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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_01CLASS201000×100088—8119.53
CLASS/cl_01_020_02CLASS201000×100055—86.66.46
CLASS/cl_01_020_03CLASS201000×100089+172.229.33
CLASS/cl_01_020_04CLASS201000×100056+178.335.02
CLASS/cl_01_020_05CLASS201000×100066—896.03
CLASS/cl_01_020_06CLASS201000×100099—81.786.3
CLASS/cl_01_020_07CLASS201000×100066—88.335.78
CLASS/cl_01_020_08CLASS201000×100066—84.56
CLASS/cl_01_020_09CLASS201000×100088—76.885.9
CLASS/cl_01_020_10CLASS201000×100088—837.38
CLASS/cl_01_040_01CLASS401000×10001010—89.513.33
CLASS/cl_01_040_02CLASS401000×10001112+189.1714.37
CLASS/cl_01_040_03CLASS401000×10001617+181.7616.15
CLASS/cl_01_040_04CLASS401000×10001414—89.0717.8
CLASS/cl_01_040_05CLASS401000×10001515—91.7313.51
CLASS/cl_01_040_06CLASS401000×10001414—75.7916.6
CLASS/cl_01_040_07CLASS401000×10001112+189.513.19
CLASS/cl_01_040_08CLASS401000×10001819+176.5318.11
CLASS/cl_01_040_09CLASS401000×10001111—91.6410.99
CLASS/cl_01_040_10CLASS401000×10001112+185.512.96
CLASS/cl_01_060_01CLASS601000×10002223+187.2629.24
CLASS/cl_01_060_02CLASS601000×10001919—92.9520.99
CLASS/cl_01_060_03CLASS601000×10002121—86.5223.26
CLASS/cl_01_060_04CLASS601000×10002222—82.8625.76
CLASS/cl_01_060_05CLASS601000×10001919—86.7927.32
CLASS/cl_01_060_06CLASS601000×10001718+192.1724.27
CLASS/cl_01_060_07CLASS601000×10001616—92.524.47
CLASS/cl_01_060_08CLASS601000×10002121—89.6731.67
CLASS/cl_01_060_09CLASS601000×10001819+191.4223.52
CLASS/cl_01_060_10CLASS601000×10002424—87.8330.44
CLASS/cl_01_080_01CLASS801000×10002525—90.9638.28
CLASS/cl_01_080_02CLASS801000×10002626—92.5837.88
CLASS/cl_01_080_03CLASS801000×10002727—85.1131.04
CLASS/cl_01_080_04CLASS801000×10002727—90.329.38
CLASS/cl_01_080_05CLASS801000×10002626—90.4636.19
CLASS/cl_01_080_06CLASS801000×10002828—90.0437
CLASS/cl_01_080_07CLASS801000×10003131—85.8138.29
CLASS/cl_01_080_08CLASS801000×10002929—91.1732.01
CLASS/cl_01_080_09CLASS801000×10003031+189.934.21
CLASS/cl_01_080_10CLASS801000×10002626—93.3132.58
CLASS/cl_01_100_01CLASS1001000×10002829+194.2448.5
CLASS/cl_01_100_02CLASS1001000×10003132+19544.88
CLASS/cl_01_100_03CLASS1001000×10002929—9246.75
CLASS/cl_01_100_04CLASS1001000×10003031+192.9446.07
CLASS/cl_01_100_05CLASS1001000×10003232—94.2248.57
CLASS/cl_01_100_06CLASS1001000×10003737—91.349.75
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_10CLASS1001000×10003838—89.9257.65
CLASS/cl_02_020_01CLASS201020×102011—726.31
CLASS/cl_02_020_02CLASS201020×102011—48.118.85
CLASS/cl_02_020_03CLASS201020×102011—72.225.54
CLASS/cl_02_020_04CLASS201020×102011—52.228.84
CLASS/cl_02_020_05CLASS201020×102011—59.338.18
CLASS/cl_02_020_06CLASS201020×102011—81.784.56
CLASS/cl_02_020_07CLASS201020×102011—58.898.36
CLASS/cl_02_020_08CLASS201020×102011—56.338.29
CLASS/cl_02_020_09CLASS201020×102011—68.337.28
CLASS/cl_02_020_10CLASS201020×102011—73.786.94
CLASS/cl_02_040_01CLASS401020×102012+149.7220.98
CLASS/cl_02_040_02CLASS401020×102022—59.4418.45
CLASS/cl_02_040_03CLASS401020×102022—77.2213.63
CLASS/cl_02_040_04CLASS401020×102022—69.2818.39
CLASS/cl_02_040_05CLASS401020×102022—76.4411.72
CLASS/cl_02_040_06CLASS401020×102022—58.9416.79
CLASS/cl_02_040_07CLASS401020×102022—59.6716.32
CLASS/cl_02_040_08CLASS401020×102022—80.7814.09
CLASS/cl_02_040_09CLASS401020×102022—5619.51
CLASS/cl_02_040_10CLASS401020×102022—5720.12
CLASS/cl_02_060_01CLASS601020×102033—74.3328.33
CLASS/cl_02_060_02CLASS601020×102023+165.4130
CLASS/cl_02_060_03CLASS601020×102033—67.329.32
CLASS/cl_02_060_04CLASS601020×102033—67.5230.34
CLASS/cl_02_060_05CLASS601020×102022—91.6115.38
CLASS/cl_02_060_06CLASS601020×102022—92.1725.69
CLASS/cl_02_060_07CLASS601020×102022—82.2220
CLASS/cl_02_060_08CLASS601020×102033—69.7427.39
CLASS/cl_02_060_09CLASS601020×102022—96.527.17
CLASS/cl_02_060_10CLASS601020×102033—78.0722.72
CLASS/cl_02_080_01CLASS801020×102033—84.2226.88
CLASS/cl_02_080_02CLASS801020×102033—89.1527.56
CLASS/cl_02_080_03CLASS801020×102033—85.1126.09
CLASS/cl_02_080_04CLASS801020×102033—90.324.9
CLASS/cl_02_080_05CLASS801020×102033—87.1126.33
CLASS/cl_02_080_06CLASS801020×102033—93.3738.74
CLASS/cl_02_080_07CLASS801020×102033—98.5236.5
CLASS/cl_02_080_08CLASS801020×102033—97.9335.12
CLASS/cl_02_080_09CLASS801020×102044—77.4235.06
CLASS/cl_02_080_10CLASS801020×102033—89.8528.08
CLASS/cl_02_100_01CLASS1001020×102044—75.9246.31
CLASS/cl_02_100_02CLASS1001020×102044—84.4437.91
CLASS/cl_02_100_03CLASS1001020×102034+174.1147.32
CLASS/cl_02_100_04CLASS1001020×102044—80.0336.11
CLASS/cl_02_100_05CLASS1001020×102044—83.7534.85
CLASS/cl_02_100_06CLASS1001020×102044—93.8333.74
CLASS/cl_02_100_07CLASS1001020×102044—76.0345.32
CLASS/cl_02_100_08CLASS1001020×102044—86.6936.84
CLASS/cl_02_100_09CLASS1001020×102044—82.9438.86
CLASS/cl_02_100_10CLASS1001020×102044—94.9239.09
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_04CLASS201000×100044—77.563.39
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_08CLASS201000×100044—80.613.76
CLASS/cl_03_020_09CLASS201000×100056+170.17.23
