module moplayground.utils.pareto

---

function get_nondominated

get_nondominated(F, epsilon=None)

---

function hypervolume_from_nondominated

hypervolume_from_nondominated(F_min)

Compute the hypervolume of a non-dominated front in minimization space.

Uses the origin as the reference point, so callers must pass an already-non-dominated, already-negated front (see get_pareto_statistics for the typical pipeline).

Args:

• F_min: (n_points, n_objectives) array of points in minimization space (i.e. negated objective values).

Returns: Hypervolume as a float, computed by pymoo.indicators.hv.HV.

---

function sparsity_from_normalized_nondominated

sparsity_from_normalized_nondominated(F_min_norm)

---

function get_pareto_statistics

get_pareto_statistics(F)

Compute hypervolume and sparsity for a set of objective vectors.

Extracts the non-dominated front of F (treated as a maximization problem), normalizes it, converts to minimization space, and returns the resulting hypervolume and spacing-based sparsity. When the front contains only one point, it is duplicated so the spacing indicator has at least two points to work with.

Args:

• F: (n_points, n_objectives) array of objective vectors (higher is better).

Returns: Tuple (hypervolume, sparsity).