Operators and selection

These items were open on the DEAP tracker, or were defects inherited from the original sources.

1. mut_polynomial_bounded clamps each gene into [low, up] before the Deb powers and requires eta > 0, so an out-of-box gene no longer writes NaN or a complex value.
2. cx_simulated_binary_bounded uses the same clamp and eta guard. Out-of-box parents no longer raise TypeError on complex arithmetic. The second child uses the opposite sign of \(\beta_q\), matching Deb / DEAP (c2 is the upper child, not a second lower child).
3. cx_blend_bounded is the boxed form of blend crossover: the same \(\gamma\) draw as cx_blend, then a clamp on each child gene.
4. cx_partially_matched, uniform PMX, and cx_ordered map alleles by value. Permutations of named cities or other non-{0..n-1} encodings no longer IndexError or silently write the wrong genes.
5. mut_heterogeneous applies one mutator per gene, so a mixed encoding (bit + int range + choice) does not need a one-off mutator. cx_heterogeneous is the matching mate dispatcher: one callable per gene, or one existing cx_* per slice.
6. assign_crowding_dist can crowd on wvalues via use_weights=True. The default, and sel_nsga_2, still use raw values.
7. sel_tournament_dcd (also) accepts any 1 ≤ k ≤ len(individuals). When k is a multiple of 4 the original paired-shuffle path is used; other counts run pairwise contests until k winners are collected. k ≤ 0 returns an empty list.
8. sel_roulette and sel_stochastic_universal_sampling spin the wheel on wvalues[0]. A negative floor is shifted so a minimization weight still has a positive slice. When every slice is zero the draw is uniform instead of an empty list. An empty pool or sel_count ≤ 0 returns [].
9. mig_ring evicts by object identity. Two individuals with equal genes are no longer treated as the same slot. Emigrants are cloned when a replacement operator is set, so the source deme is not aliased into the destination. Duplicate draws take the next unused index instead of writing one vacancy twice.
10. cx_messy_one_point cuts each parent independently, so lengths can change. Equal-length parents no longer degenerate into a shared-interval two-point swap.
11. Sequence crossovers copy slices before assignment. NumPy views are not aliased, so a one-point or uniform swap does not destroy a parent. cx_es_two_point_copy applies the same copy to the strategy vector.
12. sel_spea_2 uses the full distance row for density, with the self-distance set to infinity, so the \(k\)-th neighbour is not the zero pad of the upper triangle. The density is \(1 / (\sigma_i^k + 2)\) with \(k = \lfloor\sqrt{N}\rfloor\) (Zitzler, Laumanns and Thiele, 2001), not the \((k+1)\)-th neighbour. An empty pool returns [].
13. sel_nsga_3 intercepts on the success path are \(1/x + \mathrm{best}\). Association treats a near-zero \(\mathrm{intercepts} - \mathrm{best}\) gap as \(1\) so the niche distance is not NaN. Niching stops when the last front is exhausted, so a \(k\) larger than the pool does not loop forever.
14. cx_one_point, cx_two_point, cx_ordered, and mut_shuffle_indexes no-op when a parent is shorter than two genes, so a length-1 individual no longer hits an empty randint interval or a two-cut sample on a one-gene permutation.
15. broadcast_param treats numbers.Integral and numbers.Real as scalars, so a NumPy integer or float32 / float16 bound no longer raises TypeError from len() on a NumPy scalar.
16. sel_lexicase and sel_epsilon_lexicase accept cases= to filter on a per-generation subset of fitness indices. Defaults still use every case. sample_informed_cases builds that subset by farthest-first traversal of Hamming distances between case solve vectors, so synonymous cases are not over-sampled. fitness_case_matrix packs fitness.values into a dense matrix; optional matrix= and trust_matrix= let lexicase and informed down-sampling reuse one pack per generation.
17. sel_sms_emoa reduces a pool by non-dominated sorting, then removes the least hypervolume contributor on the critical front until the quota is met. Optional ref_point follows the same minimization-space convention as hypervolume and least_contrib. Works on parents + offspring or steady-state parents + [child].