CLASS/cl_03_020_10CLASS201000×100077—66.057.29
CLASS/cl_03_040_01CLASS401000×100067+180.0113.92
CLASS/cl_03_040_02CLASS401000×100089+179.1710.84
CLASS/cl_03_040_03CLASS401000×10001111—82.5512.91
CLASS/cl_03_040_04CLASS401000×10001010—82.3510.25
CLASS/cl_03_040_05CLASS401000×10001212—78.6617.34
CLASS/cl_03_040_06CLASS401000×10001010—69.7312.43
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_08CLASS601000×10001515—85.2223.83
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_08CLASS801000×10002222—8236.07
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_01CLASS201000×100011—68.718.06
CLASS/cl_04_020_02CLASS201000×100011—41.699.41
CLASS/cl_04_020_03CLASS201000×100011—70.556.23
CLASS/cl_04_020_04CLASS201000×100011—49.649.82
CLASS/cl_04_020_05CLASS201000×100011—55.28.52
CLASS/cl_04_020_06CLASS201000×100011—76.056.87
CLASS/cl_04_020_07CLASS201000×100011—54.478.55
CLASS/cl_04_020_08CLASS201000×100011—51.599.62
CLASS/cl_04_020_09CLASS201000×100011—67.37.84
CLASS/cl_04_020_10CLASS201000×100011—73.986.01
CLASS/cl_04_040_01CLASS401000×100011—89.6823.94
CLASS/cl_04_040_02CLASS401000×100022—5720.45
CLASS/cl_04_040_03CLASS401000×100022—72.6418.08
CLASS/cl_04_040_04CLASS401000×100022—65.8818.43
CLASS/cl_04_040_05CLASS401000×100022—75.5116.86
CLASS/cl_04_040_06CLASS401000×100022—55.7817.08
CLASS/cl_04_040_07CLASS401000×100022—58.121.85
CLASS/cl_04_040_08CLASS401000×100022—79.5113.79
CLASS/cl_04_040_09CLASS401000×100022—53.5520.45
CLASS/cl_04_040_10CLASS401000×100022—53.8323.66
CLASS/cl_04_060_01CLASS601000×100033—71.8927.23
CLASS/cl_04_060_02CLASS601000×100022—91.126.98
CLASS/cl_04_060_03CLASS601000×100023+165.5531.43
CLASS/cl_04_060_04CLASS601000×100023+165.5432.1
CLASS/cl_04_060_05CLASS601000×100022—87.0325.09
CLASS/cl_04_060_06CLASS601000×100022—88.5226.21
CLASS/cl_04_060_07CLASS601000×100022—79.6827.66
CLASS/cl_04_060_08CLASS601000×100033—68.1828.24
CLASS/cl_04_060_09CLASS601000×100022—92.5530.54
CLASS/cl_04_060_10CLASS601000×100033—77.6525.23
CLASS/cl_04_080_01CLASS801000×100033—80.8635.47
CLASS/cl_04_080_02CLASS801000×100033—84.8234.84
CLASS/cl_04_080_03CLASS801000×100033—82.7735.16
CLASS/cl_04_080_04CLASS801000×100033—87.0932.84
CLASS/cl_04_080_05CLASS801000×100033—83.1936.69
CLASS/cl_04_080_06CLASS801000×100033—91.5537.72
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_10CLASS801000×100033—86.4831.45
CLASS/cl_04_100_01CLASS1001000×100034+171.8157.1
CLASS/cl_04_100_02CLASS1001000×100044—83.149.72
CLASS/cl_04_100_03CLASS1001000×100033—94.0849.28
CLASS/cl_04_100_04CLASS1001000×100044—76.3152.56
CLASS/cl_04_100_05CLASS1001000×100044—80.8247
CLASS/cl_04_100_06CLASS1001000×100044—91.934.17
CLASS/cl_04_100_07CLASS1001000×100034+173.6156.27
CLASS/cl_04_100_08CLASS1001000×100044—83.5646.1
CLASS/cl_04_100_09CLASS1001000×100044—78.7552.47
CLASS/cl_04_100_10CLASS1001000×100044—92.9753.37
CLASS/cl_05_020_01CLASS201000×100078+167.148.28
CLASS/cl_05_020_02CLASS201000×100045+164.738.93
CLASS/cl_05_020_03CLASS201000×100077—78.914.89
CLASS/cl_05_020_04CLASS201000×100055—77.784.29
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_08CLASS201000×100055—80.937.2
CLASS/cl_05_020_09CLASS201000×100077—75.386.2
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_03CLASS401000×10001515—76.9118.46
CLASS/cl_05_040_04CLASS401000×10001213+180.2220.7
CLASS/cl_05_040_05CLASS401000×10001315+279.3417.86
CLASS/cl_05_040_06CLASS401000×10001212—73.1412.04
CLASS/cl_05_040_07CLASS401000×10001011+182.413.62
CLASS/cl_05_040_08CLASS401000×10001717—73.5414.19
CLASS/cl_05_040_09CLASS401000×1000910+183.9814.93
CLASS/cl_05_040_10CLASS401000×10001011+176.8416.6
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BENG/BENG01BENG202500×100044—74.17.22
BENG/BENG02BENG402500×100067+181.1414.97
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A/A11A7242550×21004450+686.66364.37
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A/A13A3042550×21001215+379.09119.5
A/A14A8092550×21006570+590.12592.97
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A/A16A7442550×21008185+491.69431.93
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A/A26A612550×210078+179.8524.72
A/A27A1802550×21001920+189.7860.96
A/A28A1062550×21001112+182.5561.31
A/A29A2182550×21002629+387.2284.68
A/A3A172750×122088—60.617.17
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A/A33A3092550×21003436+290.68136.84
A/A34A462550×210056+176.5620.99
A/A35A1442550×21001617+188.8997.49
A/A36A522550×210099—72.1124.89
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A/A38A1602550×21002124+384.0441.63
A/A39A222550×210034+168.310.45
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A/A5A1382470×20801213+185.8190.09
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CLASS-R/rcl_01_020_01CLASS-R201000×100077—79.863.27
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CLASS-R/rcl_06_080_03CLASS-R801200×120033—8141.05
CLASS-R/rcl_06_080_04CLASS-R801200×120033—82.9243.31
CLASS-R/rcl_06_080_05CLASS-R801200×120022—72.8141.79
CLASS-R/rcl_06_080_06CLASS-R801200×120033—76.3241.32
