopulationSelectionStrategy
Inherited Members

Constructors

NSGAIIIElitePopulationSelectionStrategy(int, LazyRandomState, Func<FrozenTrial, IEnumerable<double>>?, double[,]?, int)

Configures nondomination ranking and reference-point niching to a fixed population size.

public NSGAIIIElitePopulationSelectionStrategy(int populationSize, LazyRandomState rng, Func<FrozenTrial, IEnumerable<double>>? constraintsFunc = null, double[,]? referencePoints = null, int dividingParameter = 3)

Parameters

populationSize int

Number of individuals retained or evaluated per generation.

rng LazyRandomState

Random stream whose draw order is shared with the reference algorithm.

constraintsFunc Func<FrozenTrial, IEnumerable<double>>

Optional legacy callback returning constraint values; positive values violate a constraint.

referencePoints double[,]

Reference vectors, one row per point and one column per objective.

dividingParameter int

Number of simplex divisions used to generate reference points.

Exceptions

ValueError

Population size is below two.

Methods

Select(Study, List<FrozenTrial>)

Select the elite population from the given trials by the NSGA-III algorithm (Python call).

public List<FrozenTrial> Select(Study study, List<FrozenTrial> population)

Parameters

study Study

Study supplying trial history, objective directions, and storage.

population List<FrozenTrial>

Individuals available for survival or reproduction.

Returns

List<FrozenTrial>

The individuals retained by the configured survival rule, in selection order.

Exceptions

ValueError

The reference-point dimension does not match the study objective count.

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