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Benchmarkok

A legtöbb szabásprogram egy kihozatal-százalékot közöl. Egy százalék viszont önmagában semmit nem jelent, amíg nem tudjuk, mi lett volna elérhető — 80 % az egyik munkán optimális, a másikon pazarlás. Ezért mi az elméleti minimumhoz mérünk: minden tesztmunkára kiszámoljuk, hány táblánál vagy szálnál kevesebbet semmilyen terv nem használhat, majd megmutatjuk, milyen messze van ettől a mi tervünk. A bemenetek publikált akadémiai teszthalmazok, az eredmények lent vannak, és az egészet újra tudod futtatni.

89,3 %
a lap-munkákból a korláton van, vagy egyetlen táblával fölötte
53,0 %
bizonyítottan optimális — pontosan a korláton
1,48 %
átlagos rés a korláttól lineáris munkákon
1259
teszt-instance, 8 teszthalmazból

A lap-számok a 553 kanonikus instance-ra vonatkoznak, kerf 0 mellett, forgatás nélkül — ez az irodalmi konvenció, tehát összevethetők az ugyanezeken az instance-eken publikált munkákkal.

Hogyan számoljuk a korlátot

Az alsó korlát az a táblaszám, ami alá semmilyen terv nem mehet. Ha a tervünk eltalálja, akkor az a terv arra a munkára bizonyítottan optimális — jobb nem létezik. Két korlátot számolunk, és a nagyobbat használjuk; mindkettőt munkánként kiírjuk, hogy látszódjon, melyik mit tesz hozzá.

LB1 — területalapú, a fűrészlapra korrigálva

Adjunk minden lerakott darabhoz egy fél fűrészlapnyival minden oldalról megnövelt lábnyomot. Egy guillotine-elrendezésben bármely két darabot legalább egy vágás választ el, és minden vágás elvisz egy lapnyit — így ezek a lábnyomok soha nem fedik át egymást, és mind belefér a fél lapnyival megnövelt hasznos táblába. Az összegük olyan korlátot ad, amit egyetlen elrendezés sem tud alulmúlni. Kerf 0-nál ez a klasszikus területkorlát.

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

LB2 — dual feasible függvények

A területkorlát vak az alakra: öt darab 600 × 600-as elem egy 1000 × 1000-es táblán csak 1,8 tábla területét foglalja, mégis csak egy fér el táblánként, tehát öt tábla kell. A dual feasible függvény a méretek olyan átalakítása, ami megőrzi a megvalósíthatóságot — ettől a területérvelés meglátja ezt a szerkezetet. Két családot használunk, a Martello–Toth és a Fekete–Schepers függvényeket, egymástól függetlenül a szélességekre és a magasságokra, és a teljes paraméterrács legjobb eredményét vesszük. Forgatás mellett minden darabot a két orientációja közül a kisebbel terhelünk, különben a korlát meghaladhatná a valódi optimumot.

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

Miért skálázzuk az instance-eket

A publikált instance-ek kis, mértékegység nélküli egészeket használnak — némelyiknek 10 × 10-es a táblája. A packerünk eldobja az egy egységnél vékonyabb szabad sávokat, ami egy 10 × 10-es táblán a tábla tizede lenne. Ezért minden instance-t egész számmal szorzunk, amíg a rövidebb oldala el nem éri az 1000 egységet. Az egész számmal való skálázás egzakt átalakítás: az optimális táblaszám nem változik, az instance csak kikerül ennek a küszöbnek a hatóköréből.

Újrafuttathatóság

Az optimalizáló determinisztikus — ugyanaz a bemenet mindig ugyanazt a tervet adja. A teljes korpuszt kétszer futtattuk le, gyorsítótár nélkül, és az időzítéseken kívül minden mező bájtra azonosan jött vissza. Az instance-forrásokat SHA-256 rögzíti, tehát egy újrafuttatás bizonyítani tudja, hogy ugyanazokat a bájtokat mérte. És minden munkát ellenőrzünk arra az invariánsra, hogy a korlát soha nem haladhatja meg a ténylegesen előállított tervet; egyetlen sértés leállítja a futást, ahelyett hogy számot publikálnánk.

