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Benchmarks

La mayoría del software de corte cita un porcentaje de aprovechamiento. Un porcentaje no dice nada sin saber qué era alcanzable — un 80 % puede ser óptimo en un trabajo y un derroche en otro. Por eso medimos frente al mínimo teórico: para cada trabajo de prueba calculamos una cota inferior del número de tableros o barras que cualquier plan podría usar, y luego informamos de a qué distancia queda nuestro plan. Las entradas son instancias académicas publicadas, los resultados están abajo, y puede volver a ejecutarlo todo usted mismo.

89,3 %
de los trabajos de tablero caen en la cota o a un tablero de ella
53,0 %
son demostrablemente óptimos — exactamente en la cota
1,48 %
diferencia media respecto a la cota en trabajos lineales
1259
instancias de prueba, 8 conjuntos de referencia

Las cifras de tablero son las 553 instancias canónicas con kerf 0 y rotación desactivada — la convención que usa la literatura, para que sean comparables con el trabajo publicado sobre las mismas instancias.

Cómo se calcula la cota

Una cota inferior es un número de tableros por debajo del cual ningún plan puede bajar. Si nuestro plan la iguala, el plan es demostrablemente óptimo para ese trabajo — no existe uno mejor. Se calculan dos cotas y se usa la mayor; ambas se informan por trabajo para que vea qué aporta cada una.

LB1 — área, corregida por el ancho de corte (kerf)

Dé a cada pieza colocada una huella ampliada medio kerf por cada lado. En una disposición de guillotina, dos piezas cualesquiera están separadas por al menos un corte, y cada corte consume un kerf, así que esas huellas nunca se solapan — y todas caben dentro del tablero útil crecido medio kerf por cada lado. Sumarlas da una cota que ninguna disposición puede batir. Con kerf 0 esta es la cota de área clásica.

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

LB2 — funciones dualmente factibles

La cota de área es ciega a la forma: cinco piezas de 600 × 600 usan solo el área de 1,8 tableros en un tablero de 1000 × 1000, y sin embargo solo cabe una por tablero, así que hacen falta cinco. Una función dualmente factible es una transformación de los tamaños que preserva la factibilidad, y permite que el argumento de área vea esa estructura. Se usan dos familias — Martello–Toth y Fekete–Schepers — aplicadas de forma independiente a anchos y altos, y se toma el mejor resultado sobre toda la rejilla de parámetros. Bajo rotación, a cada pieza se le imputa la menor de sus dos orientaciones; de lo contrario, la cota podría superar el óptimo real.

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

Por qué se escalan las instancias

Las instancias publicadas usan enteros pequeños sin unidad — algunas tienen un contenedor de 10 × 10. Nuestro empaquetador descarta las tiras libres de menos de una unidad de grosor, lo que en un contenedor de 10 × 10 sería una décima parte del tablero. Por eso cada instancia se multiplica por un número entero hasta que su lado corto sea de al menos 1000 unidades. El escalado entero es una transformación exacta: el número óptimo de tableros no cambia, la instancia solo se aleja del alcance de ese umbral.

Reproducibilidad

El optimizador es determinista — la misma entrada siempre produce el mismo plan. Todo el corpus se ejecutó dos veces con la caché desactivada y todos los campos salvo los tiempos volvieron byte a byte idénticos. Las fuentes de las instancias están fijadas por SHA-256, de modo que una nueva ejecución puede demostrar que midió los mismos bytes. Y cada trabajo se comprueba contra la invariante de que la cota nunca supera el plan realmente producido; una sola violación detiene la ejecución en lugar de publicar un número.

