建議 - 應用時窗離散策略與可回溯式門檻接受法求解VRPBTW問題之研究

本研究經過實驗測試的過程之後，提出以下幾點建議以供未來可能的相關研究參考：

1. 本研究將有時間窗的問題作離散化，消除其時間窗限制，並採用問題規模精簡策略縮小問題規模，對於原作業點時間窗寬度較小且均勻的問題，求解效

果不錯，未來可應用於求解相同型態之問題。

2. 在離散時間間隔δ 值的使用上，基於電腦資料存取空間之限制，對於時間窗寬度較大的問題無法進行測試。未來可藉由資料結構上的改進或電腦運算能力的提升，使用較小的δ 值進行離散化求解。

3. 經過本研究之測試後，發現可回溯式門檻接受法為一相當有效的巨集啟發式方法，未來可直接應用於求解VRPB 問題。

參考文獻

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附錄本研究最佳結果之成本及路線圖

例題編號：BHR101A

文獻已知最佳解之車輛數／總旅行距離：22 / 1818.86 本研究之車輛數／總旅行距離：22 / 1837.27

路線編號經過節點順序

1 0, 5, 83, 61, 84, 0

2 0, 39, 23, 67, 55, 4, 25, 0 3 0, 28, 76, 0

4 0, 31, 30, 51, 50, 0

5 0, 92, 42, 15, 87, 57, 97, 0 6 0, 59, 99, 85, 37, 91, 100, 0 7 0, 14, 44, 38, 43, 13, 0 8 0, 65, 81, 0

9 0, 36, 47, 19, 46, 60, 89, 0 10 0, 95, 98, 16, 86, 17, 93, 0 11 0, 45, 82, 18, 6, 96, 0 12 0, 12, 79, 3, 68, 0 13 0, 63, 64, 49, 48, 0 14 0, 2, 8, 0

15 0, 40, 94, 26, 0

16 0, 21, 73, 41, 56, 74, 58, 0 17 0, 33, 71, 9, 66, 1, 0 18 0, 29, 53, 0

19 0, 52, 88, 7, 10, 70, 0 20 0, 72, 75, 22, 54, 24, 80, 0 21 0, 27, 69, 78, 34, 35, 77, 0 22 0, 62, 11, 90, 20, 32, 0

例題編號：BHR101B 文獻已知最佳解之車輛數／總旅行距離：23 / 1959.52 本研究之車輛數／總旅行距離：23 / 2028.75

路線編號經過節點順序

1 0, 42, 15, 40, 0

2 0, 69, 30, 51, 20, 32, 0 3 0, 95, 98, 99, 94, 26, 0 4 0, 14, 38, 43, 91, 100, 0 5 0, 36, 64, 49, 48, 0 6 0, 47, 11, 90, 66, 1, 0 7 0, 72, 16, 96, 0

8 0, 65, 81, 50, 0 9 0, 52, 88, 6, 0

10 0, 87, 57, 97, 13, 58, 0 11 0, 5, 86, 37, 60, 89, 0 12 0, 12, 76, 79, 54, 0 13 0, 92, 2, 61, 84, 0 14 0, 27, 31, 18, 10, 0 15 0, 59, 83, 44, 85, 93, 0 16 0, 45, 82, 7, 8, 0 17 0, 28, 78, 34, 35, 70, 0 18 0, 39, 75, 22, 74, 0 19 0, 63, 62, 19, 46, 17, 0 20 0, 29, 53, 0

21 0, 21, 73, 41, 56, 4, 25, 0 22 0, 23, 67, 55, 24, 80, 0 23 0, 33, 71, 9, 3, 68, 77, 0

例題編號：BHR101C 文獻已知最佳解之車輛數／總旅行距離：24 / 1909.84 本研究之車輛數／總旅行距離：24 / 1950.46

路線編號經過節點順序

1 0, 42, 15, 43, 13, 0 2 0, 45, 82, 7, 46, 60, 89, 0 3 0, 31, 30, 10, 32, 0 4 0, 14, 38, 37, 91, 100, 0 5 0, 95, 98, 99, 94, 0 6 0, 5, 83, 16, 85, 97, 0 7 0, 59, 44, 86, 17, 93, 0 8 0, 21, 22, 68, 24, 80, 0 9 0, 11, 19, 49, 48, 0 10 0, 92, 2, 61, 84, 96, 0 11 0, 36, 47, 8, 0

12 0, 63, 64, 90, 20, 1, 0 13 0, 39, 23, 67, 55, 25, 0 14 0, 27, 69, 76, 26, 0 15 0, 41, 56, 4, 0 16 0, 87, 57, 58, 0 17 0, 52, 88, 6, 0

18 0, 28, 29, 79, 3, 54, 0 19 0, 33, 71, 78, 34, 35, 77, 0 20 0, 72, 75, 73, 74, 0

