红帽全球峰会3.13. vehicle 路由
使用一组电话，获取每个客户的对象并将其带入耗尽。每个 vehicle 都可以为多个客户提供服务，但它有有限的容量。
除了基本问题单(CVRP)外，还有一个带有时间窗(CVRPTW)的变体。
硬限制：
- vehicle 容量： vehicle 无法执行更多项目，然后其容量。
时间窗（只在 CVRPTW 中）：
- 轮转时间：从一个位置传输到另一个地方需要时间。
- 客户服务持续时间： vehicle 必须在服务持续时间内保持给客户。
- 客户就绪时间： vehicle 可在客户就绪时间之前到达，但必须等到为工作前的时间才会等待。
- 客户到期时间：在客户到期前必须及时到达时间。
软限制：
- 总距离：最小化所有 vehicles 的距离驱动的总距离(fuel 消耗)。
带容量的载体路由问题(CVRP)及其时间同步变体(CVRPTW)由 网络和早期优化(NEO) VRP 网站定义。
图 3.8. 价值
问题大小
CVRP 实例（没有时间窗）：
belgium-n50-k10 has 1 depots, 10 vehicles and 49 customers with a search space of 10^74. belgium-n100-k10 has 1 depots, 10 vehicles and 99 customers with a search space of 10^170. belgium-n500-k20 has 1 depots, 20 vehicles and 499 customers with a search space of 10^1168. belgium-n1000-k20 has 1 depots, 20 vehicles and 999 customers with a search space of 10^2607. belgium-n2750-k55 has 1 depots, 55 vehicles and 2749 customers with a search space of 10^8380. belgium-road-km-n50-k10 has 1 depots, 10 vehicles and 49 customers with a search space of 10^74. belgium-road-km-n100-k10 has 1 depots, 10 vehicles and 99 customers with a search space of 10^170. belgium-road-km-n500-k20 has 1 depots, 20 vehicles and 499 customers with a search space of 10^1168. belgium-road-km-n1000-k20 has 1 depots, 20 vehicles and 999 customers with a search space of 10^2607. belgium-road-km-n2750-k55 has 1 depots, 55 vehicles and 2749 customers with a search space of 10^8380. belgium-road-time-n50-k10 has 1 depots, 10 vehicles and 49 customers with a search space of 10^74. belgium-road-time-n100-k10 has 1 depots, 10 vehicles and 99 customers with a search space of 10^170. belgium-road-time-n500-k20 has 1 depots, 20 vehicles and 499 customers with a search space of 10^1168. belgium-road-time-n1000-k20 has 1 depots, 20 vehicles and 999 customers with a search space of 10^2607. belgium-road-time-n2750-k55 has 1 depots, 55 vehicles and 2749 customers with a search space of 10^8380. belgium-d2-n50-k10 has 2 depots, 10 vehicles and 48 customers with a search space of 10^74. belgium-d3-n100-k10 has 3 depots, 10 vehicles and 97 customers with a search space of 10^170. belgium-d5-n500-k20 has 5 depots, 20 vehicles and 495 customers with a search space of 10^1168. belgium-d8-n1000-k20 has 8 depots, 20 vehicles and 992 customers with a search space of 10^2607. belgium-d10-n2750-k55 has 10 depots, 55 vehicles and 2740 customers with a search space of 10^8380. A-n32-k5 has 1 depots, 5 vehicles and 31 customers with a search space of 10^40. A-n33-k5 has 1 depots, 5 vehicles and 32 customers with a search space of 10^41. A-n33-k6 has 1 depots, 6 vehicles and 32 customers with a search space of 10^42. A-n34-k5 has 1 depots, 5 vehicles and 33 customers with a search space of 10^43. A-n36-k5 has 1 depots, 5 vehicles and 35 customers with a search space of 10^46. A-n37-k5 has 1 depots, 5 vehicles and 36 customers with a search space of 10^48. A-n37-k6 has 1 depots, 6 vehicles and 36 customers with a search space of 10^49. A-n38-k5 has 1 depots, 5 vehicles and 37 customers with a search space of 10^49. A-n39-k5 has 1 depots, 5 vehicles and 38 customers with a search space of 10^51. A-n39-k6 has 1 depots, 6 vehicles and 38 customers with a search space of 10^52. A-n44-k7 has 1 depots, 7 vehicles and 43 customers with a search space of 10^61. A-n45-k6 has 1 depots, 6 vehicles and 44 customers with a search space of 10^62. A-n45-k7 has 1 depots, 7 vehicles and 44 customers with a search space of 10^63. A-n46-k7 has 1 depots, 7 vehicles and 45 customers with a search space of 10^65. A-n48-k7 has 1 depots, 7 vehicles and 47 customers with a search space of 10^68. A-n53-k7 has 1 depots, 7 vehicles and 52 customers with a search space of 10^77. A-n54-k7 has 1 depots, 