Amit ezek a számok NEM mondanak

  • A mi korlátunk nem a legerősebb ismert. A szakirodalomban erősebbek is vannak, tehát az itt közölt rés a valódi rés felső becslése — egy „nincs a korláton" jelölésű munka valójában lehet optimális, csak nem tudjuk bizonyítani.
  • A relatív rés kis munkákon felnagyít. Az itteni munkák mediánja nagyjából egy tucat táblát igényel, tehát egyetlen tábla is nagy százaléknak látszik. Az abszolút oszlop — hány táblával vagyunk a korlát fölött — a becsületes szám.
  • A generált családok közül kettő szándékosan ellenséges: a darabjaik hiánytalanul kicsempézik a táblákat, nulla tartalékkal, tehát bármilyen tökéletlenség egy egész táblába kerül. Ezek plafon-tesztek, nem a tipikus munka képe.
  • A méret-táblázat 150 darabos határa nem önkényes: itt vált stratégiát mindkét packer a sebesség kedvéért. A fölötte lévő munkák más kódúton futnak, tehát az ottani változás tudatos kompromisszum, nem szakadék.
  • A mérés ugyanazokat a függvényeket hívja, amiket a publikus Engine API futtat — csak folyamaton belül, nem HTTP-n, mert a hálózati késleltetés tönkretenné az időzítéseket. Ezt az azonosságot nem feltételezzük: egy minta instance-t átfuttatunk az élő API-n, és megköveteljük, hogy mezőről mezőre azonos válasz jöjjön.

Munkaméret szerint

Darabszám szerint bontva. Mindkét packer elhagyja a legdrágább keresési stratégiáját 150 darab fölött, tehát ez a határ két különböző kódutat választ el.

DarabMunkákA korlátonÁtl. rés, ha nemp95 idő
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

Mit mértünk

Két korpusz, amiket soha nem mosunk össze egyetlen számmá. A kanonikus készletek azok az instance-ek, amiket az akadémiai irodalom használ; ezeket letöltjük és hash-sel ellenőrizzük, nem másoljuk ide, mert a forrásuk nem közöl olyan licencet, ami a továbbterjesztést engedné. A generált készletek a mieink, azokat publikálhatjuk.

KészletInstanceEredetA repóban?
CLASS500JSHA-256 9f5ca94d6a…
BENG10MSHA-256 90536b0527…
A43RSHA-256 dd1804179a…
CLASS-R500Generált — a publikált generátor-paraméterekből, saját seeddel
PERFECT2D72Generált — a publikált generátor-paraméterekből, saját seeddel
UNIF1D40Generált — a publikált generátor-paraméterekből, saját seeddel
TRIPLET1D40Generált — a publikált generátor-paraméterekből, saját seeddel
RAND1D54Generált — a publikált generátor-paraméterekből, saját seeddel

Két generált család konstrukcióból bizonyított optimumot hordoz: a darabjaik hiánytalanul kicsempézik a táblákat, nulla hulladékkal, tehát ott az optimum ismert, nem csak korlátozott.

A strip-packing, knapsack és orthogonal-packing készleteket kizártuk: ezek más feladatok, más célfüggvénnyel, és rájuk a „felhasznált tábla" szám nem is értelmezhető. Az egydimenziós BPPLIB gyűjtemény licenc miatt marad ki — a szerzői CC BY-NC-ND alatt publikálják, ami nem engedi egy kereskedelmi termék benchmarkjában való felhasználást.

Minden munka

Instance-enként egy sor, a fő beállításokkal. A többi profil, motor és orientáció a letölthető eredményfájlban van.

