The HSO M=3 path called the generic 2-D base case for every last-axis
slice, which re-sorted the active prefix by axis 0 each time -- O(n^2 log n)
overall. Since `projected` is already in last-axis order, sorting the
projected indices by axis 0 once and sweeping them with a `pi > k` skip
gives O(n^2) with no per-slice allocation. The M>=4 path is unchanged
(lifted out of the inner branch verbatim).
hypervolume_nd_bench_3d n=100: 361_595 -> 291_247 (-19%, 1.24x); n=30 -16%.
The sweep visits points in the same (axis-0, then last-axis) order the
stable per-prefix sort produced -- output is bit-identical, all 606 tests
pass.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
The per-file Phase 1 test commits were written without running rustfmt
as I went; this pass formats the new test code (long assert_eq! lines
wrapped, etc.). Formatting-only — no behavioural change.
Phase 1, tier 3 of the mutation-testing campaign — the shared Pareto /
metric / selection utilities used by every multi-objective algorithm.
A scoped cargo-mutants run found 75 survivors across these files; the
tests below target them.
- metrics/hypervolume.rs: dominates() boundary cases, non_dominated_
projection retained-set pins, hso_recursive 1-D/2-D base cases,
hypervolume_nd_from_evaluations empty/non-dominating skips.
- selection/tournament.rs: challenger_wins across the full feasibility
cross-product + equal-objective tie; better_by_objective and
better_by_feasibility branch pins; stochastic_ranking_select pf=0
feasibility ordering and count-wraps-modulo-population.
- pareto/crowding.rs: exact interior crowding distance on symmetric
and asymmetric fronts (pins the (next-prev)/span arithmetic).
- pareto/sort.rs: three-non-dominated-then-one-dominated and a strict
3-chain producing three singleton fronts.
- pareto/dominance.rs: trade-off → NonDominated, better-on-one-equal-
on-other → Dominates, identical → Equal.
- pareto/archive.rs: truncate boundary, trade-off kept alongside,
equal candidate rejected, smaller-violation infeasible eviction.
- pareto/front.rs: best_candidate keeps the first of tied minima.
- metrics/spacing.rs: exact spacing for a varying-NN-distance front.
src/core/problem.rs's lone survivor (decision_schema default body
'replace with vec![]') is an equivalent mutant — Vec::new() and vec![]
are identical — and is left in the residue.
Completes the rustdoc audit — every public item now has at least one
```rust example block in its docstring, exercised by
`cargo test --doc` (55 doctests, all passing).
- Operators: BitFlipMutation, SwapMutation, RealBounds,
GaussianMutation, BoundedGaussianMutation,
SimulatedBinaryCrossover, PolynomialMutation, LevyMutation,
ClampToBounds, ProjectToSimplex.
- Metrics: hypervolume_2d, hypervolume_nd, spacing.
- Pareto utilities: pareto_compare, pareto_front, best_candidate,
non_dominated_sort, crowding_distance, das_dennis,
ParetoArchive.
Each example is short (5-15 lines) and self-contained — copy-paste
into a fresh project and it runs.
The M≥3 branch of `hso_recursive` cloned every input point into
`sorted: Vec<Vec<f64>>` solely so it could sort. Each clone is M
f64s allocated; with N points per call and ~30 HV calls per SMS-EMOA
generation × 30 k generations, that's millions of small Vec<f64>
allocations.
Sort indices into a `Vec<usize>` instead, then iterate the original
points by index. The pre-projection step still produces a
Vec<Vec<f64>> (which the active-prefix slicing requires), but we
save the outer N inner-Vec clones per call.
gungraun (instructions):
- hypervolume_nd_3d n=30: 87 969 → 70 334 (-20 %, 1.25×)
- hypervolume_nd_3d n=100: 422 767 → 367 767 (-13 %, 1.15×)
Cumulative vs the v0.3.0 baseline:
- hypervolume_nd_3d n=30: 676 902 → 70 334 (9.6×)
- hypervolume_nd_3d n=100: 13 523 760 → 367 767 (37×)
Wall-clock impact is in the noise on the compare harness because the
SMS-EMOA worst-front HV calls operate on small fronts (5–10 points
once converged). The win is most visible in synthetic dense-front
HV benchmarks.