7 vehicles and 53 customers with a search space of 10^79. A-n55-k9 has 1 depots, 9 vehicles and 54 customers with a search space of 10^82. A-n60-k9 has 1 depots, 9 vehicles and 59 customers with a search space of 10^91. A-n61-k9 has 1 depots, 9 vehicles and 60 customers with a search space of 10^93. A-n62-k8 has 1 depots, 8 vehicles and 61 customers with a search space of 10^94. A-n63-k9 has 1 depots, 9 vehicles and 62 customers with a search space of 10^97. A-n63-k10 has 1 depots, 10 vehicles and 62 customers with a search space of 10^98. A-n64-k9 has 1 depots, 9 vehicles and 63 customers with a search space of 10^99. A-n65-k9 has 1 depots, 9 vehicles and 64 customers with a search space of 10^101. A-n69-k9 has 1 depots, 9 vehicles and 68 customers with a search space of 10^108. A-n80-k10 has 1 depots, 10 vehicles and 79 customers with a search space of 10^130. F-n45-k4 has 1 depots, 4 vehicles and 44 customers with a search space of 10^60. F-n72-k4 has 1 depots, 4 vehicles and 71 customers with a search space of 10^108. F-n135-k7 has 1 depots, 7 vehicles and 134 customers with a search space of 10^240.
belgium-n50-k10 has 1 depots, 10 vehicles and 49 customers with a search space of 10^74.
belgium-n100-k10 has 1 depots, 10 vehicles and 99 customers with a search space of 10^170.
belgium-n500-k20 has 1 depots, 20 vehicles and 499 customers with a search space of 10^1168.
belgium-n1000-k20 has 1 depots, 20 vehicles and 999 customers with a search space of 10^2607.
belgium-n2750-k55 has 1 depots, 55 vehicles and 2749 customers with a search space of 10^8380.
belgium-road-km-n50-k10 has 1 depots, 10 vehicles and 49 customers with a search space of 10^74.
belgium-road-km-n100-k10 has 1 depots, 10 vehicles and 99 customers with a search space of 10^170.
belgium-road-km-n500-k20 has 1 depots, 20 vehicles and 499 customers with a search space of 10^1168.
belgium-road-km-n1000-k20 has 1 depots, 20 vehicles and 999 customers with a search space of 10^2607.
belgium-road-km-n2750-k55 has 1 depots, 55 vehicles and 2749 customers with a search space of 10^8380.
belgium-road-time-n50-k10 has 1 depots, 10 vehicles and 49 customers with a search space of 10^74.
belgium-road-time-n100-k10 has 1 depots, 10 vehicles and 99 customers with a search space of 10^170.
belgium-road-time-n500-k20 has 1 depots, 20 vehicles and 499 customers with a search space of 10^1168.
belgium-road-time-n1000-k20 has 1 depots, 20 vehicles and 999 customers with a search space of 10^2607.
belgium-road-time-n2750-k55 has 1 depots, 55 vehicles and 2749 customers with a search space of 10^8380.
belgium-d2-n50-k10 has 2 depots, 10 vehicles and 48 customers with a search space of 10^74.
belgium-d3-n100-k10 has 3 depots, 10 vehicles and 97 customers with a search space of 10^170.
belgium-d5-n500-k20 has 5 depots, 20 vehicles and 495 customers with a search space of 10^1168.
belgium-d8-n1000-k20 has 8 depots, 20 vehicles and 992 customers with a search space of 10^2607.
belgium-d10-n2750-k55 has 10 depots, 55 vehicles and 2740 customers with a search space of 10^8380.
A-n32-k5 has 1 depots, 5 vehicles and 31 customers with a search space of 10^40.
A-n33-k5 has 1 depots, 5 vehicles and 32 customers with a search space of 10^41.
A-n33-k6 has 1 depots, 6 vehicles and 32 customers with a search space of 10^42.
A-n34-k5 has 1 depots, 5 vehicles and 33 customers with a search space of 10^43.
A-n36-k5 has 1 depots, 5 vehicles and 35 customers with a search space of 10^46.
A-n37-k5 has 1 depots, 5 vehicles and 36 customers with a search space of 10^48.
A-n37-k6 has 1 depots, 6 vehicles and 36 customers with a search space of 10^49.
A-n38-k5 has 1 depots, 5 vehicles and 37 customers with a search space of 10^49.
