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Benchmarks

La plupart des logiciels de découpe citent un pourcentage d’utilisation matière. Un pourcentage ne veut rien dire sans savoir ce qui était atteignable — 80 % peut être optimal sur un travail et un gaspillage sur un autre. C’est pourquoi nous mesurons plutôt face au minimum théorique : pour chaque travail de test, nous calculons une borne inférieure du nombre de panneaux ou de barres que n’importe quel plan pourrait utiliser, puis nous indiquons à quelle distance se trouve le nôtre. Les entrées sont des instances académiques publiées, les résultats sont ci-dessous, et vous pouvez tout réexécuter vous-même.

89,3 %
des travaux de panneaux atteignent la borne ou s’en approchent à un panneau près
53,0 %
sont démontrablement optimaux — exactement sur la borne
1,48 %
écart moyen à la borne sur les travaux linéaires
1 259
instances de test, 8 jeux de référence

Les chiffres pour les panneaux portent sur les 553 instances canoniques à kerf 0 avec rotation désactivée — la convention utilisée par la littérature, afin qu’ils soient comparables aux travaux publiés sur les mêmes instances.

Comment la borne est calculée

Une borne inférieure est un nombre de panneaux en dessous duquel aucun plan ne peut descendre. Si notre plan l’égale, il est démontrablement optimal pour ce travail — aucun meilleur n’existe. Deux bornes sont calculées et la plus grande est retenue ; les deux sont indiquées par travail pour que vous voyiez ce que chacune apporte.

LB1 — surface, corrigée du trait de scie (kerf)

Donnez à chaque pièce posée une empreinte agrandie d’un demi-kerf de chaque côté. Dans une disposition guillotine, deux pièces quelconques sont séparées par au moins une coupe, et chaque coupe consomme un kerf ; ces empreintes ne se chevauchent donc jamais — et elles tiennent toutes dans le panneau utile agrandi d’un demi-kerf de chaque côté. Les additionner donne une borne qu’aucune disposition ne peut battre. À kerf 0, c’est la borne de surface classique.

LB1 = ceil( Σ (wᵢ + k)(hᵢ + k) / ((W + k)(H + k)) )

LB2 — fonctions duales réalisables

La borne de surface est aveugle à la forme : cinq pièces de 600 × 600 n’occupent que la surface de 1,8 panneau sur un panneau de 1000 × 1000, et pourtant une seule tient par panneau ; il en faut donc cinq. Une fonction duale réalisable est une transformation des tailles qui préserve la réalisabilité, ce qui permet à l’argument de surface de percevoir cette structure. Deux familles sont utilisées — Martello–Toth et Fekete–Schepers —, appliquées indépendamment aux largeurs et aux hauteurs, et le meilleur résultat sur toute la grille de paramètres est retenu. Sous rotation, chaque pièce est comptée selon la plus petite de ses deux orientations, faute de quoi la borne pourrait dépasser l’optimum réel.

LB2 = max over (f,g) of ceil( Σ f(wᵢ + k)·g(hᵢ + k) / (f(W + k)·g(H + k)) )

Pourquoi les instances sont mises à l’échelle

Les instances publiées utilisent de petits entiers sans unité — certaines ont un bac de 10 × 10. Notre placeur écarte les bandes libres plus fines qu’une unité, ce qui, sur un bac de 10 × 10, représenterait un dixième du panneau. Chaque instance est donc multipliée par un nombre entier jusqu’à ce que son petit côté atteigne au moins 1000 unités. La mise à l’échelle entière est une transformation exacte : le nombre optimal de panneaux ne change pas, l’instance sort simplement de la portée de ce seuil.

Reproductibilité

L’optimiseur est déterministe — une même entrée produit toujours le même plan. L’ensemble du corpus a été exécuté deux fois, cache désactivé, et tous les champs hormis les temps sont revenus identiques au byte près. Les sources des instances sont figées par SHA-256, si bien qu’une réexécution peut prouver qu’elle a mesuré les mêmes bytes. Et chaque travail est vérifié face à l’invariant selon lequel la borne ne dépasse jamais le plan réellement produit ; une seule violation arrête l’exécution au lieu de publier un chiffre.

Ce que ces chiffres ne disent pas

  • Notre borne n’est pas la plus forte connue. Des bornes plus fortes existent dans la littérature ; l’écart que nous indiquons est donc une estimation majorante de l’écart réel — un travail que nous marquons comme « hors de la borne » peut en réalité être optimal, sans que nous puissions le prouver.
  • Les écarts relatifs s’exagèrent sur les petits travaux. Le travail médian ici nécessite une douzaine de panneaux ; un panneau de plus se lit alors comme un gros pourcentage. La colonne absolue — combien de panneaux au-dessus de la borne — est l’honnête.
  • Deux des familles générées sont adverses par construction : leurs pièces pavent les bacs exactement, sans aucune marge, si bien que la moindre imperfection coûte un bac entier. C’est un test de plafond, pas une image du travail habituel.
  • La limite de 150 pièces dans le tableau des tailles n’est pas arbitraire — c’est là que les deux placeurs changent de stratégie pour la vitesse. Les travaux au-delà suivent un chemin de code différent ; une variation à cet endroit est donc un compromis délibéré, et non une falaise.
  • La mesure appelle les mêmes fonctions que l’Engine API publique, dans le même processus plutôt qu’en HTTP — la latence réseau fausserait les temps. Cette équivalence n’est pas supposée : un échantillon d’instances est rejoué face à l’API en direct et doit revenir identique champ par champ.

Par taille de travail

Réparti par nombre de pièces. Les deux placeurs abandonnent leur stratégie de recherche la plus coûteuse au-delà de 150 pièces ; cette limite sépare donc deux chemins de code différents.