CLASS-R/rcl_06_080_07CLASS-R801200×120023+165.8151.43
CLASS-R/rcl_06_080_08CLASS-R801200×120033—80.6842.56
CLASS-R/rcl_06_080_09CLASS-R801200×120033—70.5647.65
CLASS-R/rcl_06_080_10CLASS-R801200×120033—82.2240.05
CLASS-R/rcl_06_100_01CLASS-R1001200×120033—91.0861.98
CLASS-R/rcl_06_100_02CLASS-R1001200×120033—77.0856.5
CLASS-R/rcl_06_100_03CLASS-R1001200×120033—80.7757.26
CLASS-R/rcl_06_100_04CLASS-R1001200×120044—78.7956.16
CLASS-R/rcl_06_100_05CLASS-R1001200×120033—81.9353.71
CLASS-R/rcl_06_100_06CLASS-R1001200×120033—88.2841.92
CLASS-R/rcl_06_100_07CLASS-R1001200×120044—78.6956.22
CLASS-R/rcl_06_100_08CLASS-R1001200×120033—77.954.52
CLASS-R/rcl_06_100_09CLASS-R1001200×120044—84.6954.77
CLASS-R/rcl_06_100_10CLASS-R1001200×120033—91.0358.92
CLASS-R/rcl_07_020_01CLASS-R201000×100077—79.815.19
CLASS-R/rcl_07_020_02CLASS-R201000×100066—84.774.42
CLASS-R/rcl_07_020_03CLASS-R201000×100078+165.668.88
CLASS-R/rcl_07_020_04CLASS-R201000×100067+170.758.03
CLASS-R/rcl_07_020_05CLASS-R201000×100056+167.886.95
CLASS-R/rcl_07_020_06CLASS-R201000×100066—76.866.07
CLASS-R/rcl_07_020_07CLASS-R201000×100056+176.175.84
CLASS-R/rcl_07_020_08CLASS-R201000×100056+169.978.09
CLASS-R/rcl_07_020_09CLASS-R201000×100077—77.75.65
CLASS-R/rcl_07_020_10CLASS-R201000×100067+172.365.87
CLASS-R/rcl_07_040_01CLASS-R401000×10001112+181.4419.28
CLASS-R/rcl_07_040_02CLASS-R401000×1000910+180.2311.25
CLASS-R/rcl_07_040_03CLASS-R401000×1000910+182.2314.36
CLASS-R/rcl_07_040_04CLASS-R401000×10001010—86.4217.98
CLASS-R/rcl_07_040_05CLASS-R401000×10001011+177.9911.83
CLASS-R/rcl_07_040_06CLASS-R401000×10001212—82.4215.54
CLASS-R/rcl_07_040_07CLASS-R401000×10001212—75.9815.61
CLASS-R/rcl_07_040_08CLASS-R401000×10001010—83.6317.41
CLASS-R/rcl_07_040_09CLASS-R401000×10001212—77.2612.91
CLASS-R/rcl_07_040_10CLASS-R401000×10001212—80.7212.63
CLASS-R/rcl_07_060_01CLASS-R601000×10001617+180.0124.69
CLASS-R/rcl_07_060_02CLASS-R601000×10001314+183.3528.5
CLASS-R/rcl_07_060_03CLASS-R601000×10002121—81.9925.78
CLASS-R/rcl_07_060_04CLASS-R601000×10001818—82.2523.53
CLASS-R/rcl_07_060_05CLASS-R601000×10001717—78.9121.88
CLASS-R/rcl_07_060_06CLASS-R601000×10001717—81.6324.71
CLASS-R/rcl_07_060_07CLASS-R601000×10001717—82.2425.08
CLASS-R/rcl_07_060_08CLASS-R601000×10001818—80.3421.54
CLASS-R/rcl_07_060_09CLASS-R601000×10001617+180.6324.4
CLASS-R/rcl_07_060_10CLASS-R601000×10001415+183.7730.42
CLASS-R/rcl_07_080_01CLASS-R801000×10002121—81.8540.44
CLASS-R/rcl_07_080_02CLASS-R801000×10002323—84.9436.41
CLASS-R/rcl_07_080_03CLASS-R801000×10002223+183.1542.41
CLASS-R/rcl_07_080_04CLASS-R801000×10001919—85.3735.23
CLASS-R/rcl_07_080_05CLASS-R801000×10002122+186.1136.99
CLASS-R/rcl_07_080_06CLASS-R801000×10002223+184.5735.8
CLASS-R/rcl_07_080_07CLASS-R801000×10002527+281.2540.19
CLASS-R/rcl_07_080_08CLASS-R801000×10002122+182.5143.88
CLASS-R/rcl_07_080_09CLASS-R801000×10002021+187.6240.9
CLASS-R/rcl_07_080_10CLASS-R801000×10002122+189.1642.2
CLASS-R/rcl_07_100_01CLASS-R1001000×10002627+184.3361.22
CLASS-R/rcl_07_100_02CLASS-R1001000×10002325+285.454.73
CLASS-R/rcl_07_100_03CLASS-R1001000×10002829+182.4556.49
CLASS-R/rcl_07_100_04CLASS-R1001000×10002830+283.3361.9
CLASS-R/rcl_07_100_05CLASS-R1001000×10002425+183.5650.59
CLASS-R/rcl_07_100_06CLASS-R1001000×10002626—84.2256.06
CLASS-R/rcl_07_100_07CLASS-R1001000×10002627+184.5454.76
CLASS-R/rcl_07_100_08CLASS-R1001000×10003030—89.3559.14
CLASS-R/rcl_07_100_09CLASS-R1001000×10002828—81.7553.54
CLASS-R/rcl_07_100_10CLASS-R1001000×10002627+186.1651.13
CLASS-R/rcl_08_020_01CLASS-R201000×100055—77.16.83
CLASS-R/rcl_08_020_02CLASS-R201000×100066—65.756.36
CLASS-R/rcl_08_020_03CLASS-R201000×100077—73.665.91
CLASS-R/rcl_08_020_04CLASS-R201000×100078+175.237.15
CLASS-R/rcl_08_020_05CLASS-R201000×100088—77.876.38
CLASS-R/rcl_08_020_06CLASS-R201000×100066—75.48.36
CLASS-R/rcl_08_020_07CLASS-R201000×100099—76.318.34
CLASS-R/rcl_08_020_08CLASS-R201000×100077—78.837.35
CLASS-R/rcl_08_020_09CLASS-R201000×100056+175.826.43
CLASS-R/rcl_08_020_10CLASS-R201000×100044—81.777.55
CLASS-R/rcl_08_040_01CLASS-R401000×10001011+177.9216.49
CLASS-R/rcl_08_040_02CLASS-R401000×10001212—8017.89
CLASS-R/rcl_08_040_03CLASS-R401000×10001111—82.6720.78
CLASS-R/rcl_08_040_04CLASS-R401000×10001011+174.8620.41
CLASS-R/rcl_08_040_05CLASS-R401000×10001011+180.7116.11
CLASS-R/rcl_08_040_06CLASS-R401000×10001112+176.8313.87
CLASS-R/rcl_08_040_07CLASS-R401000×10001112+180.9417.78
CLASS-R/rcl_08_040_08CLASS-R401000×10001213+174.3821.26
CLASS-R/rcl_08_040_09CLASS-R401000×10001010—85.4519.99
CLASS-R/rcl_08_040_10CLASS-R401000×10001011+184.1616.32
CLASS-R/rcl_08_060_01CLASS-R601000×10001718+183.4432.92
CLASS-R/rcl_08_060_02CLASS-R601000×10001717—81.5831.85
CLASS-R/rcl_08_060_03CLASS-R601000×10001717—84.0832.89
CLASS-R/rcl_08_060_04CLASS-R601000×10001717—82.0530.65
CLASS-R/rcl_08_060_05CLASS-R601000×10001718+181.3626.92
CLASS-R/rcl_08_060_06CLASS-R601000×10001415+179.8130.02
CLASS-R/rcl_08_060_07CLASS-R601000×10001818—81.4633.99
CLASS-R/rcl_08_060_08CLASS-R601000×10001718+181.8129.3
