Constraints and utilities

1. DeltaPenalty and ClosestValidPenalty treat an ndarray delta or distance as a per-objective sequence. A 0-d array is broadcast; a 1-d vector is not passed to itertools.repeat.
2. SortingNetwork.evaluate copies each case, sorts the copy, and compares it to sorted(original), so integer cases are not scored as bit-count patterns.
3. case_errors reduces aligned 1D predicted and target series into one mean-squared error per case segment. Accepts explicit half-open (start, stop) ranges or a boolean mask (one case per contiguous True run). Non-finite samples are skipped; optional valid= covers the vwhere warmup trap from columnar GP.
4. duplicate_count hashes a NumPy-array key by shape, dtype, and raw bytes. Equal ndarray individuals no longer raise ValueError from sorted() or list membership.
5. nsga_convergence and nsga_diversity read fitness.values for reference individuals. A list genome is no longer treated as the objective vector when fitness is set.
6. inv_gen_dist uses the same fitness-first point extraction. Two fronts of individuals are no longer scored as gene lists.
7. nsga_diversity sorts the front by the first objective before Deb's \(\Delta\) (a permutation of the same points no longer changes the value), and returns \(1\) when the denominator is \(0\) (a single point, or several copies of one point with extremes at that point). It no longer raises ZeroDivisionError.
8. SortingNetwork.draw sizes the ASCII grid so empty and one-level networks no longer IndexError when writing wire labels or last-level spacers.
9. spawn_rng(seed, worker_id) and map_spawned give each mapped item an independent, seedable stream that does not collide with process-wide tools.rng and does not depend on pool scheduling (user-provided streams). The parent generator stays checkpointable.
10. PolicyObservation and policy_observe define the fixed Push policy observation schema. Summary helpers coerce outputs from case_errors, score_case_exams, ArchiveStats, and promoted-library counters; raw NumPy packs and column slices are rejected at the boundary. policy_exam_scores splits train vs held-out exam difficulty without exposing matrix[t]. Not a genome and not a domain metric — the firewall before a private Push loop (Push GP P11).
11. sort_non_dominated ranks only individuals with a finite, valid fitness. A mixed or all-invalid pool no longer raises ValueError or places unevaluated members on the first front. sel_count <= 0 returns [].
12. nsga_diversity returns \(1\) for an empty front. ordered[0] no longer raises IndexError.
13. nsga_convergence and inv_gen_dist return \(0\) when either point set is empty. cdist no longer raises ValueError on a 1-D empty array.
14. affine_case_errors fits Keijzer \(a + b\,f(x)\) on the same valid= mask as case_errors, applies the scaled series, and returns per-case MSE without changing the tree. Darwinian scoring default; Lamarckian write_affine_scale stays opt-in.
15. held_out_tail and train_head return last-fraction holdout and train catalog indices. case_generalization_pool and case_generalization_recipe build a CaseExamPool with a caller-marked held_out exam. make_lexicase_train_select registers lexicase on train cases only. case_halving_stages, evaluate_case_halving, and case_eval_charge implement successive halving on train-catalog prefixes and charge partial exams in case-eval units for n_evals= budgeting. Chronological meaning stays on the caller. DEAP has no held-out lexicase recipe or case-budget halving schedule. See the columnar GP tutorial.
16. structural_meta_case_columns and structural_meta_case_weights build cheap structural meta-cases (size, depth, unique opcodes, promote hits, non-finite fraction) to append to a packed case matrix for lexicase bloat and “always on” regularization without a second fitness weight. Lexicase selectors accept optional fit_weights= when the matrix is wider than fitness.values. DEAP has no equivalent. See the columnar GP tutorial.
17. resample(ind, evaluate, n) averages independent noisy draws and optionally writes fitness.values. Repeats go through EvalCache when cache= is set; noisy_draw_key pairs a caller key with the draw index so identical draws hit the cache and a noisy evaluate must vary the key per draw. race_stop runs F-Race-shaped elimination across survivors (one resample per round, drop challengers significantly worse on the first objective). race_eval_charge counts evaluate units for n_evals= budgeting. Not a domain metric and not a new algorithm loop. DEAP has no noisy resample helper.