PiècesTravauxSur la borneÉcart moyen sinonTemps p95
2D · <5021765,0 %21,0 %23.32 ms
2D · 50-15031547,6 %9,6 %77.34 ms
2D · 150+219,5 %10,1 %474.53 ms
1D · 50-1504835,4 %3,6 %7.12 ms
1D · 150+8633,7 %1,5 %280.55 ms

Ce qui a été mesuré

Deux corpus, jamais fusionnés en un seul chiffre. Les jeux canoniques sont les instances qu’utilise la littérature académique ; ils sont téléchargés et vérifiés par hachage plutôt que recopiés ici, car leur source ne déclare aucune licence autorisant la redistribution. Les jeux générés sont les nôtres et nous pouvons les publier.

JeuInstancesOrigineDans ce dépôt ?
CLASS500JSHA-256 9f5ca94d6a…
BENG10MSHA-256 90536b0527…
A43RSHA-256 dd1804179a…
CLASS-R500Générés — construits à partir des paramètres du générateur publié, avec nos propres graines
PERFECT2D72Générés — construits à partir des paramètres du générateur publié, avec nos propres graines
UNIF1D40Générés — construits à partir des paramètres du générateur publié, avec nos propres graines
TRIPLET1D40Générés — construits à partir des paramètres du générateur publié, avec nos propres graines
RAND1D54Générés — construits à partir des paramètres du générateur publié, avec nos propres graines

Deux familles générées portent un optimum démontré par construction : leurs pièces pavent les bacs exactement, sans aucune chute, si bien que l’optimum est connu et pas seulement borné.

Les jeux de strip-packing, de sac à dos (knapsack) et de placement orthogonal sont exclus : ce sont des problèmes différents aux objectifs différents, et un chiffre de « bacs utilisés » n’y est pas défini. La collection unidimensionnelle BPPLIB est exclue pour des raisons de licence — ses auteurs la publient sous CC BY-NC-ND, qui n’autorise pas son usage dans le benchmark d’un produit commercial.

Chaque travail

Une ligne par instance avec les réglages de référence. Les autres profils, moteurs et orientations figurent dans le fichier de résultats téléchargeable.