CLASS-R/rcl_08_060_09CLASS-R601000×10001515—86.6329.68
CLASS-R/rcl_08_060_10CLASS-R601000×10002020—83.131.15
CLASS-R/rcl_08_080_01CLASS-R801000×10002627+181.8747.71
CLASS-R/rcl_08_080_02CLASS-R801000×10001920+182.7145.63
CLASS-R/rcl_08_080_03CLASS-R801000×10002424—85.0942.09
CLASS-R/rcl_08_080_04CLASS-R801000×10001920+181.6641.22
CLASS-R/rcl_08_080_05CLASS-R801000×10002223+182.747.16
CLASS-R/rcl_08_080_06CLASS-R801000×10002122+183.2543.03
CLASS-R/rcl_08_080_07CLASS-R801000×10001919—85.753.18
CLASS-R/rcl_08_080_08CLASS-R801000×10002223+183.6548.02
CLASS-R/rcl_08_080_09CLASS-R801000×10002526+180.0546.58
CLASS-R/rcl_08_080_10CLASS-R801000×10002121—84.0847.44
CLASS-R/rcl_08_100_01CLASS-R1001000×10002627+183.0473.54
CLASS-R/rcl_08_100_02CLASS-R1001000×10002729+283.1364.94
CLASS-R/rcl_08_100_03CLASS-R1001000×10002727—88.6763.44
CLASS-R/rcl_08_100_04CLASS-R1001000×10002930+182.0871.6
CLASS-R/rcl_08_100_05CLASS-R1001000×10002222—86.8465.94
CLASS-R/rcl_08_100_06CLASS-R1001000×10002830+281.2363.41
CLASS-R/rcl_08_100_07CLASS-R1001000×10002324+182.6964.03
CLASS-R/rcl_08_100_08CLASS-R1001000×10002324+183.0460.67
CLASS-R/rcl_08_100_09CLASS-R1001000×10002627+187.5261.89
CLASS-R/rcl_08_100_10CLASS-R1001000×10002930+182.7565.08
CLASS-R/rcl_09_020_01CLASS-R201000×10001313—71.038.48
CLASS-R/rcl_09_020_02CLASS-R201000×10001414—54.7110.79
CLASS-R/rcl_09_020_03CLASS-R201000×10001515—65.769.01
CLASS-R/rcl_09_020_04CLASS-R201000×10001212—64.8110.29
CLASS-R/rcl_09_020_05CLASS-R201000×10001616—70.418.79
CLASS-R/rcl_09_020_06CLASS-R201000×10001213+161.848.09
CLASS-R/rcl_09_020_07CLASS-R201000×10001010—74.229.53
CLASS-R/rcl_09_020_08CLASS-R201000×10001515—60.058.35
CLASS-R/rcl_09_020_09CLASS-R201000×10001616—67.0910.77
CLASS-R/rcl_09_020_10CLASS-R201000×10001515—62.049.25
CLASS-R/rcl_09_040_01CLASS-R401000×10002929—67.9926.61
CLASS-R/rcl_09_040_02CLASS-R401000×10003435+158.8126.6
CLASS-R/rcl_09_040_03CLASS-R401000×10002424—73.3619.28
CLASS-R/rcl_09_040_04CLASS-R401000×10003030—58.1627.14
CLASS-R/rcl_09_040_05CLASS-R401000×10002727—68.1126.56
CLASS-R/rcl_09_040_06CLASS-R401000×10003132+157.6629.46
CLASS-R/rcl_09_040_07CLASS-R401000×10002627+166.5921.61
CLASS-R/rcl_09_040_08CLASS-R401000×10002526+167.820.79
CLASS-R/rcl_09_040_09CLASS-R401000×10002121—67.3320.24
CLASS-R/rcl_09_040_10CLASS-R401000×10002727—67.5821.04
CLASS-R/rcl_09_060_01CLASS-R601000×10004848—63.9851.85
CLASS-R/rcl_09_060_02CLASS-R601000×10004747—60.741.33
CLASS-R/rcl_09_060_03CLASS-R601000×10004343—63.4648.85
CLASS-R/rcl_09_060_04CLASS-R601000×10004545—57.346.84
CLASS-R/rcl_09_060_05CLASS-R601000×10004242—66.5142.76
CLASS-R/rcl_09_060_06CLASS-R601000×10004141—62.8843.25
CLASS-R/rcl_09_060_07CLASS-R601000×10004545—63.8135.46
CLASS-R/rcl_09_060_08CLASS-R601000×10003636—62.8339.24
CLASS-R/rcl_09_060_09CLASS-R601000×10003737—66.0642.62
CLASS-R/rcl_09_060_10CLASS-R601000×10004646—59.4251.21
CLASS-R/rcl_09_080_01CLASS-R801000×10005656—64.0864.06
CLASS-R/rcl_09_080_02CLASS-R801000×10005858—62.3782.98
CLASS-R/rcl_09_080_03CLASS-R801000×10005758+165.0872.67
CLASS-R/rcl_09_080_04CLASS-R801000×10006161—62.8971.54
CLASS-R/rcl_09_080_05CLASS-R801000×10005555—59.4169.65
CLASS-R/rcl_09_080_06CLASS-R801000×10005252—6567.08
CLASS-R/rcl_09_080_07CLASS-R801000×10004647+166.5370.81
CLASS-R/rcl_09_080_08CLASS-R801000×10005556+162.8767.6
CLASS-R/rcl_09_080_09CLASS-R801000×10005151—65.5572.84
CLASS-R/rcl_09_080_10CLASS-R801000×10005555—64.5557.63
CLASS-R/rcl_09_100_01CLASS-R1001000×10007272—63.16103.02
CLASS-R/rcl_09_100_02CLASS-R1001000×10006262—65.0386.7
CLASS-R/rcl_09_100_03CLASS-R1001000×10007373—66.51107.25
CLASS-R/rcl_09_100_04CLASS-R1001000×10006464—64.796.05
CLASS-R/rcl_09_100_05CLASS-R1001000×10006969—60.12110.26
CLASS-R/rcl_09_100_06CLASS-R1001000×10006565—64.55102.37
CLASS-R/rcl_09_100_07CLASS-R1001000×10007676—63.2594.15
CLASS-R/rcl_09_100_08CLASS-R1001000×10006869+162.24108.1
CLASS-R/rcl_09_100_09CLASS-R1001000×10008080—60.35123.89
CLASS-R/rcl_09_100_10CLASS-R1001000×10007677+162.55103.18
CLASS-R/rcl_10_020_01CLASS-R201000×100044—82.236.87
CLASS-R/rcl_10_020_02CLASS-R201000×100033—77.695.49
CLASS-R/rcl_10_020_03CLASS-R201000×100056+174.298.8
CLASS-R/rcl_10_020_04CLASS-R201000×100044—86.987.03
CLASS-R/rcl_10_020_05CLASS-R201000×100044—75.266.45
CLASS-R/rcl_10_020_06CLASS-R201000×100034+165.46.77
CLASS-R/rcl_10_020_07CLASS-R201000×100056+163.719.9
CLASS-R/rcl_10_020_08CLASS-R201000×100033—89.197.43
CLASS-R/rcl_10_020_09CLASS-R201000×100022—83.387.67
CLASS-R/rcl_10_020_10CLASS-R201000×100033—79.436.59
CLASS-R/rcl_10_040_01CLASS-R401000×100066—88.5916.7
CLASS-R/rcl_10_040_02CLASS-R401000×100056+169.7417.51
CLASS-R/rcl_10_040_03CLASS-R401000×100056+181.7713.95
CLASS-R/rcl_10_040_04CLASS-R401000×100067+179.9216.76
CLASS-R/rcl_10_040_05CLASS-R401000×100066—86.5815.09
CLASS-R/rcl_10_040_06CLASS-R401000×100055—84.6419.31
CLASS-R/rcl_10_040_07CLASS-R401000×100077—86.7717.17
CLASS-R/rcl_10_040_08CLASS-R401000×1000910+178.816.02
CLASS-R/rcl_10_040_09CLASS-R401000×100077—85.1711.25
CLASS-R/rcl_10_040_10CLASS-R401000×100067+182.616.81