Lo que estos números no dicen

  • Nuestra cota no es la más fuerte que se conoce. En la literatura existen cotas más fuertes, así que la diferencia que informamos es una estimación superior de la diferencia real — un trabajo que marcamos como «no en la cota» puede de hecho ser óptimo, y simplemente no podemos demostrarlo.
  • Las diferencias relativas se exageran en trabajos pequeños. El trabajo mediano de aquí necesita alrededor de una docena de tableros, así que un tablero de más se lee como un porcentaje grande. La columna absoluta — cuántos tableros por encima de la cota — es la honesta.
  • Dos de las familias generadas son adversas por construcción: sus piezas cubren los contenedores exactamente, sin dejar holgura, así que cualquier imperfección cuesta un contenedor entero. Son una prueba de techo, no un retrato del trabajo típico.
  • El límite de 150 piezas de la tabla de tamaños no es arbitrario — es donde ambos empaquetadores cambian de estrategia por velocidad. Los trabajos por encima de él siguen un camino de código distinto, así que un cambio ahí es un compromiso deliberado, no un precipicio.
  • La medición llama a las mismas funciones que ejecuta la Engine API pública, en el mismo proceso en lugar de por HTTP — la latencia de red corrompería los tiempos. Esa equivalencia no se da por supuesta: se reproduce una muestra de instancias contra la API en vivo y se exige que vuelva idéntica campo por campo.

Por tamaño de trabajo

Dividido por número de piezas. Ambos empaquetadores abandonan su estrategia de búsqueda más costosa por encima de 150 piezas, así que ese límite separa dos caminos de código distintos.

PiezasTrabajosEn la cotaDif. media si noTiempo 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

Qué se midió

Dos corpus, nunca mezclados en un solo número. Los conjuntos canónicos son las instancias que usa la literatura académica; se descargan y se verifican por hash en lugar de copiarse aquí, porque su fuente no declara ninguna licencia que permita la redistribución. Los conjuntos generados son nuestros y podemos publicarlos.

ConjuntoInstanciasOrigen¿En este repositorio?
CLASS500JSHA-256 9f5ca94d6a…
BENG10MSHA-256 90536b0527…
A43RSHA-256 dd1804179a…
CLASS-R500Generados — construidos a partir de los parámetros del generador publicado, con nuestras propias semillas
PERFECT2D72Generados — construidos a partir de los parámetros del generador publicado, con nuestras propias semillas
UNIF1D40Generados — construidos a partir de los parámetros del generador publicado, con nuestras propias semillas
TRIPLET1D40Generados — construidos a partir de los parámetros del generador publicado, con nuestras propias semillas
RAND1D54Generados — construidos a partir de los parámetros del generador publicado, con nuestras propias semillas

Dos familias generadas llevan un óptimo demostrado por construcción: sus piezas cubren los contenedores exactamente, con cero desperdicio, así que el óptimo se conoce y no está meramente acotado.

Los conjuntos de strip-packing, mochila (knapsack) y empaquetado ortogonal quedan excluidos: son problemas distintos con objetivos distintos, y una cifra de «contenedores usados» no está definida para ellos. La colección unidimensional BPPLIB se excluye por motivos de licencia — sus autores la publican bajo CC BY-NC-ND, que no permite su uso en el benchmark de un producto comercial.

Cada trabajo

Una fila por instancia con los ajustes de referencia. Los demás perfiles, motores y orientaciones están en el archivo de resultados descargable.