Affichage de 1 259 sur 1 259

InstanceJeuPiècesStockBorneUtilisésExcédentUtil. mat.ms
CLASS/cl_01_020_01CLASS201000×1000888119.53
CLASS/cl_01_020_02CLASS201000×10005586.66.46
CLASS/cl_01_020_03CLASS201000×100089+172.229.33
CLASS/cl_01_020_04CLASS201000×100056+178.335.02
CLASS/cl_01_020_05CLASS201000×100066896.03
CLASS/cl_01_020_06CLASS201000×10009981.786.3
CLASS/cl_01_020_07CLASS201000×10006688.335.78
CLASS/cl_01_020_08CLASS201000×10006684.56
CLASS/cl_01_020_09CLASS201000×10008876.885.9
CLASS/cl_01_020_10CLASS201000×100088837.38
CLASS/cl_01_040_01CLASS401000×1000101089.513.33
CLASS/cl_01_040_02CLASS401000×10001112+189.1714.37
CLASS/cl_01_040_03CLASS401000×10001617+181.7616.15
CLASS/cl_01_040_04CLASS401000×1000141489.0717.8
CLASS/cl_01_040_05CLASS401000×1000151591.7313.51
CLASS/cl_01_040_06CLASS401000×1000141475.7916.6
CLASS/cl_01_040_07CLASS401000×10001112+189.513.19
CLASS/cl_01_040_08CLASS401000×10001819+176.5318.11
CLASS/cl_01_040_09CLASS401000×1000111191.6410.99
CLASS/cl_01_040_10CLASS401000×10001112+185.512.96
CLASS/cl_01_060_01CLASS601000×10002223+187.2629.24
CLASS/cl_01_060_02CLASS601000×1000191992.9520.99
CLASS/cl_01_060_03CLASS601000×1000212186.5223.26
CLASS/cl_01_060_04CLASS601000×1000222282.8625.76
CLASS/cl_01_060_05CLASS601000×1000191986.7927.32
CLASS/cl_01_060_06CLASS601000×10001718+192.1724.27
CLASS/cl_01_060_07CLASS601000×1000161692.524.47
CLASS/cl_01_060_08CLASS601000×1000212189.6731.67
CLASS/cl_01_060_09CLASS601000×10001819+191.4223.52
CLASS/cl_01_060_10CLASS601000×1000242487.8330.44
CLASS/cl_01_080_01CLASS801000×1000252590.9638.28
CLASS/cl_01_080_02CLASS801000×1000262692.5837.88
CLASS/cl_01_080_03CLASS801000×1000272785.1131.04
CLASS/cl_01_080_04CLASS801000×1000272790.329.38
CLASS/cl_01_080_05CLASS801000×1000262690.4636.19
CLASS/cl_01_080_06CLASS801000×1000282890.0437
CLASS/cl_01_080_07CLASS801000×1000313185.8138.29
CLASS/cl_01_080_08CLASS801000×1000292991.1732.01
CLASS/cl_01_080_09CLASS801000×10003031+189.934.21
CLASS/cl_01_080_10CLASS801000×1000262693.3132.58
CLASS/cl_01_100_01CLASS1001000×10002829+194.2448.5
CLASS/cl_01_100_02CLASS1001000×10003132+19544.88
CLASS/cl_01_100_03CLASS1001000×100029299246.75
CLASS/cl_01_100_04CLASS1001000×10003031+192.9446.07
CLASS/cl_01_100_05CLASS1001000×1000323294.2248.57
CLASS/cl_01_100_06CLASS1001000×1000373791.349.75
CLASS/cl_01_100_07CLASS1001000×10002829+194.3844.77
CLASS/cl_01_100_08CLASS1001000×10003334+191.7949.86
CLASS/cl_01_100_09CLASS1001000×10003132+193.3150.22
CLASS/cl_01_100_10CLASS1001000×1000383889.9257.65
CLASS/cl_02_020_01CLASS201020×102011726.31
CLASS/cl_02_020_02CLASS201020×10201148.118.85
CLASS/cl_02_020_03CLASS201020×10201172.225.54
CLASS/cl_02_020_04CLASS201020×10201152.228.84
CLASS/cl_02_020_05CLASS201020×10201159.338.18
CLASS/cl_02_020_06CLASS201020×10201181.784.56
CLASS/cl_02_020_07CLASS201020×10201158.898.36
CLASS/cl_02_020_08CLASS201020×10201156.338.29
CLASS/cl_02_020_09CLASS201020×10201168.337.28
CLASS/cl_02_020_10CLASS201020×10201173.786.94
CLASS/cl_02_040_01CLASS401020×102012+149.7220.98
CLASS/cl_02_040_02CLASS401020×10202259.4418.45
CLASS/cl_02_040_03CLASS401020×10202277.2213.63
CLASS/cl_02_040_04CLASS401020×10202269.2818.39
CLASS/cl_02_040_05CLASS401020×10202276.4411.72
CLASS/cl_02_040_06CLASS401020×10202258.9416.79
CLASS/cl_02_040_07CLASS401020×10202259.6716.32
CLASS/cl_02_040_08CLASS401020×10202280.7814.09
CLASS/cl_02_040_09CLASS401020×1020225619.51
CLASS/cl_02_040_10CLASS401020×1020225720.12
CLASS/cl_02_060_01CLASS601020×10203374.3328.33
CLASS/cl_02_060_02CLASS601020×102023+165.4130
CLASS/cl_02_060_03CLASS601020×10203367.329.32
CLASS/cl_02_060_04CLASS601020×10203367.5230.34
CLASS/cl_02_060_05CLASS601020×10202291.6115.38
CLASS/cl_02_060_06CLASS601020×10202292.1725.69
CLASS/cl_02_060_07CLASS601020×10202282.2220
CLASS/cl_02_060_08CLASS601020×10203369.7427.39
CLASS/cl_02_060_09CLASS601020×10202296.527.17
CLASS/cl_02_060_10CLASS601020×10203378.0722.72
CLASS/cl_02_080_01CLASS801020×10203384.2226.88
CLASS/cl_02_080_02CLASS801020×10203389.1527.56
CLASS/cl_02_080_03CLASS801020×10203385.1126.09
CLASS/cl_02_080_04CLASS801020×10203390.324.9
CLASS/cl_02_080_05CLASS801020×10203387.1126.33
CLASS/cl_02_080_06CLASS801020×10203393.3738.74
CLASS/cl_02_080_07CLASS801020×10203398.5236.5
CLASS/cl_02_080_08CLASS801020×10203397.9335.12
CLASS/cl_02_080_09CLASS801020×10204477.4235.06
CLASS/cl_02_080_10CLASS801020×10203389.8528.08
CLASS/cl_02_100_01CLASS1001020×10204475.9246.31
CLASS/cl_02_100_02CLASS1001020×10204484.4437.91
CLASS/cl_02_100_03CLASS1001020×102034+174.1147.32
CLASS/cl_02_100_04CLASS1001020×10204480.0336.11
CLASS/cl_02_100_05CLASS1001020×10204483.7534.85
CLASS/cl_02_100_06CLASS1001020×10204493.8333.74
CLASS/cl_02_100_07CLASS1001020×10204476.0345.32
CLASS/cl_02_100_08CLASS1001020×10204486.6936.84
CLASS/cl_02_100_09CLASS1001020×10204482.9438.86
CLASS/cl_02_100_10CLASS1001020×10204494.9239.09
CLASS/cl_03_020_01CLASS201000×100056+171.576.48
CLASS/cl_03_020_02CLASS201000×100034+165.146.35
CLASS/cl_03_020_03CLASS201000×100056+173.495.17