21 0, 65, 81, 50, 0 22 0, 51, 9, 66, 70, 0 23 0, 62, 18, 0 24 0, 12, 40, 53, 0

例題編號：BHR102A 文獻已知最佳解之車輛數／總旅行距離：19 / 1653.19 本研究之車輛數／總旅行距離：20 / 1664.19

路線編號經過節點順序

1 0, 18, 46, 83, 60, 0

2 0, 14, 44, 38, 43, 100, 95, 0 3 0, 63, 11, 90, 20, 32, 0 4 0, 36, 64, 49, 48, 0

5 0, 92, 37, 98, 59, 99, 6, 94, 97, 13, 0 6 0, 27, 69, 51, 9, 66, 70, 0

7 0, 45, 5, 61, 84, 89, 0 8 0, 28, 76, 0

9 0, 1, 30, 79, 68, 77, 0 10 0, 21, 39, 23, 67, 55, 25, 0 11 0, 73, 22, 75, 56, 4, 0 12 0, 87, 57, 2, 0

13 0, 52, 7, 62, 88, 10, 31, 0 14 0, 96, 85, 91, 16, 86, 17, 93, 0 15 0, 82, 47, 19, 8, 0

16 0, 40, 26, 54, 24, 80, 12, 0 17 0, 50, 33, 71, 78, 34, 35, 3, 0 18 0, 65, 81, 0

19 0, 42, 15, 41, 74, 72, 58, 0 20 0, 29, 53, 0

例題編號：BHR102B 文獻已知最佳解之車輛數／總旅行距離：21 / 1764.3 本研究之車輛數／總旅行距離：22 / 1775.79

路線編號經過節點順序

1 0, 28, 29, 79, 54, 0 2 0, 3, 78, 34, 35, 77, 0

3 0, 21, 73, 22, 75, 56, 74, 72, 2, 0 4 0, 92, 85, 16, 93, 96, 0

5 0, 26, 39, 23, 67, 55, 4, 25, 0 6 0, 69, 30, 51, 20, 32, 31, 0 7 0, 41, 68, 24, 80, 12, 0 8 0, 65, 81, 50, 0

9 0, 63, 11, 19, 46, 60, 89, 0 10 0, 61, 84, 0

11 0, 14, 38, 43, 100, 37, 0 12 0, 52, 7, 62, 88, 90, 10, 0 13 0, 36, 64, 49, 48, 0 14 0, 45, 47, 82, 8, 83, 0 15 0, 95, 98, 91, 44, 59, 0 16 0, 18, 0

17 0, 87, 57, 97, 13, 58, 0 18 0, 99, 6, 0

19 0, 33, 71, 9, 66, 70, 1, 0 20 0, 27, 76, 53, 0

21 0, 94, 86, 17, 5, 0 22 0, 42, 15, 40, 0

例題編號：BHR102C 文獻已知最佳解之車輛數／總旅行距離：21 / 1745.7 本研究之車輛數／總旅行距離：22 / 1786.19

路線編號經過節點順序

1 0, 41, 56, 4, 58, 0 2 0, 22, 68, 24, 80, 12, 0 3 0, 37, 91, 44, 43, 2, 0 4 0, 36, 64, 49, 82, 0 5 0, 42, 15, 40, 0

6 0, 98, 16, 86, 85, 93, 59, 0 7 0, 63, 11, 19, 46, 60, 89, 0 8 0, 94, 99, 6, 0

9 0, 52, 7, 62, 18, 0

10 0, 92, 61, 84, 17, 5, 96, 0 11 0, 27, 69, 30, 10, 31, 0 12 0, 28, 29, 79, 3, 54, 0 13 0, 33, 71, 78, 34, 35,77, 0 14 0, 21, 73, 74, 75, 72, 0 15 0, 45, 47, 48, 8, 83, 0 16 0, 39, 23, 67, 5, 25, 26, 0 17 0, 65, 81, 50, 0

18 0, 88, 90, 20, 32, 0 19 0, 14, 38, 100, 95, 0 20 0, 1, 51, 9, 66,70, 0 21 0, 87, 57, 97, 13, 0 22 0, 76, 53, 0

例題編號：BHR103A 文獻已知最佳解之車輛數／總旅行距離：15 / 1371.6 本研究之車輛數／總旅行距離：16 / 1410.29

路線編號經過節點順序

1 0, 50, 33, 78, 34, 35, 3, 77, 28, 0 2 0, 60, 45, 46, 8, 0

3 0, 97, 42, 15, 41, 74, 21, 2, 0 4 0, 76, 53, 0

5 0, 96, 99, 6, 5, 17, 83, 1, 0

6 0, 92, 91, 44, 38, 86, 16, 61, 85, 93, 0 7 0, 27, 69, 79, 68, 80, 12, 0

8 0, 94, 95, 59, 98, 37, 87, 13, 58, 0 9 0, 1, 51, 30, 9, 66, 20, 70, 0 10 0, 82, 7, 88, 84, 89, 0