Mostrando 1259 de 1259

InstanciaConjuntoPiezasMaterialCotaUsadosExcesoAprov.ms
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CLASS-R/rcl_09_060_10CLASS-R601000×1000464659.4251.21
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CLASS-R/rcl_09_080_02CLASS-R801000×1000585862.3782.98
CLASS-R/rcl_09_080_03CLASS-R801000×10005758+165.0872.67
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CLASS-R/rcl_09_080_05CLASS-R801000×1000555559.4169.65
CLASS-R/rcl_09_080_06CLASS-R801000×100052526567.08
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-R801000×1000515165.5572.84
CLASS-R/rcl_09_080_10CLASS-R801000×1000555564.5557.63
CLASS-R/rcl_09_100_01CLASS-R1001000×1000727263.16103.02
CLASS-R/rcl_09_100_02CLASS-R1001000×1000626265.0386.7
CLASS-R/rcl_09_100_03CLASS-R1001000×1000737366.51107.25
CLASS-R/rcl_09_100_04CLASS-R1001000×1000646464.796.05
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CLASS-R/rcl_09_100_07CLASS-R1001000×1000767663.2594.15
CLASS-R/rcl_09_100_08CLASS-R1001000×10006869+162.24108.1
CLASS-R/rcl_09_100_09CLASS-R1001000×1000808060.35123.89
CLASS-R/rcl_09_100_10CLASS-R1001000×10007677+162.55103.18
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CLASS-R/rcl_10_020_04CLASS-R201000×10004486.987.03
CLASS-R/rcl_10_020_05CLASS-R201000×10004475.266.45
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CLASS-R/rcl_10_020_08CLASS-R201000×10003389.197.43
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CLASS-R/rcl_10_020_10CLASS-R201000×10003379.436.59
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CLASS-R/rcl_10_040_03CLASS-R401000×100056+181.7713.95
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CLASS-R/rcl_10_040_06CLASS-R401000×10005584.6419.31
CLASS-R/rcl_10_040_07CLASS-R401000×10007786.7717.17
CLASS-R/rcl_10_040_08CLASS-R401000×1000910+178.816.02
CLASS-R/rcl_10_040_09CLASS-R401000×10007785.1711.25
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CLASS-R/rcl_10_100_09CLASS-R1001000×10001314+192.5949.49
CLASS-R/rcl_10_100_10CLASS-R1001000×10001415+190.9257.59
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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
PERFECT2D/p_250x150_k3_n30_2PERFECT2D901750×105034+17549.68
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_1PERFECT2D161200×1200221004.19
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
PERFECT2D/p_300x300_k3_n8_2PERFECT2D241200×120034+1756.11
PERFECT2D/p_300x300_k3_n16_1PERFECT2D481200×120034+17518.53
PERFECT2D/p_300x300_k3_n16_2PERFECT2D481200×120034+17518.3
PERFECT2D/p_300x300_k3_n30_1PERFECT2D901200×120034+17546.08
PERFECT2D/p_300x300_k3_n30_2PERFECT2D901200×120034+17549.58
PERFECT2D/p_300x300_k5_n8_1PERFECT2D401200×120056+183.3311.55
PERFECT2D/p_300x300_k5_n8_2PERFECT2D401200×120056+183.3313.62
PERFECT2D/p_300x300_k5_n16_1PERFECT2D801200×120056+183.3331.67
PERFECT2D/p_300x300_k5_n16_2PERFECT2D801200×120056+183.3329.66
PERFECT2D/p_300x300_k5_n30_1PERFECT2D1501200×120056+183.3394.05
PERFECT2D/p_300x300_k5_n30_2PERFECT2D1501200×120056+183.3396.34
UNIF1D/u120_01UNIF1D1201050474798.757.75
UNIF1D/u120_02UNIF1D12010504849+197.655.49
UNIF1D/u120_03UNIF1D12010504849+196.754.99