CLASS/cl_03_020_04CLASS201000×10004477.563.39
CLASS/cl_03_020_05CLASS201000×100045+1697.62
CLASS/cl_03_020_06CLASS201000×100067+167.98.58
CLASS/cl_03_020_07CLASS201000×100045+168.098.69
CLASS/cl_03_020_08CLASS201000×10004480.613.76
CLASS/cl_03_020_09CLASS201000×100056+170.17.23
CLASS/cl_03_020_10CLASS201000×10007766.057.29
CLASS/cl_03_040_01CLASS401000×100067+180.0113.92
CLASS/cl_03_040_02CLASS401000×100089+179.1710.84
CLASS/cl_03_040_03CLASS401000×1000111182.5512.91
CLASS/cl_03_040_04CLASS401000×1000101082.3510.25
CLASS/cl_03_040_05CLASS401000×1000121278.6617.34
CLASS/cl_03_040_06CLASS401000×1000101069.7312.43
CLASS/cl_03_040_07CLASS401000×100089+180.714.89
CLASS/cl_03_040_08CLASS401000×10001314+170.9913.62
CLASS/cl_03_040_09CLASS401000×100078+183.6712.84
CLASS/cl_03_040_10CLASS401000×100079+274.7614.18
CLASS/cl_03_060_01CLASS601000×10001617+179.2925.75
CLASS/cl_03_060_02CLASS601000×10001214+281.3425.16
CLASS/cl_03_060_03CLASS601000×10001315+281.9324.44
CLASS/cl_03_060_04CLASS601000×10001416+276.8121
CLASS/cl_03_060_05CLASS601000×10001113+283.6924.03
CLASS/cl_03_060_06CLASS601000×10001213+185.1120.5
CLASS/cl_03_060_07CLASS601000×10001112+183.0126.61
CLASS/cl_03_060_08CLASS601000×1000151585.2223.83
CLASS/cl_03_060_09CLASS601000×10001314+182.6424.61
CLASS/cl_03_060_10CLASS601000×10001718+180.8830.46
CLASS/cl_03_080_01CLASS801000×10001718+184.2335.53
CLASS/cl_03_080_02CLASS801000×10001819+183.738.77
CLASS/cl_03_080_03CLASS801000×10001719+281.6832.44
CLASS/cl_03_080_04CLASS801000×10001819+185.9538.77
CLASS/cl_03_080_05CLASS801000×10001618+286.6638.81
CLASS/cl_03_080_06CLASS801000×10002021+181.7436.88
CLASS/cl_03_080_07CLASS801000×10002021+186.4241.99
CLASS/cl_03_080_08CLASS801000×100022228236.07
CLASS/cl_03_080_09CLASS801000×10002123+280.8642.56
CLASS/cl_03_080_10CLASS801000×10001820+281.0738.16
CLASS/cl_03_100_01CLASS1001000×10001920+189.7644.22
CLASS/cl_03_100_02CLASS1001000×10002223+190.3356.03
CLASS/cl_03_100_03CLASS1001000×10001820+288.252.97
CLASS/cl_03_100_04CLASS1001000×10002022+286.7252.01
CLASS/cl_03_100_05CLASS1001000×10002224+284.1859.79
CLASS/cl_03_100_06CLASS1001000×10002627+185.0955.79
CLASS/cl_03_100_07CLASS1001000×10002021+187.6351.69
CLASS/cl_03_100_08CLASS1001000×10002324+187.0452.84
CLASS/cl_03_100_09CLASS1001000×10002123+285.664.27
CLASS/cl_03_100_10CLASS1001000×10002930+177.4855.58
CLASS/cl_04_020_01CLASS201000×10001168.718.06
CLASS/cl_04_020_02CLASS201000×10001141.699.41
CLASS/cl_04_020_03CLASS201000×10001170.556.23
CLASS/cl_04_020_04CLASS201000×10001149.649.82
CLASS/cl_04_020_05CLASS201000×10001155.28.52
CLASS/cl_04_020_06CLASS201000×10001176.056.87
CLASS/cl_04_020_07CLASS201000×10001154.478.55
CLASS/cl_04_020_08CLASS201000×10001151.599.62
CLASS/cl_04_020_09CLASS201000×10001167.37.84
CLASS/cl_04_020_10CLASS201000×10001173.986.01
CLASS/cl_04_040_01CLASS401000×10001189.6823.94
CLASS/cl_04_040_02CLASS401000×1000225720.45
CLASS/cl_04_040_03CLASS401000×10002272.6418.08
CLASS/cl_04_040_04CLASS401000×10002265.8818.43
CLASS/cl_04_040_05CLASS401000×10002275.5116.86
CLASS/cl_04_040_06CLASS401000×10002255.7817.08
CLASS/cl_04_040_07CLASS401000×10002258.121.85
CLASS/cl_04_040_08CLASS401000×10002279.5113.79
CLASS/cl_04_040_09CLASS401000×10002253.5520.45
CLASS/cl_04_040_10CLASS401000×10002253.8323.66
CLASS/cl_04_060_01CLASS601000×10003371.8927.23
CLASS/cl_04_060_02CLASS601000×10002291.126.98
CLASS/cl_04_060_03CLASS601000×100023+165.5531.43
CLASS/cl_04_060_04CLASS601000×100023+165.5432.1
CLASS/cl_04_060_05CLASS601000×10002287.0325.09
CLASS/cl_04_060_06CLASS601000×10002288.5226.21
CLASS/cl_04_060_07CLASS601000×10002279.6827.66
CLASS/cl_04_060_08CLASS601000×10003368.1828.24
CLASS/cl_04_060_09CLASS601000×10002292.5530.54
CLASS/cl_04_060_10CLASS601000×10003377.6525.23
CLASS/cl_04_080_01CLASS801000×10003380.8635.47
CLASS/cl_04_080_02CLASS801000×10003384.8234.84
CLASS/cl_04_080_03CLASS801000×10003382.7735.16
CLASS/cl_04_080_04CLASS801000×10003387.0932.84
CLASS/cl_04_080_05CLASS801000×10003383.1936.69
CLASS/cl_04_080_06CLASS801000×10003391.5537.72
CLASS/cl_04_080_07CLASS801000×100034+172.5944.26
CLASS/cl_04_080_08CLASS801000×100034+172.1647.62
CLASS/cl_04_080_09CLASS801000×100034+174.3936.31
CLASS/cl_04_080_10CLASS801000×10003386.4831.45
CLASS/cl_04_100_01CLASS1001000×100034+171.8157.1
CLASS/cl_04_100_02CLASS1001000×10004483.149.72
CLASS/cl_04_100_03CLASS1001000×10003394.0849.28
CLASS/cl_04_100_04CLASS1001000×10004476.3152.56
CLASS/cl_04_100_05CLASS1001000×10004480.8247
CLASS/cl_04_100_06CLASS1001000×10004491.934.17
CLASS/cl_04_100_07CLASS1001000×100034+173.6156.27
CLASS/cl_04_100_08CLASS1001000×10004483.5646.1
CLASS/cl_04_100_09CLASS1001000×10004478.7552.47
CLASS/cl_04_100_10CLASS1001000×10004492.9753.37
CLASS/cl_05_020_01CLASS201000×100078+167.148.28
CLASS/cl_05_020_02CLASS201000×100045+164.738.93
CLASS/cl_05_020_03CLASS201000×10007778.914.89
CLASS/cl_05_020_04CLASS201000×10005577.784.29
CLASS/cl_05_020_05CLASS201000×100056+172.687.9
CLASS/cl_05_020_06CLASS201000×100089+166.8810.2
CLASS/cl_05_020_07CLASS201000×100056+171.097.23
