Scoring

Multi-Component Score

Every selection (intermediate or final) is evaluated by a Score with four components, in strict priority order:

Component	Range	Meaning
size	0 to 1	1.0 when exactly k vectors are selected. Used internally during initialization; always 1.0 in a final solution.
constraints	0 to 1	1.0 when all fairness constraints are satisfied. Lower values indicate more constraint violations.
diversity	0+	The main diversity metric value (higher is better).
div_tie_breakers	0+	Secondary diversity metrics, used to break ties.

When comparing two solutions, the solver checks components in priority order: a solution with higher constraints score always beats one with higher diversity, regardless of how large the diversity difference is. Within the same constraint satisfaction level, higher diversity wins.

Why Priority Ordering?

Consider a problem with fairness constraints. Without priority ordering, the solver might find a highly diverse selection that badly violates constraints. The strict ordering ensures that:

• The solver always moves towards feasible solutions first
• Diversity is only optimized within the space of equally-feasible solutions
• Infeasible problems gracefully degrade to the least-violated solution

Diversity Tie-Breakers

Some diversity metrics produce many tied scores, which makes it hard for swap-based optimization to make progress. Tie-breakers are additional diversity metrics that help distinguish between solutions with equal primary diversity scores.

The solver automatically selects appropriate tie-breakers based on your chosen diversity metric:

Primary Metric	Default Tie-Breakers	Why
MIN_SEPARATION	APPROX_GEOMEAN_SEPARATION, NON_ZERO_SEPARATION_FRAC	Min-separation only depends on the closest pair. Swapping any other vector doesn't change the score, causing many ties. The geomean tie-breaker guides the solver towards improving the overall spread.
GEOMEAN_SEPARATION	NON_ZERO_SEPARATION_FRAC	Geomean is zero if any separation is zero. When multiple separations are zero, single swaps can't improve the score. The non-zero fraction tie-breaker guides the solver towards eliminating zero-distance vectors.
MEAN_SEPARATION	(none)	Mean separation rarely produces ties.

You can override the defaults via MaxDivSolverBuilder.with_diversity_tie_breakers().

Soft Constraints (Advanced)

By default, constraints are hard: constraint score strictly outranks diversity. The solver's optimization strategies support a constraint_softness parameter (0.0 to 1.0) that blends diversity into the constraint score:

• 0.0 -- fully hard constraints (default)
• 0.0 < s < 1.0 -- partially soft: constraint_score^(1-s) * diversity^s
• 1.0 -- fully soft: constraints are ignored, only diversity matters

This is configured at the strategy level and is primarily useful for advanced solver tuning. The built-in presets use hard constraints with a brief initial phase where infeasible diversity is ignored, allowing the solver to focus on reaching feasibility before optimizing diversity.