UNIF1D/u120_04UNIF1D1201050525298.1711.44
UNIF1D/u120_05UNIF1D1201050515198.074.13
UNIF1D/u120_06UNIF1D12010505052+295.914.52
UNIF1D/u120_07UNIF1D12010505152+198.054.68
UNIF1D/u120_08UNIF1D12010504950+197.434.14
UNIF1D/u120_09UNIF1D12010505152+196.824.76
UNIF1D/u120_10UNIF1D1201050454598.434.42
UNIF1D/u250_01UNIF1D250105099101+297.919.47
UNIF1D/u250_02UNIF1D2501050102104+297.5318.79
UNIF1D/u250_03UNIF1D2501050959599.1619.77
UNIF1D/u250_04UNIF1D2501050102103+198.5222.85
UNIF1D/u250_05UNIF1D2501050104106+298.0919.32
UNIF1D/u250_06UNIF1D2501050101103+297.6119.05
UNIF1D/u250_07UNIF1D250105010010099.2516.68
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_02UNIF1D500105019619699.9480.92
UNIF1D/u500_03UNIF1D5001050204206+298.6379.14
UNIF1D/u500_04UNIF1D5001050196198+298.9579.26
UNIF1D/u500_05UNIF1D500105019919999.6778.27
UNIF1D/u500_06UNIF1D500105020420499.7279.14
UNIF1D/u500_07UNIF1D5001050202205+398.5378.48
UNIF1D/u500_08UNIF1D5001050200202+298.5979
UNIF1D/u500_09UNIF1D500105020020099.7474
UNIF1D/u500_10UNIF1D500105019719799.776.38
UNIF1D/u1000_01UNIF1D1000105040340399.96292.33
UNIF1D/u1000_02UNIF1D10001050398399+199.52309.11
UNIF1D/u1000_03UNIF1D1000105040140199.95303.68
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_08UNIF1D1000105039839899.85277.36
UNIF1D/u1000_09UNIF1D1000105039939999.98279.3
UNIF1D/u1000_10UNIF1D10001050403405+299.42271.44
TRIPLET1D/t60_01TRIPLET1D6010002021+195.247.12
TRIPLET1D/t60_02TRIPLET1D6010002021+195.240.87
TRIPLET1D/t60_03TRIPLET1D6010002021+195.240.89
TRIPLET1D/t60_04TRIPLET1D6010002021+195.240.84
TRIPLET1D/t60_05TRIPLET1D6010002021+195.241.14
TRIPLET1D/t60_06TRIPLET1D6010002021+195.240.92
TRIPLET1D/t60_07TRIPLET1D6010002021+195.240.82
TRIPLET1D/t60_08TRIPLET1D6010002021+195.240.82
TRIPLET1D/t60_09TRIPLET1D6010002021+195.240.82
TRIPLET1D/t60_10TRIPLET1D6010002021+195.240.82
TRIPLET1D/t120_01TRIPLET1D12010004041+197.562.92
TRIPLET1D/t120_02TRIPLET1D12010004041+197.563.01
TRIPLET1D/t120_03TRIPLET1D12010004041+197.562.96
TRIPLET1D/t120_04TRIPLET1D12010004041+197.563.32
TRIPLET1D/t120_05TRIPLET1D12010004041+197.563.23
TRIPLET1D/t120_06TRIPLET1D12010004041+197.562.88
TRIPLET1D/t120_07TRIPLET1D12010004041+197.563
TRIPLET1D/t120_08TRIPLET1D12010004041+197.562.9
TRIPLET1D/t120_09TRIPLET1D12010004041+197.563.34
TRIPLET1D/t120_10TRIPLET1D12010004041+197.562.91
TRIPLET1D/t249_01TRIPLET1D24910008386+396.5116.84
TRIPLET1D/t249_02TRIPLET1D24910008384+198.8111.79
TRIPLET1D/t249_03TRIPLET1D24910008385+297.6512.07
TRIPLET1D/t249_04TRIPLET1D24910008386+396.5118.21
TRIPLET1D/t249_05TRIPLET1D24910008385+297.6512.73
TRIPLET1D/t249_06TRIPLET1D24910008385+297.6512.29
TRIPLET1D/t249_07TRIPLET1D24910008385+297.6512.18
TRIPLET1D/t249_08TRIPLET1D24910008385+297.6512.11
TRIPLET1D/t249_09TRIPLET1D24910008385+297.6512.01
TRIPLET1D/t249_10TRIPLET1D24910008385+297.6511.76
TRIPLET1D/t501_01TRIPLET1D5011000167171+497.6653.07
TRIPLET1D/t501_02TRIPLET1D5011000167171+497.6646.74
TRIPLET1D/t501_03TRIPLET1D5011000167171+497.6646.6
TRIPLET1D/t501_04TRIPLET1D5011000167171+497.6651.66
TRIPLET1D/t501_05TRIPLET1D5011000167171+497.6655.78
TRIPLET1D/t501_06TRIPLET1D5011000167170+398.2455.08