CLASS/cl_05_020_08CLASS201000×10005580.937.2
CLASS/cl_05_020_09CLASS201000×10007775.386.2
CLASS/cl_05_020_10CLASS201000×100078+173.029.76
CLASS/cl_05_040_01CLASS401000×100089+177.2415.04
CLASS/cl_05_040_02CLASS401000×10001011+181.0314.13
CLASS/cl_05_040_03CLASS401000×1000151576.9118.46
CLASS/cl_05_040_04CLASS401000×10001213+180.2220.7
CLASS/cl_05_040_05CLASS401000×10001315+279.3417.86
CLASS/cl_05_040_06CLASS401000×1000121273.1412.04
CLASS/cl_05_040_07CLASS401000×10001011+182.413.62
CLASS/cl_05_040_08CLASS401000×1000171773.5414.19
CLASS/cl_05_040_09CLASS401000×1000910+183.9814.93
CLASS/cl_05_040_10CLASS401000×10001011+176.8416.6
CLASS/cl_05_060_01CLASS601000×10001921+281.2724.76
CLASS/cl_05_060_02CLASS601000×10001618+280.1230.37
CLASS/cl_05_060_03CLASS601000×10001820+277.3431.61
CLASS/cl_05_060_04CLASS601000×1000202077.4628
CLASS/cl_05_060_05CLASS601000×10001516+185.4131.02
CLASS/cl_05_060_06CLASS601000×10001517+281.5627.1
CLASS/cl_05_060_07CLASS601000×10001415+183.0631.52
CLASS/cl_05_060_08CLASS601000×1000191984.7830.86
CLASS/cl_05_060_09CLASS601000×10001617+185.3832.27
CLASS/cl_05_060_10CLASS601000×10002324+176.4929.53
CLASS/cl_05_080_01CLASS801000×10002224+279.2737.27
CLASS/cl_05_080_02CLASS801000×10002224+283.6643.15
CLASS/cl_05_080_03CLASS801000×10002425+178.0843.26
CLASS/cl_05_080_04CLASS801000×10002425+181.839.72
CLASS/cl_05_080_05CLASS801000×10002224+281.7637.58
CLASS/cl_05_080_06CLASS801000×10002526+182.9746.66
CLASS/cl_05_080_07CLASS801000×10002728+181.2745.66
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PERFECT2D/p_120x80_k5_n16_1PERFECT2D801560×104056+183.3333.04
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PERFECT2D/p_120x80_k5_n30_1PERFECT2D1501560×104056+183.3388
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PERFECT2D/p_250x150_k2_n8_1PERFECT2D161750×105023+166.675.5
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PERFECT2D/p_250x150_k2_n16_1PERFECT2D321750×105023+166.6712.54
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PERFECT2D/p_250x150_k3_n30_2PERFECT2D901750×105034+17549.68
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PERFECT2D/p_250x150_k5_n30_1PERFECT2D1501750×105056+183.3395.87
PERFECT2D/p_250x150_k5_n30_2PERFECT2D1501750×105056+183.3390.32
PERFECT2D/p_300x300_k2_n8_1PERFECT2D161200×1200221004.19
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PERFECT2D/p_300x300_k2_n16_1PERFECT2D321200×120023+166.6711.62
PERFECT2D/p_300x300_k2_n16_2PERFECT2D321200×120023+166.6711.9
PERFECT2D/p_300x300_k2_n30_1PERFECT2D601200×120023+166.6729.61
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PERFECT2D/p_300x300_k3_n8_1PERFECT2D241200×120034+1756.85
PERFECT2D/p_300x300_k3_n8_2PERFECT2D241200×120034+1756.11
PERFECT2D/p_300x300_k3_n16_1PERFECT2D481200×120034+17518.53
PERFECT2D/p_300x300_k3_n16_2PERFECT2D481200×120034+17518.3
PERFECT2D/p_300x300_k3_n30_1PERFECT2D901200×120034+17546.08
PERFECT2D/p_300x300_k3_n30_2PERFECT2D901200×120034+17549.58
PERFECT2D/p_300x300_k5_n8_1PERFECT2D401200×120056+183.3311.55
PERFECT2D/p_300x300_k5_n8_2PERFECT2D401200×120056+183.3313.62
PERFECT2D/p_300x300_k5_n16_1PERFECT2D801200×120056+183.3331.67
PERFECT2D/p_300x300_k5_n16_2PERFECT2D801200×120056+183.3329.66
PERFECT2D/p_300x300_k5_n30_1PERFECT2D1501200×120056+183.3394.05
PERFECT2D/p_300x300_k5_n30_2PERFECT2D1501200×120056+183.3396.34
UNIF1D/u120_01UNIF1D1201050474798.757.75
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UNIF1D/u120_03UNIF1D12010504849+196.754.99
UNIF1D/u120_04UNIF1D1201050525298.1711.44
UNIF1D/u120_05UNIF1D1201050515198.074.13
UNIF1D/u120_06UNIF1D12010505052+295.914.52
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UNIF1D/u120_08UNIF1D12010504950+197.434.14
UNIF1D/u120_09UNIF1D12010505152+196.824.76
UNIF1D/u120_10UNIF1D1201050454598.434.42
UNIF1D/u250_01UNIF1D250105099101+297.919.47
UNIF1D/u250_02UNIF1D2501050102104+297.5318.79
UNIF1D/u250_03UNIF1D2501050959599.1619.77
UNIF1D/u250_04UNIF1D2501050102103+198.5222.85
UNIF1D/u250_05UNIF1D2501050104106+298.0919.32
UNIF1D/u250_06UNIF1D2501050101103+297.6119.05
UNIF1D/u250_07UNIF1D250105010010099.2516.68
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UNIF1D/u250_09UNIF1D2501050102103+198.4321.17
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UNIF1D/u500_01UNIF1D5001050199200+199.4479.63
UNIF1D/u500_02UNIF1D500105019619699.9480.92
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UNIF1D/u500_05UNIF1D500105019919999.6778.27
UNIF1D/u500_06UNIF1D500105020420499.7279.14
UNIF1D/u500_07UNIF1D5001050202205+398.5378.48
UNIF1D/u500_08UNIF1D5001050200202+298.5979
UNIF1D/u500_09UNIF1D500105020020099.7474
UNIF1D/u500_10UNIF1D500105019719799.776.38
UNIF1D/u1000_01UNIF1D1000105040340399.96292.33
UNIF1D/u1000_02UNIF1D10001050398399+199.52309.11
UNIF1D/u1000_03UNIF1D1000105040140199.95303.68
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UNIF1D/u1000_05UNIF1D10001050399400+199.73280.16
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UNIF1D/u1000_08UNIF1D1000105039839899.85277.36
UNIF1D/u1000_09UNIF1D1000105039939999.98279.3
