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Otvoreno mjerenje

Mjerila

Većina softvera za rezanje navodi postotak iskoristivosti. Postotak je besmislen ako se ne zna što je bilo ostvarivo — 80 % može biti optimalno na jednom zadatku, a rasipno na drugom. Zato umjesto toga mjerimo prema teorijskom minimumu: za svaki testni zadatak izračunamo donju granicu broja ploča ili šipki koje bi bilo koji plan mogao upotrijebiti, a zatim izvještavamo koliko je naš plan udaljen od nje. Ulazi su objavljene akademske instance, rezultati su niže, a cijelo mjerenje možete ponovno pokrenuti sami.

89,3 %
zadataka s pločama pada na granicu ili unutar jedne ploče od nje
53,0 %
dokazivo je optimalno — točno na granici
1,48 %
prosječan razmak do granice na linearnim zadacima
1.259
testnih instanci, 8 skupova mjerila

Brojke za ploče odnose se na 553 kanonskih instanci pri rezu 0 s onemogućenom rotacijom — konvencija koju literatura koristi, pa su usporedive s objavljenim radovima na istim instancama.

Kako se izračunava granica

Donja granica je broj ploča ispod kojega nijedan plan ne može ići. Ako je naš plan dosegne, plan je dokazivo optimalan za taj zadatak — boljega nema. Izračunavaju se dvije granice i uzima se veća; obje se izvještavaju po zadatku kako biste vidjeli što svaka doprinosi.

LB1 — površina, korigirana za rez pile

Svakom postavljenom komadu dodijeli otisak proširen za pola reza sa svake strane. U giljotinskom rasporedu bilo koja dva komada razdvojena su barem jednim rezom, a svaki rez troši jedan rez, pa se ti otisci nikada ne preklapaju — i svi stanu unutar korisne ploče proširene za pola reza sa svake strane. Njihov zbroj daje granicu koju nijedan raspored ne može nadmašiti. Pri rezu 0 to je klasična granica površine.

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

LB2 — dualno izvedive funkcije

Granica površine slijepa je za oblik: pet komada 600 × 600 zauzima samo 1,8 ploča površine na ploči 1000 × 1000, a ipak stane samo jedan po ploči, pa je potrebno pet ploča. Dualno izvediva funkcija je transformacija veličina koja čuva izvedivost, što omogućuje da argument površine uoči tu strukturu. Koriste se dvije obitelji — Martello–Toth i Fekete–Schepers — primijenjene nezavisno na širine i visine, i uzima se najbolji rezultat na cijeloj rešetki parametara. Pod rotacijom se svaki komad naplaćuje po manjoj od svoje dvije orijentacije, inače bi granica mogla premašiti pravi optimum.

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

Zašto se instance skaliraju

Objavljene instance koriste male cjelobrojne vrijednosti bez mjerne jedinice — neke imaju kutiju 10 × 10. Naš packer odbacuje slobodne trake tanje od jedne jedinice, što bi na kutiji 10 × 10 bila desetina ploče. Svaka se instanca stoga množi cijelim brojem dok joj kraća stranica nije barem 1000 jedinica. Cjelobrojno skaliranje je egzaktna transformacija: optimalan broj ploča se ne mijenja, instanca se samo izmiče dosegu tog praga.

Ponovljivost

Optimizator je determinističan — isti ulaz uvijek daje isti plan. Cijeli korpus pokrenut je dvaput s onemogućenim predmemoriranjem i svako polje osim vremena vratilo se bajt po bajt identično. Izvori instanci fiksirani su SHA-256 hashem, pa ponovno pokretanje može dokazati da je mjerilo iste bajtove. I svaki se zadatak provjerava prema invarijanti da granica nikad ne premašuje stvarno proizvedeni plan; jedno kršenje zaustavlja pokretanje umjesto da objavi broj.

Što ovi brojevi ne govore

  • Naša granica nije najjača poznata. U literaturi postoje jače granice, pa je razmak koji izvještavamo gornja procjena stvarnog razmaka — zadatak koji označimo kao „nije na granici" zapravo može biti optimalan, a mi to jednostavno ne možemo dokazati.
  • Relativni razmaci pretjeruju na malim zadacima. Medijanski zadatak ovdje treba oko desetak ploča, pa se jedna dodatna ploča čita kao veliki postotak. Apsolutni stupac — koliko ploča iznad granice — onaj je pošten.
  • Dvije od generiranih obitelji protivničke su po konstrukciji: njihovi komadi popločavaju kutije točno, ne ostavljajući nimalo zazora, pa svaka nesavršenost košta cijelu kutiju. To je test stropa, a ne slika tipičnog rada.
  • Granica od 150 komada u tablici veličina nije proizvoljna — to je mjesto na kojem oba packera mijenjaju strategiju radi brzine. Zadaci iznad nje idu drugim kodnim putem, pa je promjena ondje namjeran kompromis, a ne litica.
  • Mjerenje poziva iste funkcije koje pokreće javni Engine API, unutar procesa umjesto preko HTTP-a — mrežna latencija pokvarila bi vremena. Ta se istovjetnost ne pretpostavlja: uzorak instanci ponovno se pušta prema živom API-ju i mora se vratiti identičan polje po polje.

Prema veličini zadatka

Podijeljeno prema broju komada. Oba packera napuštaju svoju najskuplju strategiju pretraživanja iznad 150 komada, pa ta granica razdvaja dva različita kodna puta.

KomadiZadaciNa graniciPros. razmak kad nijep95 vrijeme
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

Što je izmjereno

Dva korpusa, nikad pomiješana u jedan broj. Kanonski skupovi su instance koje akademska literatura koristi; preuzimaju se i provjeravaju hashem umjesto da se ovdje kopiraju, jer njihov izvor ne navodi licencu koja dopušta redistribuciju. Generirani skupovi su naši za objavu.