TRIPLET1D/t501_07TRIPLET1D5011000167171+497.6652.44
TRIPLET1D/t501_08TRIPLET1D5011000167171+497.6646.9
TRIPLET1D/t501_09TRIPLET1D5011000167171+497.6646.52
TRIPLET1D/t501_10TRIPLET1D5011000167171+497.6654.43
RAND1D/r_50_100_0.1_0.7_1RAND1D5010002122+194.593.18
RAND1D/r_50_100_0.1_0.7_2RAND1D501000212196.571.62
RAND1D/r_50_100_0.1_0.7_3RAND1D5010002020971.49
RAND1D/r_50_100_0.2_0.8_1RAND1D501000282890.611.49
RAND1D/r_50_100_0.2_0.8_2RAND1D5010002626931.39
RAND1D/r_50_100_0.2_0.8_3RAND1D5010002324+194.631.4
RAND1D/r_50_150_0.1_0.7_1RAND1D501050202095.831.53
RAND1D/r_50_150_0.1_0.7_2RAND1D501050202095.631.39
RAND1D/r_50_150_0.1_0.7_3RAND1D5010502223+194.71.5
RAND1D/r_50_150_0.2_0.8_1RAND1D501050313180.691.63
RAND1D/r_50_150_0.2_0.8_2RAND1D501050303085.185.51
RAND1D/r_50_150_0.2_0.8_3RAND1D501050252595.761.23
RAND1D/r_50_1000_0.1_0.7_1RAND1D5010002122+193.10.68
RAND1D/r_50_1000_0.1_0.7_2RAND1D5010002021+194.890.63
RAND1D/r_50_1000_0.1_0.7_3RAND1D501000212196.710.67
RAND1D/r_50_1000_0.2_0.8_1RAND1D501000292988.750.71
RAND1D/r_50_1000_0.2_0.8_2RAND1D501000303089.930.71
RAND1D/r_50_1000_0.2_0.8_3RAND1D501000282891.310.64
RAND1D/r_200_100_0.1_0.7_1RAND1D20010007879+197.759.76
RAND1D/r_200_100_0.1_0.7_2RAND1D20010007879+198.6211.04
RAND1D/r_200_100_0.1_0.7_3RAND1D2001000828298.9911.08
RAND1D/r_200_100_0.2_0.8_1RAND1D200100010110198.1914.01
RAND1D/r_200_100_0.2_0.8_2RAND1D200100011011092.949.21
RAND1D/r_200_100_0.2_0.8_3RAND1D200100010810894.889.27
RAND1D/r_200_150_0.1_0.7_1RAND1D2001050828298.8510.62
RAND1D/r_200_150_0.1_0.7_2RAND1D20010507778+198.3610.73
RAND1D/r_200_150_0.1_0.7_3RAND1D20010508081+198.219.84
RAND1D/r_200_150_0.2_0.8_1RAND1D200105010010097.079.6
RAND1D/r_200_150_0.2_0.8_2RAND1D2001050101102+196.9314.27
RAND1D/r_200_150_0.2_0.8_3RAND1D200105010010098.069.41
RAND1D/r_200_1000_0.1_0.7_1RAND1D20010008485+198.489.5
RAND1D/r_200_1000_0.1_0.7_2RAND1D20010007677+198.029.56
RAND1D/r_200_1000_0.1_0.7_3RAND1D20010008081+197.859.03
RAND1D/r_200_1000_0.2_0.8_1RAND1D20010009899+198.158.85
RAND1D/r_200_1000_0.2_0.8_2RAND1D200100010610695.248.67
RAND1D/r_200_1000_0.2_0.8_3RAND1D200100010810894.29.4
RAND1D/r_500_100_0.1_0.7_1RAND1D5001000196197+199.3264.83
RAND1D/r_500_100_0.1_0.7_2RAND1D500100020420499.969.21
RAND1D/r_500_100_0.1_0.7_3RAND1D500100020020099.6970.26
RAND1D/r_500_100_0.2_0.8_1RAND1D5001000263264+196.4362.33
RAND1D/r_500_100_0.2_0.8_2RAND1D5001000249250+198.5462.99
RAND1D/r_500_100_0.2_0.8_3RAND1D500100025625697.5364.82
RAND1D/r_500_150_0.1_0.7_1RAND1D500105020220299.8971.84
RAND1D/r_500_150_0.1_0.7_2RAND1D500105020420499.6573.46
RAND1D/r_500_150_0.1_0.7_3RAND1D500105019219299.7575.24
RAND1D/r_500_150_0.2_0.8_1RAND1D500105026126196.7264.54
RAND1D/r_500_150_0.2_0.8_2RAND1D500105025025098.8764.97
RAND1D/r_500_150_0.2_0.8_3RAND1D500105027027095.2663.52
RAND1D/r_500_1000_0.1_0.7_1RAND1D5001000194196+298.6659.23
RAND1D/r_500_1000_0.1_0.7_2RAND1D5001000198201+398.4462.32
RAND1D/r_500_1000_0.1_0.7_3RAND1D5001000199200+199.0957.15
RAND1D/r_500_1000_0.2_0.8_1RAND1D5001000260261+196.9264.69
RAND1D/r_500_1000_0.2_0.8_2RAND1D5001000261262+196.262.77
RAND1D/r_500_1000_0.2_0.8_3RAND1D5001000259262+396.3258.46