UNIF1D/u1000_10UNIF1D10001050403405+299.42271.44
TRIPLET1D/t60_01TRIPLET1D6010002021+195.247.12
TRIPLET1D/t60_02TRIPLET1D6010002021+195.240.87
TRIPLET1D/t60_03TRIPLET1D6010002021+195.240.89
TRIPLET1D/t60_04TRIPLET1D6010002021+195.240.84
TRIPLET1D/t60_05TRIPLET1D6010002021+195.241.14
TRIPLET1D/t60_06TRIPLET1D6010002021+195.240.92
TRIPLET1D/t60_07TRIPLET1D6010002021+195.240.82
TRIPLET1D/t60_08TRIPLET1D6010002021+195.240.82
TRIPLET1D/t60_09TRIPLET1D6010002021+195.240.82
TRIPLET1D/t60_10TRIPLET1D6010002021+195.240.82
TRIPLET1D/t120_01TRIPLET1D12010004041+197.562.92
TRIPLET1D/t120_02TRIPLET1D12010004041+197.563.01
TRIPLET1D/t120_03TRIPLET1D12010004041+197.562.96
TRIPLET1D/t120_04TRIPLET1D12010004041+197.563.32
TRIPLET1D/t120_05TRIPLET1D12010004041+197.563.23
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TRIPLET1D/t120_07TRIPLET1D12010004041+197.563
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TRIPLET1D/t120_09TRIPLET1D12010004041+197.563.34
TRIPLET1D/t120_10TRIPLET1D12010004041+197.562.91
TRIPLET1D/t249_01TRIPLET1D24910008386+396.5116.84
TRIPLET1D/t249_02TRIPLET1D24910008384+198.8111.79
TRIPLET1D/t249_03TRIPLET1D24910008385+297.6512.07
TRIPLET1D/t249_04TRIPLET1D24910008386+396.5118.21
TRIPLET1D/t249_05TRIPLET1D24910008385+297.6512.73
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TRIPLET1D/t249_07TRIPLET1D24910008385+297.6512.18
TRIPLET1D/t249_08TRIPLET1D24910008385+297.6512.11
TRIPLET1D/t249_09TRIPLET1D24910008385+297.6512.01
TRIPLET1D/t249_10TRIPLET1D24910008385+297.6511.76
TRIPLET1D/t501_01TRIPLET1D5011000167171+497.6653.07
TRIPLET1D/t501_02TRIPLET1D5011000167171+497.6646.74
TRIPLET1D/t501_03TRIPLET1D5011000167171+497.6646.6
TRIPLET1D/t501_04TRIPLET1D5011000167171+497.6651.66
TRIPLET1D/t501_05TRIPLET1D5011000167171+497.6655.78
TRIPLET1D/t501_06TRIPLET1D5011000167170+398.2455.08
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TRIPLET1D/t501_08TRIPLET1D5011000167171+497.6646.9
TRIPLET1D/t501_09TRIPLET1D5011000167171+497.6646.52
TRIPLET1D/t501_10TRIPLET1D5011000167171+497.6654.43
RAND1D/r_50_100_0.1_0.7_1RAND1D5010002122+194.593.18
RAND1D/r_50_100_0.1_0.7_2RAND1D501000212196.571.62
RAND1D/r_50_100_0.1_0.7_3RAND1D5010002020971.49
RAND1D/r_50_100_0.2_0.8_1RAND1D501000282890.611.49
RAND1D/r_50_100_0.2_0.8_2RAND1D5010002626931.39
RAND1D/r_50_100_0.2_0.8_3RAND1D5010002324+194.631.4
RAND1D/r_50_150_0.1_0.7_1RAND1D501050202095.831.53
RAND1D/r_50_150_0.1_0.7_2RAND1D501050202095.631.39
RAND1D/r_50_150_0.1_0.7_3RAND1D5010502223+194.71.5
RAND1D/r_50_150_0.2_0.8_1RAND1D501050313180.691.63
RAND1D/r_50_150_0.2_0.8_2RAND1D501050303085.185.51
RAND1D/r_50_150_0.2_0.8_3RAND1D501050252595.761.23
RAND1D/r_50_1000_0.1_0.7_1RAND1D5010002122+193.10.68
RAND1D/r_50_1000_0.1_0.7_2RAND1D5010002021+194.890.63
RAND1D/r_50_1000_0.1_0.7_3RAND1D501000212196.710.67
RAND1D/r_50_1000_0.2_0.8_1RAND1D501000292988.750.71
RAND1D/r_50_1000_0.2_0.8_2RAND1D501000303089.930.71
RAND1D/r_50_1000_0.2_0.8_3RAND1D501000282891.310.64
RAND1D/r_200_100_0.1_0.7_1RAND1D20010007879+197.759.76
RAND1D/r_200_100_0.1_0.7_2RAND1D20010007879+198.6211.04
RAND1D/r_200_100_0.1_0.7_3RAND1D2001000828298.9911.08
RAND1D/r_200_100_0.2_0.8_1RAND1D200100010110198.1914.01
RAND1D/r_200_100_0.2_0.8_2RAND1D200100011011092.949.21
RAND1D/r_200_100_0.2_0.8_3RAND1D200100010810894.889.27
RAND1D/r_200_150_0.1_0.7_1RAND1D2001050828298.8510.62
RAND1D/r_200_150_0.1_0.7_2RAND1D20010507778+198.3610.73
RAND1D/r_200_150_0.1_0.7_3RAND1D20010508081+198.219.84
RAND1D/r_200_150_0.2_0.8_1RAND1D200105010010097.079.6
RAND1D/r_200_150_0.2_0.8_2RAND1D2001050101102+196.9314.27
RAND1D/r_200_150_0.2_0.8_3RAND1D200105010010098.069.41
RAND1D/r_200_1000_0.1_0.7_1RAND1D20010008485+198.489.5
RAND1D/r_200_1000_0.1_0.7_2RAND1D20010007677+198.029.56
RAND1D/r_200_1000_0.1_0.7_3RAND1D20010008081+197.859.03
RAND1D/r_200_1000_0.2_0.8_1RAND1D20010009899+198.158.85
RAND1D/r_200_1000_0.2_0.8_2RAND1D200100010610695.248.67
RAND1D/r_200_1000_0.2_0.8_3RAND1D200100010810894.29.4
RAND1D/r_500_100_0.1_0.7_1RAND1D5001000196197+199.3264.83
RAND1D/r_500_100_0.1_0.7_2RAND1D500100020420499.969.21
RAND1D/r_500_100_0.1_0.7_3RAND1D500100020020099.6970.26
RAND1D/r_500_100_0.2_0.8_1RAND1D5001000263264+196.4362.33
RAND1D/r_500_100_0.2_0.8_2RAND1D5001000249250+198.5462.99
RAND1D/r_500_100_0.2_0.8_3RAND1D500100025625697.5364.82
RAND1D/r_500_150_0.1_0.7_1RAND1D500105020220299.8971.84
RAND1D/r_500_150_0.1_0.7_2RAND1D500105020420499.6573.46
RAND1D/r_500_150_0.1_0.7_3RAND1D500105019219299.7575.24
RAND1D/r_500_150_0.2_0.8_1RAND1D500105026126196.7264.54
RAND1D/r_500_150_0.2_0.8_2RAND1D500105025025098.8764.97
RAND1D/r_500_150_0.2_0.8_3RAND1D500105027027095.2663.52
RAND1D/r_500_1000_0.1_0.7_1RAND1D5001000194196+298.6659.23
RAND1D/r_500_1000_0.1_0.7_2RAND1D5001000198201+398.4462.32
RAND1D/r_500_1000_0.1_0.7_3RAND1D5001000199200+199.0957.15
RAND1D/r_500_1000_0.2_0.8_1RAND1D5001000260261+196.9264.69
RAND1D/r_500_1000_0.2_0.8_2RAND1D5001000261262+196.262.77
RAND1D/r_500_1000_0.2_0.8_3RAND1D5001000259262+396.3258.46