CLASS-R/rcl_10_060_01CLASS-R601000×10001010—89.0724.99
CLASS-R/rcl_10_060_02CLASS-R601000×10001011+189.225.45
CLASS-R/rcl_10_060_03CLASS-R601000×1000910+183.8624.85
CLASS-R/rcl_10_060_04CLASS-R601000×100089+182.0624.38
CLASS-R/rcl_10_060_05CLASS-R601000×100078+180.2526.42
CLASS-R/rcl_10_060_06CLASS-R601000×10001112+189.1831.78
CLASS-R/rcl_10_060_07CLASS-R601000×10001011+184.0631.21
CLASS-R/rcl_10_060_08CLASS-R601000×10001616—78.7632.21
CLASS-R/rcl_10_060_09CLASS-R601000×100067+183.1225.15
CLASS-R/rcl_10_060_10CLASS-R601000×100078+183.7324.47
CLASS-R/rcl_10_080_01CLASS-R801000×1000910+186.9729.42
CLASS-R/rcl_10_080_02CLASS-R801000×10001314+189.137.24
CLASS-R/rcl_10_080_03CLASS-R801000×10001415+190.0242.9
CLASS-R/rcl_10_080_04CLASS-R801000×10001213+191.0836.54
CLASS-R/rcl_10_080_05CLASS-R801000×10001112+185.8838.98
CLASS-R/rcl_10_080_06CLASS-R801000×10001516+183.7236.9
CLASS-R/rcl_10_080_07CLASS-R801000×10001213+185.4837.54
CLASS-R/rcl_10_080_08CLASS-R801000×10001112+185.0340.2
CLASS-R/rcl_10_080_09CLASS-R801000×10001516+188.6839.67
CLASS-R/rcl_10_080_10CLASS-R801000×10001112+185.5439
CLASS-R/rcl_10_100_01CLASS-R1001000×10002021+185.8958.35
CLASS-R/rcl_10_100_02CLASS-R1001000×10001617+190.7357.87
CLASS-R/rcl_10_100_03CLASS-R1001000×10001415+187.2354.59
CLASS-R/rcl_10_100_04CLASS-R1001000×10001415+191.4852.8
CLASS-R/rcl_10_100_05CLASS-R1001000×10001820+285.8164.95
CLASS-R/rcl_10_100_06CLASS-R1001000×10001719+285.0560.12
CLASS-R/rcl_10_100_07CLASS-R1001000×10001617+191.2954.94
CLASS-R/rcl_10_100_08CLASS-R1001000×10001415+186.755.61
CLASS-R/rcl_10_100_09CLASS-R1001000×10001314+192.5949.49
CLASS-R/rcl_10_100_10CLASS-R1001000×10001415+190.9257.59
PERFECT2D/p_100x100_k2_n8_1PERFECT2D161000×100022—1003.8
PERFECT2D/p_100x100_k2_n8_2PERFECT2D161000×100023+166.674.4
PERFECT2D/p_100x100_k2_n16_1PERFECT2D321000×100023+166.6711.05
PERFECT2D/p_100x100_k2_n16_2PERFECT2D321000×100023+166.6712.75
PERFECT2D/p_100x100_k2_n30_1PERFECT2D601000×100023+166.6726.25
PERFECT2D/p_100x100_k2_n30_2PERFECT2D601000×100023+166.6728.59
PERFECT2D/p_100x100_k3_n8_1PERFECT2D241000×100034+1756.56
PERFECT2D/p_100x100_k3_n8_2PERFECT2D241000×100034+1757.41
PERFECT2D/p_100x100_k3_n16_1PERFECT2D481000×100034+17516.58
PERFECT2D/p_100x100_k3_n16_2PERFECT2D481000×100034+17517.28
PERFECT2D/p_100x100_k3_n30_1PERFECT2D901000×100034+17544.03
PERFECT2D/p_100x100_k3_n30_2PERFECT2D901000×100034+17550.94
PERFECT2D/p_100x100_k5_n8_1PERFECT2D401000×100056+183.3310.77
PERFECT2D/p_100x100_k5_n8_2PERFECT2D401000×100056+183.3311.69
PERFECT2D/p_100x100_k5_n16_1PERFECT2D801000×100056+183.3331.95
PERFECT2D/p_100x100_k5_n16_2PERFECT2D801000×100056+183.3340.47
PERFECT2D/p_100x100_k5_n30_1PERFECT2D1501000×100056+183.3381.51
PERFECT2D/p_100x100_k5_n30_2PERFECT2D1501000×100056+183.3383.66
PERFECT2D/p_120x80_k2_n8_1PERFECT2D161560×104023+166.673.61
PERFECT2D/p_120x80_k2_n8_2PERFECT2D161560×104023+166.674.88
PERFECT2D/p_120x80_k2_n16_1PERFECT2D321560×104023+166.6712.55
PERFECT2D/p_120x80_k2_n16_2PERFECT2D321560×104023+166.6711.31
PERFECT2D/p_120x80_k2_n30_1PERFECT2D601560×104023+166.6728.79
PERFECT2D/p_120x80_k2_n30_2PERFECT2D601560×104023+166.6728.06
PERFECT2D/p_120x80_k3_n8_1PERFECT2D241560×104034+1757.43
PERFECT2D/p_120x80_k3_n8_2PERFECT2D241560×104034+1759.02
PERFECT2D/p_120x80_k3_n16_1PERFECT2D481560×104034+17514.88
PERFECT2D/p_120x80_k3_n16_2PERFECT2D481560×104034+17516.36
PERFECT2D/p_120x80_k3_n30_1PERFECT2D901560×104034+17548.19
PERFECT2D/p_120x80_k3_n30_2PERFECT2D901560×104034+17542.48
PERFECT2D/p_120x80_k5_n8_1PERFECT2D401560×104056+183.338.61
PERFECT2D/p_120x80_k5_n8_2PERFECT2D401560×104056+183.3311.24
PERFECT2D/p_120x80_k5_n16_1PERFECT2D801560×104056+183.3333.04
PERFECT2D/p_120x80_k5_n16_2PERFECT2D801560×104056+183.3332.04
PERFECT2D/p_120x80_k5_n30_1PERFECT2D1501560×104056+183.3388
PERFECT2D/p_120x80_k5_n30_2PERFECT2D1501560×104056+183.3386.98
PERFECT2D/p_250x150_k2_n8_1PERFECT2D161750×105023+166.675.5
PERFECT2D/p_250x150_k2_n8_2PERFECT2D161750×105023+166.674.99
PERFECT2D/p_250x150_k2_n16_1PERFECT2D321750×105023+166.6712.54
PERFECT2D/p_250x150_k2_n16_2PERFECT2D321750×105023+166.6710.63
PERFECT2D/p_250x150_k2_n30_1PERFECT2D601750×105023+166.6729.92
PERFECT2D/p_250x150_k2_n30_2PERFECT2D601750×105023+166.6730.07
PERFECT2D/p_250x150_k3_n8_1PERFECT2D241750×105034+1756.47
PERFECT2D/p_250x150_k3_n8_2PERFECT2D241750×105034+1756.98
PERFECT2D/p_250x150_k3_n16_1PERFECT2D481750×105034+17520.5
PERFECT2D/p_250x150_k3_n16_2PERFECT2D481750×105034+17519.23
PERFECT2D/p_250x150_k3_n30_1PERFECT2D901750×105034+17543.53
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PERFECT2D/p_250x150_k5_n8_1PERFECT2D401750×105057+271.4314.81
PERFECT2D/p_250x150_k5_n8_2PERFECT2D401750×105056+183.338.86
PERFECT2D/p_250x150_k5_n16_1PERFECT2D801750×105056+183.3333.97
PERFECT2D/p_250x150_k5_n16_2PERFECT2D801750×105056+183.3334.59
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_1PERFECT2D161200×120022—1004.19
PERFECT2D/p_300x300_k2_n8_2PERFECT2D161200×120023+166.673.41
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