18. sel_moead and SelMOEADWithMemory pick one winner per decomposition weight from uniform_reference_points, using Tchebycheff or PBI scalarization with Pareto-rank-aware tie breaks and NSGA-II-style crowding on the fill pass.
19. sel_age_moea_2 and SelAGE2WithMemory advance front by front: geodesic diversity on partial \(F_1\), inverse Minkowski on later partial fronts, with Newton–Raphson curvature on the first front.
20. mut_gaussian_bounded applies the same \(N(\mu, \sigma)\) draw as mut_gaussian, then clamps each mutated gene into [low, up]. Bounds may be scalars or per-gene sequences, matching mut_polynomial_bounded. Empty intervals are skipped.
21. mut_de writes a DE/rand/1/bin trial in place: \(a_i + F(b_i - c_i)\) on a binomial gene subset (cx_prob, at least one gene). Optional low / up clamp the written genes. Selection stays on the caller. DEAP only has this loop in examples.
22. constraint_dominates is Deb's feasibility-first comparison: feasible beats infeasible; two feasibles use ordinary Pareto; two infeasibles prefer the smaller constraint violation. sel_nsga_2 accepts optional feasible= / violation= callables and ranks with that rule. Defaults stay unconstrained NSGA-II. Fitness values are not rewritten.
23. sel_team assembles sel_count individuals by greedy maximum coverage of cases solved at 0. Optional cases=, matrix=, and trust_matrix= match lexicase. The team is a sequence of pool members; member fitness is not rewritten. Team scoring stays on the caller. sel_team_archive pools occupied MAP-Elites cells via list(archive) and delegates to sel_team. DEAP has no team selector.
24. CaseExam and CaseExamPool store case subsets as ranges or a 1-D bool mask — the same shapes case_errors and sel_lexicase(..., cases=) consume — not as a new genome. score_case_exams ranks exams on elites by unsolved count or Hamming distance from the all-solved vector (solved ≡ \(0\)). mut_case_ranges / mut_case_mask vary bounds or flip mask runs; guard_case_exams blocks the empty exam and the all-solved collapse. next_lexicase_cases returns the mutated or guarded winner as the next cases= list. informed=True (the default) is a guard repair path only — it does not overwrite a healthy exam. Chronological splits stay on the caller.
25. mig_ring pairs source emigrants with dest vacancies by length, and stops claiming slots once a deme is full. Unequal island sizes, or sel_random with k larger than a deme, no longer IndexError or StopIteration. An unreplaced home vacancy clones the leftover emigrant so two demes do not share one object.
26. sel_best and sel_worst return [] when sel_count <= 0. A negative count is no longer a Python slice that drops individuals from the other end of the ranked list.
27. mig_ring clones an emigrant that is already present in the destination, so a selector that returns the same object twice does not write that object into two dest slots.
28. sel_spea_2 returns [] when sel_count <= 0. A negative count no longer enters archive truncation and IndexErrors on an empty list. Matches sel_nsga_2 and sel_best.
29. cx_partially_matched no-ops when a parent is shorter than two genes. Empty permutations no longer hit randint(0, -1).
30. broadcast_param treats a 0-d ndarray as a scalar, so numpy.array(0.0) bounds no longer raise TypeError from len() on an unsized object.
31. policy_held_out_fitness scores policy individuals only on a caller-marked held_out exam. guard_policy_fitness_exam refuses train exams or a freshly mutated exam as the objective. Train quality stays in policy_exam_scores / policy_observe; record_policy_generalization_gap logs train, held-out, and gap as a generalization_gap Logbook chapter (Push GP P13).
32. PolicyActionGuard and guard_policy_action enforce hard caps on apply_policy_action: max promotes per generation, promote cooldown, max inner tune generations, minimum exam size, and rejection when an action would exceed remaining n_evals. Rejected actions return PolicyActionResult(rejected=True) without raising — the observation surface for last_action_rejected. DEAP has no policy action firewall (Push GP P14).