Imbrication à forme réelle

Les chiffres ci-dessus concernent l’imbriquateur guillotine, qui découpe des rectangles. L’imbrication à forme réelle est un moteur différent pour un problème différent : elle imbrique des POLYGONES ARBITRAIRES — pour le laser, le plasma et le jet d’eau — en laissant les pièces s’emboîter dans les poches concaves les unes des autres. Sur un travail représentatif de 272 pièces, elle utilise 6 panneaux, là où les mêmes pièces confiées à un imbriquateur rectangulaire par leur rectangle englobant en nécessitent 9 — un tiers de matière en moins, rien que par la forme.

6
panneaux · forme réelle
5
panneaux · moteur max, 60 s
9
panneaux · rectangle englobant
4
panneaux · minimum théorique

Pourquoi nous rapportons le nombre de panneaux, pas la densité

Un imbriquateur par rectangle englobant compte le vide des encoches à l’intérieur du rectangle de chaque pièce comme plein, si bien que son « rendement » paraît plus élevé pour un moins bon résultat — le plan à 9 panneaux semble plus dense que celui à 6 panneaux. La seule métrique honnête et comparable est le nombre de panneaux dont les mêmes pièces physiques ont réellement besoin. C’est le chiffre ci-dessus.

Le plan à 6 panneaux est le moteur rapide par défaut, qui répond dans la même requête. Le moteur asynchrone max (engine:"max") continue ensuite de chercher moins de panneaux : mesuré sur notre serveur de production le 22 septembre 2026, il a utilisé 5 panneaux sur 4 exécutions avec son budget par défaut de 60 secondes, et 5 sur 2 exécutions avec le maximum de 180 secondes. Il est limité dans le temps, si bien qu’une exécution peut se terminer différemment d’une autre — nous montrons la plage sur l’ensemble des exécutions, pas la meilleure. Chaque disposition a été vérifiée indépendamment : chaque pièce posée et sur son panneau, aucune paire de pièces ne se chevauchant de plus de 0,01 mm — une marge pour les coordonnées arrondies que renvoie l’API, car des pièces qui se touchent peuvent sinon sembler se croiser de quelques millièmes de millimètre.