PERFECT2D/p_300x300_k2_n30_2PERFECT2D601200×120023+166.6731.47
PERFECT2D/p_300x300_k3_n8_1PERFECT2D241200×120034+1756.85
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PERFECT2D/p_300x300_k3_n16_1PERFECT2D481200×120034+17518.53
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PERFECT2D/p_300x300_k3_n30_1PERFECT2D901200×120034+17546.08
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PERFECT2D/p_300x300_k5_n8_1PERFECT2D401200×120056+183.3311.55
PERFECT2D/p_300x300_k5_n8_2PERFECT2D401200×120056+183.3313.62
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PERFECT2D/p_300x300_k5_n30_1PERFECT2D1501200×120056+183.3394.05
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UNIF1D/u120_03UNIF1D12010504849+196.754.99
UNIF1D/u120_04UNIF1D12010505252—98.1711.44
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UNIF1D/u120_07UNIF1D12010505152+198.054.68
UNIF1D/u120_08UNIF1D12010504950+197.434.14
UNIF1D/u120_09UNIF1D12010505152+196.824.76
UNIF1D/u120_10UNIF1D12010504545—98.434.42
UNIF1D/u250_01UNIF1D250105099101+297.919.47
UNIF1D/u250_02UNIF1D2501050102104+297.5318.79
UNIF1D/u250_03UNIF1D25010509595—99.1619.77
UNIF1D/u250_04UNIF1D2501050102103+198.5222.85
UNIF1D/u250_05UNIF1D2501050104106+298.0919.32
UNIF1D/u250_06UNIF1D2501050101103+297.6119.05
UNIF1D/u250_07UNIF1D2501050100100—99.2516.68
UNIF1D/u250_08UNIF1D2501050105106+198.4118.45
UNIF1D/u250_09UNIF1D2501050102103+198.4321.17
UNIF1D/u250_10UNIF1D250105098100+297.6118.34
UNIF1D/u500_01UNIF1D5001050199200+199.4479.63
UNIF1D/u500_02UNIF1D5001050196196—99.9480.92
UNIF1D/u500_03UNIF1D5001050204206+298.6379.14
UNIF1D/u500_04UNIF1D5001050196198+298.9579.26
UNIF1D/u500_05UNIF1D5001050199199—99.6778.27
UNIF1D/u500_06UNIF1D5001050204204—99.7279.14
UNIF1D/u500_07UNIF1D5001050202205+398.5378.48
UNIF1D/u500_08UNIF1D5001050200202+298.5979
UNIF1D/u500_09UNIF1D5001050200200—99.7474
UNIF1D/u500_10UNIF1D5001050197197—99.776.38
UNIF1D/u1000_01UNIF1D10001050403403—99.96292.33
UNIF1D/u1000_02UNIF1D10001050398399+199.52309.11
UNIF1D/u1000_03UNIF1D10001050401401—99.95303.68
UNIF1D/u1000_04UNIF1D10001050392393+199.66280.55
UNIF1D/u1000_05UNIF1D10001050399400+199.73280.16
UNIF1D/u1000_06UNIF1D10001050403404+199.63278.34
UNIF1D/u1000_07UNIF1D10001050409410+199.65295.87
UNIF1D/u1000_08UNIF1D10001050398398—99.85277.36
UNIF1D/u1000_09UNIF1D10001050399399—99.98279.3
UNIF1D/u1000_10UNIF1D10001050403405+299.42271.44
TRIPLET1D/t60_01TRIPLET1D6010002021+195.247.12
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TRIPLET1D/t60_04TRIPLET1D6010002021+195.240.84
TRIPLET1D/t60_05TRIPLET1D6010002021+195.241.14
TRIPLET1D/t60_06TRIPLET1D6010002021+195.240.92
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TRIPLET1D/t60_10TRIPLET1D6010002021+195.240.82
TRIPLET1D/t120_01TRIPLET1D12010004041+197.562.92
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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
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_2RAND1D5010002121—96.571.62
RAND1D/r_50_100_0.1_0.7_3RAND1D5010002020—971.49
RAND1D/r_50_100_0.2_0.8_1RAND1D5010002828—90.611.49
RAND1D/r_50_100_0.2_0.8_2RAND1D5010002626—931.39
RAND1D/r_50_100_0.2_0.8_3RAND1D5010002324+194.631.4
RAND1D/r_50_150_0.1_0.7_1RAND1D5010502020—95.831.53
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RAND1D/r_50_150_0.1_0.7_3RAND1D5010502223+194.71.5
RAND1D/r_50_150_0.2_0.8_1RAND1D5010503131—80.691.63
RAND1D/r_50_150_0.2_0.8_2RAND1D5010503030—85.185.51
RAND1D/r_50_150_0.2_0.8_3RAND1D5010502525—95.761.23
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_3RAND1D5010002121—96.710.67
RAND1D/r_50_1000_0.2_0.8_1RAND1D5010002929—88.750.71
RAND1D/r_50_1000_0.2_0.8_2RAND1D5010003030—89.930.71
RAND1D/r_50_1000_0.2_0.8_3RAND1D5010002828—91.310.64
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_3RAND1D20010008282—98.9911.08
RAND1D/r_200_100_0.2_0.8_1RAND1D2001000101101—98.1914.01
RAND1D/r_200_100_0.2_0.8_2RAND1D2001000110110—92.949.21
RAND1D/r_200_100_0.2_0.8_3RAND1D2001000108108—94.889.27
RAND1D/r_200_150_0.1_0.7_1RAND1D20010508282—98.8510.62
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_1RAND1D2001050100100—97.079.6
RAND1D/r_200_150_0.2_0.8_2RAND1D2001050101102+196.9314.27
RAND1D/r_200_150_0.2_0.8_3RAND1D2001050100100—98.069.41
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_2RAND1D2001000106106—95.248.67
RAND1D/r_200_1000_0.2_0.8_3RAND1D2001000108108—94.29.4
RAND1D/r_500_100_0.1_0.7_1RAND1D5001000196197+199.3264.83
RAND1D/r_500_100_0.1_0.7_2RAND1D5001000204204—99.969.21
RAND1D/r_500_100_0.1_0.7_3RAND1D5001000200200—99.6970.26
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_3RAND1D5001000256256—97.5364.82
RAND1D/r_500_150_0.1_0.7_1RAND1D5001050202202—99.8971.84
RAND1D/r_500_150_0.1_0.7_2RAND1D5001050204204—99.6573.46
RAND1D/r_500_150_0.1_0.7_3RAND1D5001050192192—99.7575.24
RAND1D/r_500_150_0.2_0.8_1RAND1D5001050261261—96.7264.54
RAND1D/r_500_150_0.2_0.8_2RAND1D5001050250250—98.8764.97
RAND1D/r_500_150_0.2_0.8_3RAND1D5001050270270—95.2663.52
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

