MinMax Arena
中/EN
P81 · Packing and covering · Classic · Applied frontier

Irregular strip nesting

VERIFIED CONSTRUCTIONoccupied length 47298.787
GARDEYN2 · 50 pieces, all differentCurrent record · open

Given the strip height H, a set of piece polygons, and the demanded count of each type, place every piece inside the strip so that the maximum x-coordinate over all placed vertices (the occupied length L) is minimised. Pieces may only be translated and rotated about their local origin by 0°, 90°, 180°, or 270°; boundary contact is permitted, but interiors may not overlap and no piece may extend outside the strip.

Formal definition

  • ContainerThe closed strip {x ≥ 0, 0 ≤ y ≤ H}; boundary contact is permitted. The height H is fixed per instance: 20000 for GARDEYN1, 10000 for GARDEYN2, and 44 for GARDEYN9
  • SubmissionOne placement record per piece copy specifying its type, rotation angle, and translation. The piece polygons (which may be concave and asymmetric), demand counts, and strip height are fixed by the instance
  • MovesEach copy is rotated about its local origin by 0°, 90°, 180°, or 270° and then translated by (x, y); reflections, scaling, and arbitrary rotation angles are not allowed
  • No overlapNo two copies may have intersecting interiors: edge or vertex contact is permitted, whereas containment or any positive-area overlap is forbidden
  • Exact verificationCoordinates are decimal strings of at most 24 fractional places, scaled by 10²⁴ to exact integers that remain integral under all four right-angle rotations. Every polygon is triangulated exactly, and every pair of triangles is tested via separating axes using BigInt cross products; touching projection endpoints count as valid contact rather than overlap
  • ScoreThe maximum x-coordinate L over all placed vertices, exact to 24 decimal places; smaller is better. The reference container length in the source file and any self-reported score in the payload are ignored
  • ObjectiveMinimise the occupied length L over all valid placements

Getting a feel for it

Three industrial nesting instances

The GARDEYN benchmark instances originate from garment cutting and direct-to-film (DTF) printing orders featuring concave, asymmetric outlines. GARDEYN1 consists of 10 piece types with 5 copies each (50 pieces total), GARDEYN2 has 50 distinct garment pieces, and GARDEYN9 packs 47 distinct print motifs into a strip of height 44.

90° rotations and exact rational verification

While some heuristic nesting solvers allow continuous rotation, arbitrary angles introduce irrational trigonometric coordinates that prevent tolerance-free verification. Restricting rotations to 0°, 90°, 180°, and 270° keeps all vertices in exact decimal arithmetic, enabling zero-tolerance contact and overlap checks.

Sparrow reference layouts and baselines

The Sparrow repository provides reference layouts for the three instances with occupied lengths of 16181.169, 47382.125, and 65.792223, all of which pass exact verification under our rules. Applying local exact compaction to those layouts reduces the lengths to 16177.649, 47319.670679, and 65.769735999999999, which serve as the initial baselines in the table (bylined MinMax Arena). Both the original Sparrow layouts and weaker 20-second search layouts can be loaded in the editor for comparison.

Source

Data source

Instance geometries and reference layouts are taken from the Sparrow repository (Jeroen Gardeyn, Greet Vanden Berghe, and Tony Wauters, KU Leuven; MIT License) at revision 649d4c78, preserving the exact decimal vertex coordinates without floating-point truncation. Input hashes and source links for each instance are available in the editor.

Source
ONE LEADERBOARD PER n

Current best solutions by n

Each parameter n is an independently scored sub-problem. Select any card to inspect the current record construction or submit a stronger solution.

Discussion (4) ↓
InstanceGARDEYN1 · 50 pieces, 10 types
CURRENT RECORD16052.54859406119588349420966
Hard
Record holder邱仲普
Solution methodAI · OpenAI: GPT-5.6 Sol
InstanceGARDEYN2 · 50 pieces, all different
CURRENT RECORD47298.787288135972630698
Hard
Record holderzzzcy
Solution methodAI · OpenAI: GPT-6 Astra
InstanceGARDEYN9 · 47 pieces, all different
CURRENT RECORD65.66321416511283334
Hard
Record holderzzzcy
Solution methodAI · OpenAI: GPT-6 Astra

Data and citation

All sub-problems in this family — authoritative scores, proof status, coordinates, and sources — are published at the stable URL below under CC BY 4.0. Because scores update as records fall, please cite the file's generatedAt timestamp.

GET https://minmaxarena.com/data/irregular-strip-nesting.json

Cite the frozen 2026-10 edition: live records change, whereas a frozen edition stays fixed and reproducible.

GET https://minmaxarena.com/data/editions/2026-10/irregular-strip-nesting.json
BibTeX (click to copy)
@misc{minmaxarena-irregular-strip-nesting-2026-10,
  title  = {{Irregular strip nesting} (P81)},
  author = {{MinMax Arena}},
  year   = {2026},
  note   = {Machine-verified records, 2026-10 edition},
  url    = {https://minmaxarena.com/data/editions/2026-10/irregular-strip-nesting.json},
  license = {CC BY 4.0}
}
DISCUSSION

Discussion

Discuss strategies, share construction methods, or ask questions. Any signed-in user can post under their public byline and unique #UID. New posts appear after moderation.

第一题大概已经最优解了吧XSsMC#2506 replies精度太高了也是个很麻烦的问题啊Tmrg#342 replies可能是有史以来对AI最不友好的题目NUE_13#314 replies问题大草NUE_13#310 replies