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Măsurare deschisă

Benchmarks

Cele mai multe programe de tăiere citează un procent de randament. Un procent nu spune nimic fără să știi ce era realizabil — 80 % poate fi optim la o lucrare și risipitor la alta. De aceea măsurăm în schimb față de minimul teoretic: pentru fiecare lucrare de test calculăm o limită inferioară a numărului de plăci sau bare pe care orice plan le-ar putea folosi, apoi raportăm cât de departe se află planul nostru de ea. Intrările sunt instanțe academice publicate, rezultatele sunt mai jos și poți rula totul din nou tu însuți.

89,3 %
dintre lucrările pe plăci ajung pe limită sau la o placă distanță de ea
53,0 %
sunt demonstrabil optime — exact pe limită
1,48 %
diferența medie față de limită la lucrările liniare
1.259
instanțe de test, 8 seturi de referință

Cifrele pe plăci sunt cele 553 instanțe canonice la kerf 0 cu rotația dezactivată — convenția pe care o folosește literatura, astfel încât sunt comparabile cu lucrările publicate pe aceleași instanțe.

Cum se calculează limita

O limită inferioară este un număr de plăci sub care niciun plan nu poate coborî. Dacă planul nostru o egalează, planul este demonstrabil optim pentru acea lucrare — nu există unul mai bun. Se calculează două limite și se folosește cea mai mare; ambele sunt raportate pe fiecare lucrare, ca să vezi cu ce contribuie fiecare.

LB1 — arie, corectată pentru grosimea pânzei (kerf)

Dă fiecărei piese plasate o amprentă mărită cu o jumătate de kerf pe fiecare latură. Într-un layout de ghilotină, oricare două piese sunt separate de cel puțin o tăiere, iar fiecare tăiere consumă un kerf, astfel încât acele amprente nu se suprapun niciodată — și toate încap în interiorul plăcii utile crescute cu o jumătate de kerf pe fiecare latură. Însumarea lor dă o limită pe care niciun layout nu o poate depăși. La kerf 0 aceasta este limita clasică de arie.

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

LB2 — funcții dual fezabile

Limita de arie este oarbă la formă: cinci piese de 600 × 600 folosesc aria a doar 1,8 plăci pe o placă de 1000 × 1000, și totuși încape doar una pe placă, deci sunt necesare cinci plăci. O funcție dual fezabilă este o transformare a dimensiunilor care păstrează fezabilitatea, ceea ce îi permite argumentului de arie să vadă acea structură. Se folosesc două familii — Martello–Toth și Fekete–Schepers — aplicate independent lățimilor și înălțimilor, iar se ia cel mai bun rezultat pe întreaga grilă de parametri. Sub rotație, fiecărei piese i se atribuie cea mai mică dintre cele două orientări ale sale, altfel limita ar putea depăși optimul real.

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

De ce sunt scalate instanțele

Instanțele publicate folosesc numere întregi mici, fără unitate — unele au un container de 10 × 10. Împachetatorul nostru elimină fâșiile libere mai subțiri de o unitate, ceea ce pe un container de 10 × 10 ar fi o zecime din placă. De aceea fiecare instanță este înmulțită cu un număr întreg până când latura scurtă are cel puțin 1000 de unități. Scalarea cu numere întregi este o transformare exactă: numărul optim de plăci nu se schimbă, instanța doar se îndepărtează de pragul acelui prag.

Reproductibilitate

Optimizatorul este determinist — aceeași intrare produce întotdeauna același plan. Întregul corpus a fost rulat de două ori cu cache-ul dezactivat, iar fiecare câmp în afară de timpi a revenit identic byte cu byte. Sursele instanțelor sunt fixate prin SHA-256, astfel încât o nouă rulare poate dovedi că a măsurat aceiași bytes. Și fiecare lucrare este verificată față de invarianta că limita nu depășește niciodată planul efectiv produs; o singură încălcare oprește rularea în loc să publice o cifră.

Ce nu spun aceste cifre

  • Limita noastră nu este cea mai puternică cunoscută. În literatură există limite mai puternice, așa că diferența pe care o raportăm este o estimare superioară a diferenței reale — o lucrare pe care o marcăm ca „nu pe limită” poate fi de fapt optimă, și pur și simplu nu o putem demonstra.
  • Diferențele relative exagerează la lucrările mici. Lucrarea mediană de aici are nevoie de aproximativ o duzină de plăci, așa că o placă în plus se citește ca un procent mare. Coloana absolută — cu câte plăci peste limită — este cea onestă.
  • Două dintre familiile generate sunt adverse prin construcție: piesele lor acoperă containerele exact, fără să lase joc, așa că orice imperfecțiune costă un container întreg. Sunt un test de plafon, nu o imagine a lucrului tipic.
  • Limita de 150 de piese din tabelul de dimensiuni nu este arbitrară — este locul unde ambele împachetatoare își schimbă strategia pentru viteză. Lucrările de peste ea urmează o cale de cod diferită, așa că o modificare acolo este un compromis deliberat, nu o prăpastie.
  • Măsurarea apelează aceleași funcții pe care le rulează Engine API-ul public, în același proces în loc de prin HTTP — latența rețelei ar corupe timpii. Această echivalență nu este presupusă: un eșantion de instanțe este reluat față de API-ul în funcțiune și i se cere să revină identic câmp cu câmp.