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
5
ploča · max motor, 60 s
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.

Plan brzog zadanog motora (broj ploča: 6) nastaje unutar istog zahtjeva. Asinkroni max motor (engine:"max") zatim nastavlja tražiti manji broj ploča: izmjereno na našem produkcijskom poslužitelju 22. rujna 2026. — sa zadanim proračunom od 60 sekundi broj ploča bio je 5 (broj pokretanja: 4), a s maksimumom od 180 sekundi 5 (broj pokretanja: 2). Vremenski je ograničen, pa jedno pokretanje može završiti drukčije od drugog — prikazujemo raspon svih pokretanja, a ne najbolje od njih. Svaki raspored provjeren je nezavisno: svaki dio postavljen i na svojoj ploči, nijedna dva dijela ne preklapaju se više od 0,01 mm — margina za zaokružene koordinate koje vraća API, jer dijelovi koji se dodiruju inače mogu izgledati kao da se križaju za nekoliko tisućinki milimetra.

Teorijska donja granica broja ploča na ovom poslu iznosi 4 — ukupna površina dijelova podijeljena površinom jedne ploče. Nijedan plan ne može upotrijebiti manje; kod nepravilnih oblika zrak između dijelova znači da plan tu granicu rijetko doseže.

Te brojke nemaju razmak između dijelova. Uz razmak od 5 mm između dijelova i na rubu ploče — uobičajenu lasersku postavku — za isti posao broj potrebnih ploča sa zadanim motorom iznosi 6, a s max motorom 5–6 (broj pokretanja: 2, svako po 60 s).