Une borne inférieure théorique sur ce travail est de 4 panneaux — l’aire totale des pièces divisée par un panneau. Aucun plan ne peut en utiliser moins ; avec des formes irrégulières, l’air entre les pièces fait qu’un plan l’atteint rarement.

Ces chiffres ne comportent aucun espace entre les pièces. Avec un espace de 5 mm entre les pièces et en bord de panneau, un réglage laser courant, le même travail nécessite 6 panneaux avec le moteur par défaut et 5–6 avec max (2 exécutions, 60 s chacune).

Les jeux d’imbrication classiques ESICUP

Le travail ci-dessus est un travail que nous avons construit. Pour que le moteur puisse aussi être vérifié sur des problèmes que nous n’avons pas choisis, nous l’avons exécuté sur les 13 jeux d’imbrication classiques ESICUP, les instances publiques de placement irrégulier utilisées par la littérature de recherche. Ce sont des problèmes de strip-packing ; nous les transformons en problèmes de panneaux comme le fait la littérature du bin-packing, avec trois tailles de panneaux carrés par jeu, ce qui donne 39 instances. Sur l’ensemble, le moteur par défaut utilise 248 panneaux et le moteur max 244 (la moins bonne de 2 exécutions, 60 s chacune), face à une borne inférieure de 153. Le moteur par défaut atteint la borne sur 7 instances et max sur 11. Max nécessite moins de panneaux que le moteur par défaut sur 4 instances, à chaque exécution.

Comment cela a été mesuré, sur notre serveur de production le 22 septembre 2026 : chaque panneau est un carré dont le côté vaut 1,1, 1,5 ou 2 fois la plus grande dimension de pièce (la convention de Martinez-Sykora et al., 2017) ; chaque jeu conserve ses propres rotations autorisées ; il n’y a aucun espace entre les pièces, comme dans la littérature ; max s’exécute avec son budget par défaut de 60 secondes et nous rapportons sa moins bonne exécution. La borne inférieure, l’aire totale des pièces divisée par un panneau, est faible pour les formes irrégulières, si bien qu’un résultat au-dessus d’elle n’est pas nécessairement dépassé par quoi que ce soit. Chaque disposition a été vérifiée en dehors du moteur : 39 instances sur 39 sont valides, chaque pièce étant posée sur son panneau et aucune paire de pièces ne se chevauchant au-delà de l’arrondi des coordonnées renvoyées. Les instances proviennent du dépôt jagua-rs à la révision à partir de laquelle notre moteur est construit (la collection ESICUP est sous CC0), et le script qui les a mesurées se trouve dans notre dépôt.

Les 39 instances
JeuCôté du panneau (× plus grande pièce)PiècesBorne inférieurePar défautMax · 60 s
albano1,124466
albano1,524333
albano224222
blaz11,128112020
blaz11,52861414
blaz1228466
dagli1,130344
dagli1,530222
dagli230111
fu1,112599
fu1,512355
fu212232
jakobs11,125699
jakobs11,525344
jakobs1225233
jakobs21,125588
jakobs21,525344
jakobs2225232
mao1,120344
mao1,520232
mao220121
marques1,124466
marques1,524333
marques224222
shapes01,14371717
shapes01,54341010
shapes0243355
shapes11,14371515
shapes11,543488
shapes1243344
shirts1,199111616
shirts1,599699
shirts299455
swim1,14861212
swim1,548466
swim248233
trousers1,164566
trousers1,564344
trousers264222

Résultats par instance (JSON)

Imbrication à forme réelle sur l’Engine API →

The max tier — closer to the proven optimum

The figures above are the default engine, which returns instantly. The optional async max engine (engine:"max") runs a tree search instead: on the same public 2DPackLib instances, judged by the same lower bound, it reaches the PROVEN minimum on 12–13 percentage points more jobs than the default, with a smaller gap on the ones that miss. The trade is time — see below.

CorpusEngineOn the boundAvg gap (off-bound)
A + BENG · 106default · heuristic44,3 %11,1 %
max · PackingSolver57,1 %6,9 %
CLASS (sample) · 168default · heuristic57,7 %12,8 %
max · PackingSolver69,6 %10,4 %

Why the max tier is asynchronous

The default engine solves in about 30 ms and runs in your browser. The max engine takes seconds to a minute per job — too long to hold an HTTP request open — so it is asynchronous: POST with engine:"max" returns a job id, and you poll until it finishes. Same public corpus, same lower-bound method, both our own engines — no competitor data.

One honest caveat: the max engine is time-boxed, so on the very hardest instances the search is cut off at the cap — a few jobs may not finish (1 of 274 here) and its figures can move by about a point between runs. The default engine is fully deterministic and always returns a plan.

The max tier on the Engine API →

Données

La mesure complète, pas un résumé.

  • results.jsonl — Tous les résultats — chaque travail, profil, moteur et orientation
  • summary.json — Agrégats — les chiffres de cette page
  • table.json — Ce tableau au format JSON
  • corpus.json — Les instances d’entrée générées — les problèmes réels que l’exécuteur a résolus. Les jeux académiques canoniques sont récupérés et vérifiés par hachage plutôt que recopiés ici, car leur source n’accorde aucune redistribution.

Pour reproduire : clonez le dépôt, exécutez npm run bench:fetch pour télécharger les instances canoniques et vérifier leurs hachages, puis npm run bench. Le corpus généré ne nécessite aucun téléchargement.

Les fichiers ci-dessus sont publiés sous CC BY 4.0 — réutilisez-les, usage commercial inclus, avec attribution à CutOptim. Cela couvre notre propre mesure et le corpus généré. Les instances académiques canoniques ne sont pas les nôtres pour les licencier et ne sont pas distribuées d’ici.

Lancez votre propre travail

Le seul chiffre qui compte est celui que produit votre propre liste de matière.