A-n39-k5 has 1 depots, 5 vehicles and 38 customers with a search space of 10^51.
A-n39-k6 has 1 depots, 6 vehicles and 38 customers with a search space of 10^52.
A-n44-k7 has 1 depots, 7 vehicles and 43 customers with a search space of 10^61.
A-n45-k6 has 1 depots, 6 vehicles and 44 customers with a search space of 10^62.
A-n45-k7 has 1 depots, 7 vehicles and 44 customers with a search space of 10^63.
A-n46-k7 has 1 depots, 7 vehicles and 45 customers with a search space of 10^65.
A-n48-k7 has 1 depots, 7 vehicles and 47 customers with a search space of 10^68.
A-n53-k7 has 1 depots, 7 vehicles and 52 customers with a search space of 10^77.
A-n54-k7 has 1 depots, 7 vehicles and 53 customers with a search space of 10^79.
A-n55-k9 has 1 depots, 9 vehicles and 54 customers with a search space of 10^82.
A-n60-k9 has 1 depots, 9 vehicles and 59 customers with a search space of 10^91.
A-n61-k9 has 1 depots, 9 vehicles and 60 customers with a search space of 10^93.
A-n62-k8 has 1 depots, 8 vehicles and 61 customers with a search space of 10^94.
A-n63-k9 has 1 depots, 9 vehicles and 62 customers with a search space of 10^97.
A-n63-k10 has 1 depots, 10 vehicles and 62 customers with a search space of 10^98.
A-n64-k9 has 1 depots, 9 vehicles and 63 customers with a search space of 10^99.
A-n65-k9 has 1 depots, 9 vehicles and 64 customers with a search space of 10^101.
A-n69-k9 has 1 depots, 9 vehicles and 68 customers with a search space of 10^108.
A-n80-k10 has 1 depots, 10 vehicles and 79 customers with a search space of 10^130.
F-n45-k4 has 1 depots, 4 vehicles and 44 customers with a search space of 10^60.
F-n72-k4 has 1 depots, 4 vehicles and 71 customers with a search space of 10^108.
F-n135-k7 has 1 depots, 7 vehicles and 134 customers with a search space of 10^240.CVRPTW 实例（使用时间窗）：
belgium-tw-d2-n50-k10 has 2 depots, 10 vehicles and 48 customers with a search space of 10^74. belgium-tw-d3-n100-k10 has 3 depots, 10 vehicles and 97 customers with a search space of 10^170. belgium-tw-d5-n500-k20 has 5 depots, 20 vehicles and 495 customers with a search space of 10^1168. belgium-tw-d8-n1000-k20 has 8 depots, 20 vehicles and 992 customers with a search space of 10^2607. belgium-tw-d10-n2750-k55 has 10 depots, 55 vehicles and 2740 customers with a search space of 10^8380. belgium-tw-n50-k10 has 1 depots, 10 vehicles and 49 customers with a search space of 10^74. belgium-tw-n100-k10 has 1 depots, 10 vehicles and 99 customers with a search space of 10^170. belgium-tw-n500-k20 has 1 depots, 20 vehicles and 499 customers with a search space of 10^1168. belgium-tw-n1000-k20 has 1 depots, 20 vehicles and 999 customers with a search space of 10^2607. belgium-tw-n2750-k55 has 1 depots, 55 vehicles and 2749 customers with a search space of 10^8380. Solomon_025_C101 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40. Solomon_025_C201 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40. Solomon_025_R101 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40. Solomon_025_R201 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40. Solomon_025_RC101 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40. Solomon_025_RC201 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40. Solomon_100_C101 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185. Solomon_100_C201 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185. Solomon_100_R101 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185. Solomon_100_R201 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185. Solomon_100_RC101 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185. Solomon_100_RC201 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185. Homberger_0200_C1_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429. Homberger_0200_C2_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429. Homberger_0200_R1_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429. Homberger_0200_R2_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429. Homberger_0200_RC1_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429. Homberger_0200_RC2_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429. Homberger_0400_C1_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978. Homberger_0400_C2_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978. Homberger_0400_R1_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978. Homberger_0400_R2_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978. Homberger_0400_RC1_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978. Homberger_0400_RC2_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978. Homberger_0600_C1_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571. Homberger_0600_C2_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571. Homberger_0600_R1_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571. Homberger_0600_R2_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571. Homberger_0600_RC1_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571. Homberger_0600_RC2_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571. Homberger_0800_C1_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195. Homberger_0800_C2_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195. Homberger_0800_R1_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195. Homberger_0800_R2_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195. Homberger_0800_RC1_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195. Homberger_0800_RC2_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195. Homberger_1000_C110_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840. Homberger_1000_C210_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840. Homberger_1000_R110_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840. Homberger_1000_R210_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840. Homberger_1000_RC110_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840. Homberger_1000_RC210_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840.