1259 / 1259 látszik

InstanceKészletDarabTáblaKorlátFelhasználtFölötteKihozatalms
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
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RAND1D/r_500_1000_0.2_0.8_3RAND1D5001000259262+396.3258.46

Valódi kontúrú elhelyezés

A fenti számok a giljotin-elhelyezőé, amely téglalapokat vág. A valódi kontúrú elhelyezés egy másik motor egy másik problémára: TETSZŐLEGES SOKSZÖGEKET helyez el — lézer-, plazma- és vízsugár-vágáshoz —, hagyva, hogy a darabok egymás konkáv zsebeibe illeszkedjenek. Egy reprezentatív, 272 darabos munkán 6 táblát használ, míg ugyanezek a darabok egy téglalapos elhelyezőnek a befoglaló téglalapjukkal átadva 9-et igényelnek — harmadával kevesebb anyag, pusztán az alakból.

6
tábla · valódi kontúr
5
tábla · max motor, 60 mp
9
tábla · befoglaló téglalap
4
tábla · matematikai minimum

Miért a táblaszámot jelentjük, nem a sűrűséget

Egy befoglaló-téglalapos elhelyező az egyes darabok téglalapján belüli beugrás-levegőt tömörnek számolja, így a „kihasználása" magasabbnak mutat egy rosszabb eredményt — a 9 táblás terv sűrűbbnek látszik, mint a 6 táblás. Az egyetlen őszinte, összehasonlítható mérőszám az, hogy ugyanazok a fizikai darabok valójában hány táblát igényelnek. Ez a fenti szám.

A 6 táblás terv a gyors alapértelmezett motoré, amely ugyanabban a kérésben válaszol. Az aszinkron max motor (engine:"max") ezután tovább keres kevesebb táblát: az éles szerverünkön mérve (2026. szeptember 22.), az alapértelmezett 60 másodperces kerettel 4 futásból 5 táblát használt, a 180 másodperces maximummal pedig 2 futásból 5 táblát. Időkorlátos, tehát egy futás más eredménnyel zárulhat, mint a másik — nem a legjobb futást mutatjuk, hanem a teljes tartományt. Minden elrendezést egymástól függetlenül ellenőriztünk: minden darab elhelyezve és a saját tábláján van, és semelyik két darab nem fedi egymást 0,01 mm-nél többel — ez a margó a kerekített koordinátáknak szól, amiket az API ad vissza, mert az egymást érintő darabok enélkül néhány ezred milliméterrel átfedőnek látszhatnak.

Ezen a munkán a matematikai alsó korlát 4 tábla — a teljes darabterület osztva egy tábla területével. Ennél kevesebbet semmilyen terv nem használhat; szabálytalan alakoknál a darabok közötti levegő miatt egy terv ritkán éri el ezt.

Ezek a számok darabok közötti rés nélkül értendők. Egy gyakori lézeres beállítással, 5 mm réssel a darabok között és a tábla szélén, ugyanaz a munka 6 táblát igényel az alapértelmezett motorral, a max motorral pedig 5–6 táblát (2 futás, egyenként 60 mp).

A klasszikus ESICUP elhelyezési készletek

A fenti munkát mi állítottuk össze. Hogy a motort olyan feladatokon is ellenőrizni tudjuk, amiket nem mi választottunk, lefuttattuk a 13 klasszikus ESICUP elhelyezési készleten — ezek azok a nyilvános, szabálytalan alakú elhelyezési instance-ek, amiket a kutatási irodalom használ. Ezek strip-packing feladatok; a bin-packing szakirodalom módszerével tábla-feladatokká alakítjuk őket, készletenként három négyzet alakú tábla mérettel, ami összesen 39 instance-t ad. Az összes instance-en együttvéve az alapértelmezett motor 248 táblát használ, a max motor pedig 244 táblát (a 2 futás közül a rosszabbikat, egyenként 60 mp), a 153 táblás alsó korláttal szemben. Az alapértelmezett 7 instance-en éri el a korlátot, a max 11 instance-en. A max 4 instance-en igényel kevesebb táblát, mint az alapértelmezett — minden futásban.