SkupInstancePodrijetloU ovom repozitoriju?
CLASS500JSHA-256 9f5ca94d6a…
BENG10MSHA-256 90536b0527…
A43RSHA-256 dd1804179a…
CLASS-R500Generirani — izgrađeni iz objavljenih parametara generatora, naša vlastita sjemena
PERFECT2D72Generirani — izgrađeni iz objavljenih parametara generatora, naša vlastita sjemena
UNIF1D40Generirani — izgrađeni iz objavljenih parametara generatora, naša vlastita sjemena
TRIPLET1D40Generirani — izgrađeni iz objavljenih parametara generatora, naša vlastita sjemena
RAND1D54Generirani — izgrađeni iz objavljenih parametara generatora, naša vlastita sjemena

Dvije generirane obitelji nose dokazan optimum po konstrukciji: njihovi komadi popločavaju kutije točno bez otpada, pa je optimum poznat, a ne samo ograničen.

Skupovi za strip-packing, naprtnjaču i ortogonalno pakiranje isključeni su: to su drugačiji problemi s drugačijim ciljevima, a brojka „iskorištenih kutija" za njih je nedefinirana. Jednodimenzionalna BPPLIB zbirka isključena je zbog licence — njezini je autori objavljuju pod CC BY-NC-ND, što ne dopušta uporabu u mjerilu komercijalnog proizvoda.

Svaki zadatak

Jedan redak po instanci pri naslovnim postavkama. Ostali profili, mehanizmi i orijentacije nalaze se u datoteci rezultata dostupnoj za preuzimanje.

Prikazano 1.259 od 1.259

InstancaSkupKomadiZalihaGranicaIskorištenoIznadIskoristivostms
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
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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_10UNIF1D1201050454598.434.42
UNIF1D/u250_01UNIF1D250105099101+297.919.47
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UNIF1D/u250_03UNIF1D2501050959599.1619.77
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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
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UNIF1D/u500_05UNIF1D500105019919999.6778.27
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UNIF1D/u500_07UNIF1D5001050202205+398.5378.48
UNIF1D/u500_08UNIF1D5001050200202+298.5979
UNIF1D/u500_09UNIF1D500105020020099.7474
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UNIF1D/u1000_01UNIF1D1000105040340399.96292.33
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UNIF1D/u1000_03UNIF1D1000105040140199.95303.68
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UNIF1D/u1000_07UNIF1D10001050409410+199.65295.87
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
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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
TRIPLET1D/t120_06TRIPLET1D12010004041+197.562.88
TRIPLET1D/t120_07TRIPLET1D12010004041+197.563
TRIPLET1D/t120_08TRIPLET1D12010004041+197.562.9
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
TRIPLET1D/t249_06TRIPLET1D24910008385+297.6512.29
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
TRIPLET1D/t501_07TRIPLET1D5011000167171+497.6652.44
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
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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
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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

Ugniježđivanje pravih oblika

Gornji brojevi odnose se na giljotinski pakirač, koji reže pravokutnike. Ugniježđivanje pravih oblika drukčiji je motor za drukčiji problem: pakira PROIZVOLJNE POLIGONE — za lasersko, plazma i rezanje vodenim mlazom — puštajući dijelove da se uklope u konkavne džepove jedni drugih. Na reprezentativnom poslu od 272 dijela koristi 6 ploča, dok istim dijelovima predanima pravokutnom pakiraču prema njihovom graničnom okviru treba 9 — trećinu manje materijala, i to samo iz oblika.

6
ploča · pravi oblik
9
ploča · granični okvir
4
ploča · teorijski minimum

Zašto izvještavamo o broju ploča, a ne o gustoći

Pakirač po graničnom okviru broji zrak u usjecima unutar pravokutnika svakog dijela kao pun, pa mu „iskoristivost” izgleda viša za lošiji rezultat — plan od 9 ploča izgleda gušće od plana od 6 ploča. Jedina iskrena, usporediva metrika jest broj ploča koje isti fizički dijelovi doista trebaju. To je broj iznad.

Teorijska donja granica na ovom poslu jest 4 ploča (ukupna površina dijelova podijeljena s jednom pločom). Trenutni motor doseže 6; razlika u gustoći do 4 jest ono čemu ide sljedeća iteracija motora.

Ugniježđivanje pravih oblika na Engine API-ju →

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 →

Podaci

Potpuno mjerenje, ne njegov sažetak.

  • results.jsonl — Svi rezultati — svaki zadatak, profil, mehanizam i orijentacija
  • summary.json — Agregati — brojevi na ovoj stranici
  • table.json — Ova tablica kao JSON
  • corpus.json — Generirane ulazne instance — stvarni problemi koje je pokretač riješio. Kanonski akademski skupovi dohvaćaju se i provjeravaju hashem umjesto da se ovdje kopiraju, jer njihov izvor ne odobrava redistribuciju.

Za reprodukciju: kloniraj repozitorij, pokreni npm run bench:fetch da preuzmeš kanonske instance i provjeriš njihove hasheve, zatim npm run bench. Generirani korpus ne treba preuzimanje.

Gore navedene datoteke objavljene su pod CC BY 4.0 — koristite ih, uključujući komercijalno, uz navođenje CutOptima. To pokriva naše vlastito mjerenje i generirani korpus. Kanonske akademske instance nisu naše za licenciranje i ne distribuiraju se odavde.

Pokreni vlastiti zadatak

Jedini broj koji je bitan onaj je koji proizvede vaš vlastiti popis materijala.