33. sel_novelty ranks a pool by average distance to the k nearest archive behavior descriptors via semantic_distance. Fitness stays on ind.fitness; novelty is the selection key. An empty archive falls back to sel_random. mut_iso_line interpolates toward a donor elite with t ~ Uniform(-iso, 1 + iso) and adds isotropic noise; iso_line_float, iso_line_int, and iso_line_bit compose through mut_heterogeneous on mixed genomes. ea_map_elites registers both like any other select / mutate; random_elites stays the parent source. DEAP has no novelty selector or archive-aware iso+line mutator. See the MAP-Elites example.
34. mig_fully_connected and mig_random sit next to mig_ring. Fully connected selects emigrants once per source, clones them along each outgoing edge, and claims distinct destination vacancies across incoming edges; random picks one destination per source. island_eval_keys hashes each deme's CaseExam — catalog subsets via a painted mask so mask and range storage match — and optional matrix identity for step_islands(..., eval_keys=). Custom graphs stay mig_ring(..., mig_indices=). DEAP has no named topologies. See the multiprocessing tutorial.
35. sel_batch_epsilon_lexicase shuffles active cases into batches of at most batch_size, reduces each batch (mean squared error by default), and runs epsilon-lexicase on the shorter matrix. A fresh partition is drawn per selected individual. Optional reduction= overrides the batch aggregate. matrix= / trust_matrix= / cases= match lexicase. sel_tournament_cases scores individuals on a case subset (column mean by default), then tournaments on those scalars. Informed down-sampling stays on sample_informed_cases; case_count= draws a random subset when cases is omitted. DEAP has no batch epsilon-lexicase or case-subset tournament. See the columnar GP tutorial.
36. sel_epsilon_lexicase accepts mode= on the vectorized filter: epsilon_auto / epsilon_static (population MAD and elite), epsilon_semi (population MAD, pool elite), and epsilon_dynamic (pool MAD and elite). next_downsample_cases returns the next cases= list each generation with mode= random, informed, cohort, or held_out (rotate through a caller-marked held-out exam). Chronological meaning stays on the caller. DEAP has no filter-pool epsilon modes or generation downsample schedule. See the columnar GP tutorial.
37. mut_iso_line treats NumPy integer genes as integers. A numpy.int64 gene no longer takes the float path and writes a non-integer value.
38. sel_random returns [] when the pool is empty. A positive sel_count no longer IndexErrors on rng.choice([]).
39. sel_double_tournament returns [] when the pool is empty or rounds <= 0. It no longer ValueErrors on max([]) after sel_random started returning an empty draw.
40. mut_polynomial_bounded mutates a gene when the draw is strictly below mut_prob, like every other mutator. A draw of exactly 0.0 no longer mutates at mut_prob=0.
41. mut_es_log_normal leaves an empty individual unchanged. It no longer raises ZeroDivisionError computing the learning rates from a length of \(0\).
42. mig_ring([]) is a no-op. With no demes, the default ring was [0] and raised IndexError on the missing deme.
43. sel_nsga_3 falls back to the worst point of the first front (not of every sorted front, or of the whole pool) when the hyperplane is singular or its intercepts are unusable. An objective whose nadir still sits within \(10^{-6}\) of the ideal point takes the population worst instead (Blank, Deb and Roy, 2019), so a flat axis is not normalized by a near-zero gap. sel_age_moea_2 shares the correction.
44. mig_ring with replacement=None clones an emigrant that is still present in its source deme, so a deme holding the same object twice does not end up sharing it with the next deme, and step_islands(eval_keys=...) cannot score it with the wrong deme's fitness. DEAP's migRing moved the emigrant by reference and replaced only one home slot.
45. sel_lexicase, sel_epsilon_lexicase, and sel_batch_epsilon_lexicase rank a NaN or ±inf case value as the worst value for its case, and the ε-lexicase MAD is taken over finite values only. One NaN, or inf in most of a case, used to empty the pool and turn selection uniformly random. DEAP's selLexicase, selEpsilonLexicase, and selAutomaticEpsilonLexicase emptied the pool the same way and raised IndexError from random.choice.
46. The lexicase selectors raise ValueError when any individual is unevaluated, the first one included. DEAP read the case count from the first individual, so a pool with no valid fitness had no cases and was picked uniformly at random.