Így mértük, az éles szerverünkön (2026. szeptember 22.): minden tábla egy négyzet, amelynek oldala a legnagyobb darab méretének 1,1-, 1,5- vagy 2-szerese (a Martinez-Sykora et al., 2017 konvenciója); minden készlet megtartja a saját engedélyezett forgatásait; a darabok között nincs rés, ahogy az irodalomban sem; a max a saját, alapértelmezett 60 másodperces keretével fut, és a rosszabb futását közöljük. Az alsó korlát — a teljes darabterület osztva egy tábla területével — szabálytalan alakoknál gyenge, tehát egy afölötti eredményt nem feltétlenül ver meg semmi. Minden elrendezést a motoron kívül ellenőriztünk: a 39 instance-ből 39 érvényes, minden darab a saját tábláján van elhelyezve, és semelyik két darab nem fedi egymást a visszaadott koordináták kerekítésén túl. Az instance-ek a jagua-rs repóból származnak, abból a revízióból, amiből a motorunk épül (az ESICUP gyűjtemény CC0), és a mérő szkript a mi repónkban van.

Mind a 39 instance
KészletTábla oldala (× legnagyobb darab)DarabAlsó korlátAlapértelmezettMax · 60 mp
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

Instance-enkénti eredmények (JSON)

Valódi kontúrú elhelyezés az Engine API-ban →

A max tier — közelebb a bizonyított optimumhoz

A fenti számok az alapértelmezett motoré, ami azonnal válaszol. Az opcionális, aszinkron max motor (engine:"max") ehelyett fakeresést futtat: ugyanazokon a publikus 2DPackLib példányokon, ugyanazzal az alsó korláttal mérve, 12–13 százalékponttal több munkán éri el a BIZONYÍTOTT minimumot, mint az alapértelmezett — a többin is kisebb réssel. A cserébe kért ár az idő — lásd lent.

KorpuszMotorA korlátonÁtlag rés (korláton kívül)
A + BENG · 106alapértelmezett · heuristic44,3 %11,1 %
max · PackingSolver57,1 %6,9 %
CLASS (sample) · 168alapértelmezett · heuristic57,7 %12,8 %
max · PackingSolver69,6 %10,4 %

Miért aszinkron a max tier

Az alapértelmezett motor ~30 ms alatt megold és a böngésződben fut. A max motor munkánként másodperceket–egy percet kér — túl hosszú egy nyitva tartott HTTP-kéréshez —, ezért aszinkron: az engine:"max" POST egy job-azonosítót ad vissza, amit lekérdezel, amíg el nem készül. Ugyanaz a publikus korpusz, ugyanaz az alsó-korlát-módszer, mindkét motor a miénk — nulla versenytárs-adat.

Egy őszinte kitétel: a max motor időkorlátos, ezért a legnehezebb példányokon a keresés a korlátnál megszakad — néhány munka nem fejeződik be (1 a 274-ból itt), és a számai futásonként kb. egy pontot mozoghatnak. Az alapértelmezett motor teljesen determinisztikus, és mindig ad tervet.

A max tier az Engine API-ban →

Adat

A teljes mérés, nem az összefoglalója.

  • results.jsonl — Összes eredmény — minden munka, profil, motor és orientáció
  • summary.json — Összesítők — az ezen az oldalon szereplő számok
  • table.json — Ez a táblázat JSON-ként
  • corpus.json — A generált bemeneti instance-ek — a tényleges feladatok, amiket a futtató megoldott. A kanonikus akadémiai készleteket letöltjük és hash-sel ellenőrizzük, nem másoljuk ide, mert a forrásuk nem ad terjesztési engedélyt.

Újrafuttatás: klónozd a repót, futtasd a npm run bench:fetch-et a kanonikus instance-ek letöltéséhez és hash-ellenőrzéséhez, majd a npm run bench-et. A generált korpuszhoz nem kell letöltés.

A fenti fájlok CC BY 4.0 licenc alatt jelennek meg — szabadon felhasználhatók, üzleti célra is, a CutOptim megjelölésével. Ez a saját mérésünkre és a generált korpuszra vonatkozik. A kanonikus akadémiai instance-eket nem áll módunkban licencelni, és nem is innen terjesztjük őket.

Futtasd le a saját munkádat

Az egyetlen szám, ami számít, az, amit a saját anyaglistád ad.