belgium-tw-d2-n50-k10 has 2 depots, 10 vehicles and 48 customers with a search space of 10^74.
belgium-tw-d3-n100-k10 has 3 depots, 10 vehicles and 97 customers with a search space of 10^170.
belgium-tw-d5-n500-k20 has 5 depots, 20 vehicles and 495 customers with a search space of 10^1168.
belgium-tw-d8-n1000-k20 has 8 depots, 20 vehicles and 992 customers with a search space of 10^2607.
belgium-tw-d10-n2750-k55 has 10 depots, 55 vehicles and 2740 customers with a search space of 10^8380.
belgium-tw-n50-k10 has 1 depots, 10 vehicles and 49 customers with a search space of 10^74.
belgium-tw-n100-k10 has 1 depots, 10 vehicles and 99 customers with a search space of 10^170.
belgium-tw-n500-k20 has 1 depots, 20 vehicles and 499 customers with a search space of 10^1168.
belgium-tw-n1000-k20 has 1 depots, 20 vehicles and 999 customers with a search space of 10^2607.
belgium-tw-n2750-k55 has 1 depots, 55 vehicles and 2749 customers with a search space of 10^8380.
Solomon_025_C101 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40.
Solomon_025_C201 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40.
Solomon_025_R101 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40.
Solomon_025_R201 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40.
Solomon_025_RC101 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40.
Solomon_025_RC201 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40.
Solomon_100_C101 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185.
Solomon_100_C201 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185.
Solomon_100_R101 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185.
Solomon_100_R201 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185.
Solomon_100_RC101 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185.
Solomon_100_RC201 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185.
Homberger_0200_C1_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429.
Homberger_0200_C2_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429.
Homberger_0200_R1_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429.
Homberger_0200_R2_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429.
Homberger_0200_RC1_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429.
Homberger_0200_RC2_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429.
Homberger_0400_C1_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978.
Homberger_0400_C2_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978.
Homberger_0400_R1_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978.
Homberger_0400_R2_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978.
Homberger_0400_RC1_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978.
Homberger_0400_RC2_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978.
Homberger_0600_C1_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571.
Homberger_0600_C2_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571.
Homberger_0600_R1_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571.
Homberger_0600_R2_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571.
Homberger_0600_RC1_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571.
Homberger_0600_RC2_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571.
Homberger_0800_C1_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195.
Homberger_0800_C2_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195.
Homberger_0800_R1_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195.
Homberger_0800_R2_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195.
Homberger_0800_RC1_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195.
Homberger_0800_RC2_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195.
Homberger_1000_C110_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840.
Homberger_1000_C210_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840.
Homberger_1000_R110_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840.
Homberger_1000_R210_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840.
Homberger_1000_RC110_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840.
Homberger_1000_RC210_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840.3.13.1. Vehicle 路由的域模型
复制链接链接已复制到粘贴板!
带有时间窗域模型的 vehicle 路由大量使用 shadow 变量功能。这允许它更自然地表达限制，因为 arrivalTime 和 departureTime 等属性直接在域模型中可用。
临时区分无线差异
在真实世界中，vehicles 不能从位置到位置跟随行：它们必须使用 roads 和 highways。从一个角度来说，这很重要：
对于优化算法，只要可以查找两个点之间的距离（最好是预先计算）。road 成本甚至不需要是一个距离。它还有可能是大量时间、经济的成本或加权功能。一些技术可用于预先计算 road 成本，如 GraphHopper (embeddable, offline Java engine), Open MapQuest (web service)和 Google Maps Client API (web service)。
另外，还有一些技术来呈现它，如 开发人员的 Leaflet 和 Google Map。
甚至可以使用 GraphHopper 或 Google Map Directions 呈现实际 road 路由，但由于路由对高路重叠，看不到顺序：
请特别注意两个点之间的 road 成本与 OptaPlanner 中使用的优化标准相同。例如，GraphHopper 默认返回最快的路由，而不是最短的路由。不要使用最快速的 GPS 路由的 km （或 miles）距离来优化 OptaPlanner 中最短的往返：这会导致子优化解决方案，如下所示：
与流行不同，大多数用户都不希望使用最短的路由：他们希望使用最快的路由。它们更喜欢通常高路。它们更喜欢在 dirt roads 上正常的 roads。在现实环境中，最快速且最短的路由很少相同。
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