După mărimea lucrării

Împărțit după numărul de piese. Ambele împachetatoare renunță la strategia lor de căutare cea mai costisitoare peste 150 de piese, așa că acea limită separă două căi de cod diferite.

PieseLucrăriPe limităDif. medie dacă nuTimp 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 a fost măsurat

Două corpusuri, niciodată amestecate într-o singură cifră. Seturile canonice sunt instanțele pe care le folosește literatura academică; sunt descărcate și verificate prin hash în loc să fie copiate aici, deoarece sursa lor nu declară nicio licență care să permită redistribuirea. Seturile generate sunt ale noastre și le putem publica.

SetInstanțeOrigineÎn acest repository?
CLASS500JSHA-256 9f5ca94d6a…
BENG10MSHA-256 90536b0527…
A43RSHA-256 dd1804179a…
CLASS-R500Generate — construite din parametrii generatorului publicat, cu propriile noastre semințe
PERFECT2D72Generate — construite din parametrii generatorului publicat, cu propriile noastre semințe
UNIF1D40Generate — construite din parametrii generatorului publicat, cu propriile noastre semințe
TRIPLET1D40Generate — construite din parametrii generatorului publicat, cu propriile noastre semințe
RAND1D54Generate — construite din parametrii generatorului publicat, cu propriile noastre semințe

Două familii generate poartă un optim demonstrat prin construcție: piesele lor acoperă containerele exact, cu zero deșeu, așa că optimul este cunoscut și nu doar mărginit.

Seturile de strip-packing, rucsac (knapsack) și împachetare ortogonală sunt excluse: sunt probleme diferite cu obiective diferite, iar o cifră de „containere folosite” este nedefinită pentru ele. Colecția unidimensională BPPLIB este exclusă din motive de licență — autorii ei o publică sub CC BY-NC-ND, care nu permite folosirea în benchmarkul unui produs comercial.

Fiecare lucrare

Un rând per instanță la setările principale. Celelalte profiluri, motoare și orientări se află în fișierul de rezultate descărcabil.

Se afișează 1.259 din 1.259

InstanțăSetPieseMaterialLimităFolositePesteRandamentms
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
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PERFECT2D/p_300x300_k3_n30_1PERFECT2D901200×120034+17546.08
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PERFECT2D/p_300x300_k5_n30_1PERFECT2D1501200×120056+183.3394.05
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TRIPLET1D/t120_01TRIPLET1D12010004041+197.562.92
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TRIPLET1D/t249_01TRIPLET1D24910008386+396.5116.84
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RAND1D/r_50_100_0.1_0.7_1RAND1D5010002122+194.593.18
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RAND1D/r_50_150_0.1_0.7_1RAND1D501050202095.831.53
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RAND1D/r_200_100_0.1_0.7_1RAND1D20010007879+197.759.76
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RAND1D/r_200_100_0.2_0.8_1RAND1D200100010110198.1914.01
RAND1D/r_200_100_0.2_0.8_2RAND1D200100011011092.949.21
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RAND1D/r_200_150_0.1_0.7_1RAND1D2001050828298.8510.62
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RAND1D/r_200_150_0.1_0.7_3RAND1D20010508081+198.219.84
RAND1D/r_200_150_0.2_0.8_1RAND1D200105010010097.079.6
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RAND1D/r_200_150_0.2_0.8_3RAND1D200105010010098.069.41
RAND1D/r_200_1000_0.1_0.7_1RAND1D20010008485+198.489.5
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RAND1D/r_500_1000_0.2_0.8_3RAND1D5001000259262+396.3258.46

Nesting cu formă reală

Cifrele de mai sus provin de la packerul ghilotină, care taie dreptunghiuri. Nesting-ul cu formă reală este un motor diferit pentru o problemă diferită: așază POLIGOANE ARBITRARE — pentru laser, plasmă și jet de apă — lăsând piesele să se împletească în buzunarele concave ale celorlalte. Pe o lucrare reprezentativă de 272 piese folosește 6 foi, acolo unde exact aceleași piese trimise unui packer dreptunghiular după caseta lor de încadrare au nevoie de 9 — o treime mai puțin material, doar din formă.

6
foi · formă reală
5
foi · motorul max, 60 s
9
foi · casetă de încadrare
4
foi · minim teoretic

De ce raportăm numărul de foi, nu densitatea

Un packer cu casetă de încadrare numără aerul din crestăturile din interiorul dreptunghiului fiecărei piese ca material plin, așa că „utilizarea" lui pare mai mare pentru un rezultat mai slab — planul cu 9 foi pare mai dens decât cel cu 6 foi. Singura metrică sinceră și comparabilă între ele este numărul de foi de care au nevoie cu adevărat aceleași piese fizice. Acela este numărul de mai sus.