Anidado de forma real

Los números de arriba corresponden al empaquetador guillotina, que corta rectángulos. El anidado de forma real es un motor distinto para un problema distinto: empaqueta POLÍGONOS ARBITRARIOS — para láser, plasma y chorro de agua — dejando que las piezas encajen en los huecos cóncavos de las demás. En un trabajo representativo de 272 piezas usa 6 tableros, mientras que esas mismas piezas pasadas a un empaquetador rectangular por su caja envolvente necesitan 9 — un tercio menos de material, solo por la forma.

6
tableros · forma real
9
tableros · caja envolvente
4
tableros · mínimo teórico

Por qué informamos del número de tableros, no de la densidad

Un empaquetador por caja envolvente cuenta el aire de las muescas dentro del rectángulo de cada pieza como si fuera sólido, así que su "aprovechamiento" resulta más alto para un resultado peor — el plan de 9 tableros parece más denso que el de 6. La única métrica honesta y comparable entre sí es el número de tableros que necesitan realmente las mismas piezas físicas. Ese es el número de arriba.

Una cota inferior teórica para este trabajo es de 4 tableros (el área total de las piezas dividida por un tablero). El motor actual alcanza 6; la diferencia de densidad hasta 4 es adonde apunta la próxima iteración del motor.

Anidado de forma real en la 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 →

Datos

La medición completa, no un resumen de ella.

  • results.jsonl — Todos los resultados — cada trabajo, perfil, motor y orientación
  • summary.json — Agregados — los números de esta página
  • table.json — Esta tabla en JSON
  • corpus.json — Las instancias de entrada generadas — los problemas reales que resolvió el ejecutor. Los conjuntos académicos canónicos se obtienen y se verifican por hash en lugar de copiarse aquí, porque su fuente no concede la redistribución.

Para reproducirlo: clone el repositorio, ejecute npm run bench:fetch para descargar las instancias canónicas y verificar sus hashes, y luego npm run bench. El corpus generado no necesita descarga.

Los archivos de arriba se publican bajo CC BY 4.0 — reutilícelos, uso comercial incluido, con atribución a CutOptim. Eso cubre nuestra propia medición y el corpus generado. Las instancias académicas canónicas no son nuestras para licenciarlas y no se distribuyen desde aquí.

Ejecute su propio trabajo

El único número que importa es el que produce su propia lista de piezas.