Klasični ESICUP skupovi za ugniježđivanje

Posao prikazan iznad izradili smo sami. Kako bismo motor mogli provjeriti i na problemima koje nismo sami odabrali, pokrenuli smo ga na klasičnim ESICUP skupovima za ugniježđivanje (ukupno 13) — javnim instancama nepravilnog pakiranja koje koristi istraživačka literatura. Riječ je o strip-packing problemima; pretvaramo ih u probleme s pločama na način na koji to čini literatura o bin-packingu, s tri kvadratne veličine ploče po skupu — broj instanci: 39. U svima zajedno zadani motor koristi broj ploča 248, a max motor broj ploča 236 (uzima se lošije pokretanje; broj pokretanja: 2, svako po 60 s), naspram donje granice čiji je broj ploča 153. Broj instanci na kojima zadani motor doseže granicu iznosi 7, a za max motor 14. Broj instanci na kojima max motor u svakom pokretanju treba manje ploča nego zadani motor iznosi 11.

Kako je izmjereno, na našem produkcijskom poslužitelju 22. rujna 2026.: svaka je ploča kvadrat čija je stranica 1,1 puta, 1,5 puta ili 2 puta veća od najveće dimenzije komada (konvencija autora Martinez-Sykora i sur., 2017.); svaki skup zadržava vlastite dopuštene rotacije; između dijelova nema razmaka, kao u literaturi; max motor radi sa zadanim proračunom od 60 sekundi i izvještavamo njegovo lošije pokretanje. Donja granica — ukupna površina dijelova podijeljena površinom jedne ploče — slaba je za nepravilne oblike, pa udaljenost od nje ne pokazuje koliko je rezultat daleko od najboljeg mogućeg. Metode objavljene u znanstvenoj literaturi na mnogim od ovih instanci koriste manje ploča od našeg motora; ovaj odjeljak pokazuje gdje je motor, a ne da je optimalan. Svaki raspored provjeren je izvan motora: broj valjanih instanci iznosi 39 od ukupno 39, pri čemu je svaki dio postavljen na svojoj ploči i nijedna dva dijela ne preklapaju se izvan zaokruživanja vraćenih koordinata. Instance dolaze iz jagua-rs repozitorija, u reviziji na kojoj je izgrađen naš motor (ESICUP zbirka je CC0), a skripta kojom su izmjerene nalazi se u našem repozitoriju.

Sve instance (39)
SkupStranica ploče (× najveći komad)DijeloviDonja granicaZadanoMax · 60 s
albano1,124466
albano1,524333
albano224222
blaz11,128112020
blaz11,52861412
blaz1228466
dagli1,130344
dagli1,530222
dagli230111
fu1,112598
fu1,512354
fu212232
jakobs11,125699
jakobs11,525344
jakobs1225232
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
shirts299454
swim1,14861211
swim1,548466
swim248233
trousers1,164565
trousers1,564344
trousers264222

Rezultati po instanci (JSON)

Pravokutni dijelovi za lasersko rezanje

Poslovi s limom uglavnom su pravokutnici i gotovo pravokutni oblici, a upravo tu motor za ugniježđivanje koji uzorkuje položaje zaostaje: rijetko pogodi točnu mrežu. Zato oba motora pakiraju i granične okvire dijelova točnim pravokutnim pakiračem i zadržavaju bolji plan. Na poslovima s pravokutnim dijelovima (broj poslova: 20, ukupan broj dijelova: 1.226) zadani motor koristi broj ploča 70, naspram donje granice čiji je broj ploča 63; broj poslova na kojima doseže granicu iznosi 14. Svaki posao s točnom mrežom (5 od 5) ispada optimalan.

Kako je izmjereno, na našem produkcijskom poslužitelju 28. rujna 2026.: četiri vrste poslova, svi sintetički i definirani u našoj skripti — identični dijelovi koji točno popunjavaju ploču bez razmaka, ista vrsta mreže s laserskim razmakom i razmakom od ruba, mješovite narudžbe pravokutnika te limeni dijelovi sa zaobljenim kutovima i rupama za vijke. Rotacija je slobodna, što je zadana postavka API-ja; max motor radi s proračunom od 15 sekundi i izvještavamo njegovo najlošije pokretanje (broj pokretanja: 2). Donja granica je ukupna površina dijelova podijeljena površinom jedne ploče; zanemaruje razmak, pa na poslovima s razmakom stvarni minimum može biti iznad nje. Svaki raspored provjeren je izvan motora: broj valjanih poslova iznosi 20 od ukupno 20, pri čemu je svaki dio postavljen, nijedna dva se ne preklapaju i nijedan nije bliže drugom dijelu od zadanog razmaka ni rubu ploče od razmaka od ruba.

Max motor na svakom je ovdašnjem poslu upotrijebio točno onoliko ploča koliko i zadani motor: kod pravokutnika posao već obavlja točni pakirač, a njegova duža pretraga isplati se na nepravilnim oblicima poput onih iznad.

Svi poslovi (20)
PosaoPloča (mm)Razmak / rub (mm)DijeloviDonja granicaZadanoMax · 15 s
grid-5003.000 × 1.5000 / 036222
grid-2503.000 × 1.5000 / 0144222
grid-1000x5003.000 × 1.5000 / 027333
grid-625x2502.500 × 1.2500 / 040222
grid-mixed3.000 × 1.5000 / 024222
spaced-4903.000 × 1.5005 / 1036222
spaced-5902.500 × 1.2505 / 1024333
spaced-980x4803.000 × 1.50010 / 518222
orders-13.000 × 1.5005 / 1092555
orders-22.500 × 1.2505 / 1064455
orders-33.000 × 1.5005 / 10103666
orders-42.500 × 1.2505 / 1075555
orders-53.000 × 1.5005 / 1046333
orders-62.500 × 1.2505 / 1095677
orders-73.000 × 1.5005 / 1039233
orders-82.500 × 1.2505 / 1071688
plates-13.000 × 1.5005 / 1035111
plates-23.000 × 1.5005 / 10104344
plates-33.000 × 1.5005 / 1071233
plates-43.000 × 1.5005 / 1082222

Rezultati po poslu (JSON)

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.

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