Planul cu 6 foi provine de la motorul implicit rapid, care răspunde în cadrul aceleiași cereri. Motorul asincron max (engine:"max") continuă apoi căutarea unui număr mai mic de foi: măsurat pe serverul nostru de producție la 22 septembrie 2026, a folosit 5 foi în 4 rulări cu bugetul său implicit de 60 de secunde, iar 5 foi în 2 rulări cu maximul de 180 de secunde. Este limitat în timp, așa că o rulare se poate încheia diferit față de alta — arătăm intervalul pe toate rulările, nu doar pe cea mai bună. Fiecare layout a fost verificat independent: fiecare piesă plasată și pe foaia ei, fără ca două piese să se suprapună cu mai mult de 0,01 mm — o marjă pentru coordonatele rotunjite pe care le returnează API-ul, deoarece piesele care se ating pot altfel părea să se intersecteze cu câteva miimi de milimetru.

O limită inferioară teoretică pentru această lucrare este 4 foi — aria totală a pieselor împărțită la o foaie. Niciun plan nu poate folosi mai puține; la forme neregulate, aerul dintre piese face ca un plan să ajungă rar la ea.

Aceste cifre nu au nicio distanță între piese. Cu o distanță de 5 mm între piese și față de marginea foii — o setare obișnuită pentru laser —, aceeași lucrare are nevoie de un total de foi: 6 cu motorul implicit, respectiv 5–6 cu max (2 rulări, fiecare de 60 s).

Seturile clasice de nesting ESICUP

Lucrarea de mai sus este una construită de noi. Pentru ca motorul să poată fi verificat și pe probleme pe care nu noi le-am ales, l-am rulat pe seturile clasice de nesting ESICUP — 13 la număr —, instanțele publice de împachetare neregulată folosite de literatura de cercetare. Sunt probleme de strip-packing; le transformăm în probleme pe foi așa cum procedează literatura de bin-packing, cu trei mărimi de foaie pătrată per set, ceea ce dă un total de instanțe: 39. Pe ansamblul lor, motorul implicit folosește un total de foi: 248, iar motorul max, 244 (cel mai slab rezultat din rulările efectuate — 2 la număr —, fiecare de 60 s), față de o limită inferioară de 153. Motorul implicit atinge limita la un total de instanțe: 7, iar max la 11. Max are nevoie de mai puține foi decât motorul implicit la un total de instanțe: 4, și anume în fiecare rulare.

Cum a fost măsurat, pe serverul nostru de producție la 22 septembrie 2026: fiecare foaie este un pătrat a cărui latură este de 1,1, 1,5 sau 2 ori dimensiunea celei mai mari piese (convenția lui Martinez-Sykora et al., 2017); fiecare set își păstrează propriile rotații permise; nu există distanță între piese, ca în literatură; max rulează cu bugetul său implicit de 60 de secunde, iar noi raportăm rularea sa cea mai slabă. Limita inferioară — aria totală a pieselor împărțită la o foaie — este slabă pentru forme neregulate, așa că un rezultat de peste ea nu este neapărat depășit de nimic. Fiecare layout a fost verificat în afara motorului: 39 din 39 sunt valide, cu fiecare piesă plasată pe foaia ei și fără ca două piese să se suprapună dincolo de rotunjirea coordonatelor returnate. Instanțele provin din repository-ul jagua-rs, la revizia din care este construit motorul nostru (colecția ESICUP este CC0), iar scriptul care le-a măsurat se află în repository-ul nostru.

Toate instanțele (39)
SetLatura foii (× cea mai mare piesă)PieseLimită inferioarăImplicitMax · 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

Rezultate per instanță (JSON)

Nesting cu formă reală în 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 →

Date

Măsurarea completă, nu un rezumat al ei.

  • results.jsonl — Toate rezultatele — fiecare lucrare, profil, motor și orientare
  • summary.json — Agregate — cifrele de pe această pagină
  • table.json — Acest tabel în format JSON
  • corpus.json — Instanțele de intrare generate — problemele reale pe care le-a rezolvat executorul. Seturile academice canonice sunt obținute și verificate prin hash în loc să fie copiate aici, deoarece sursa lor nu acordă redistribuirea.

Pentru a reproduce: clonează repository-ul, rulează npm run bench:fetch pentru a descărca instanțele canonice și a le verifica hash-urile, apoi npm run bench. Corpusul generat nu are nevoie de descărcare.

Fișierele de mai sus sunt publicate sub CC BY 4.0 — refolosește-le, inclusiv comercial, cu atribuire către CutOptim. Aceasta acoperă propria noastră măsurare și corpusul generat. Instanțele academice canonice nu sunt ale noastre pentru a le licenția și nu sunt distribuite de aici.

Rulează-ți propria lucrare

Singura cifră care contează este cea pe care o produce propria ta listă de materiale.