The HSO recursion in `hypervolume_nd` had three overheads that
dominated SMS-EMOA's per-generation cost on DTLZ2 (5.6 s baseline,
~30 k generations × ~40 HV calls per generation = ~1.2 M HV calls
per run):
1. `active = sorted.clone()` plus `active.iter().position(...)`
linear scan to remove the just-processed point each band — O(N)
per band, total O(N²) per HV call.
2. Per-band re-projection
`active.iter().map(|q| q[..last].to_vec())` — full
Vec<Vec<f64>> rebuild for every band, O(N·M) allocations per HV
call.
3. `non_dominated_projection` called even when recursing into the
M=2 base case, whose sweep already filters dominated points
internally.
Replace (1) with prefix-slicing `projected_all[..=k]` (sort points
ascending by last axis once; the active set at each band is just a
prefix). Pre-project once outside the loop (2). Skip the explicit
non-dominance filter when the inner recursion is M=2 (3).
Bit-identical output verified by re-running the compare harness and
diffing against the v0.3.0 snapshot — every quality metric matches
to the last decimal.
gungraun (instructions):
- hypervolume_nd_3d n=30: 676 902 → 87 969 (-87 %, 7.7×)
- hypervolume_nd_3d n=100: 13 523 760 → 422 767 (-97 %, 32×)
Wall-clock (compare harness, 10-seed mean):
- SMS-EMOA / DTLZ2: 5643 ms → 1413 ms (-4230 ms, -75 %)
Corne, Jerram, Knowles & Oates 2001: divides objective space into a
hyperbox grid and uses per-box population counts to drive selection
toward sparsely-populated regions.
Each generation:
- Maintain an external archive of non-dominated members
- Build a hyperbox grid (`grid_divisions` per axis on the archive's
current axis ranges); count members per box
- Selection picks two parents by region-based tournament: choose two
random non-empty boxes and take a uniform-random member from the
one with fewer occupants
- Variation produces an offspring; insert into archive, dropping
dominated members and (if archive overflows) the most-crowded
occupant of the most-occupied box
Tests cover non-empty front on Schaffer N.1, deterministic reruns,
and panic on `archive_size == 0`.
Generalizes the existing 2-D hypervolume to arbitrary M ≥ 1 dimensions
using the standard recursive Hypervolume-by-Slicing-Objectives (HSO)
algorithm from While et al. 2006:
- For M = 1: return reference[0] - min(points[0])
- For M = 2: sort by axis 0, sweep accumulating rectangles (matches
hypervolume_2d's existing exact behavior)
- For M ≥ 3: sort by the last axis, peel off slices of increasing
thickness and recursively compute the (M−1)-dimensional HV of each
slice's projected non-dominated subset
Direction-aware: minimization-oriented input is the entry point, so
maximize objectives are negated by the caller via
`ObjectiveSpace::as_minimization` before the recursion runs.
Tested against:
- the existing 2-D analytical case (3 points → area 6)
- a known 3-D unit-cube case (1 point at origin, ref [1,1,1] → 1)
- empty front → 0
- agreement with hypervolume_2d on random 2-D fronts
Exact 2D dominated hypervolume against a fixed reference point. Sorts
points by the first minimization-oriented objective ascending, then
sweeps and accumulates the dominated rectangle area against the
reference. Points that don't strictly dominate the reference are
ignored. Panics with a clear message if the objective space does not
have exactly two objectives (spec §14.2).
Tests cover a known-area front, the no-coverage case, and the panic on
non-2D problems.
swaitsandClaude Opus 4.7