11 0, 73, 72, 22, 75, 56, 4, 25, 54, 0 12 0, 26, 39, 23, 67, 55, 24, 29, 0 13 0, 52, 31, 62, 11, 10, 63, 90, 32, 0 14 0, 36, 64, 49, 19, 47, 48, 0

15 0, 40, 57, 43, 14, 100, 0 16 0, 71, 65, 81, 0

例題編號：BHR103B 文獻已知最佳解之車輛數／總旅行距離：15 / 1390.33 本研究之車輛數／總旅行距離：15 / 1511.17

路線編號經過節點順序

1 0, 36, 64, 49, 47, 46, 48, 0

2 0, 21, 39, 23, 67, 55, 24, 80, 28, 0 3 0, 98, 86, 38, 14, 91, 17, 100, 37, 0 4 0, 27, 76, 53, 0

5 0, 94, 95, 97, 87, 13, 58, 0 6 0, 42, 15, 40, 72, 74, 2, 0 7 0, 1, 33, 34, 78, 35, 20, 0 8 0, 52, 69, 30, 9, 66, 51, 70, 0 9 0, 92, 16, 44, 61, 84, 96, 0 10 0, 82, 7, 88, 8, 83, 18, 89, 0 11 0, 57, 41, 43, 85, 93, 59, 0

12 0, 60, 45, 5, 99, 6, 68, 3, 77, 50, 0 13 0, 73, 22, 75, 56, 4, 25, 26, 0 14 0, 19, 62, 11, 63, 90, 10, 32, 31, 0 15 0, 71, 65, 79, 81, 29, 54, 12, 0

例題編號：BHR103C 文獻已知最佳解之車輛數／總旅行距離：16 / 1486.56 本研究之車輛數／總旅行距離：17 / 1544.19

路線編號經過節點順序

1 0, 62, 8, 17, 83, 18, 0 2 0, 1, 51, 9, 35, 77, 28, 0 3 0, 76, 53, 0

4 0, 60, 45, 99, 6, 96, 5, 89, 0 5 0, 33, 34, 78, 24, 68, 80, 12, 0 6 0, 36, 64, 49, 47, 48, 0

7 0, 71, 65, 79, 29, 3, 81, 50, 0 8 0, 21, 22, 75, 74, 72, 73, 0 9 0, 27, 69, 30, 32, 10, 31, 0 10 0, 88, 7, 46, 82, 52, 0 11 0, 87, 98, 91, 100, 37, 0 12 0, 19, 11, 63, 90, 66, 20, 70, 0 13 0, 95, 97, 15, 40, 26, 55, 25, 54, 0 14 0, 57, 41, 2, 13, 0

15 0, 92, 86, 44, 84, 61, 16, 85, 93, 59, 0 16 0, 94, 42, 38, 14, 43, 0

17 0, 39, 23, 67, 56, 4, 58, 0

例題編號：BHR104A 文獻已知最佳解之車輛數／總旅行距離：11 / 1084.17 本研究之車輛數／總旅行距離：13 / 1259.03

路線編號經過節點順序

1 0, 27, 1, 50, 33, 79, 78, 34, 35, 71, 51, 0 2 0, 69, 60, 84, 89, 0

3 0, 92, 42, 87, 13, 58, 0

4 0, 52, 7, 62, 49, 64, 63, 90, 32, 0

5 0, 57, 43, 15, 41, 22, 75, 74, 72, 21, 40, 0 6 0, 95, 96, 59, 93, 99, 61, 16, 86, 91, 100, 37, 0 7 0, 54, 29, 76, 53, 2, 0

8 0, 6, 85, 44, 38, 14, 98, 97, 94, 0 9 0, 73, 56, 23, 67, 39, 4, 77, 28, 0 10 0, 12, 80, 68, 3, 24, 55, 25, 26, 0

11 0, 31, 88, 10, 11, 19, 36, 47, 46, 82, 18, 0 12 0, 70, 30, 20, 66, 9, 65, 81, 0

13 0, 5, 17, 45, 83, 8, 48, 0

例題編號：BHR104B 文獻已知最佳解之車輛數／總旅行距離：11 / 1154.84 本研究之車輛數／總旅行距離：13 / 1285.49

路線編號經過節點順序

1 0, 73, 22, 41, 57, 87, 42, 97, 13, 58, 0 2 0, 45, 46, 19, 90, 63, 32, 10, 31, 0 3 0, 43, 15, 53, 2, 74, 72, 40, 0 4 0, 94, 6, 60, 5, 99, 98, 37, 59, 96, 0 5 0, 17, 86, 38, 14, 91, 100, 95, 0 6 0, 69, 76, 79, 81, 29, 12, 0 7 0, 33, 3, 68, 80, 24, 55, 25, 54, 0 8 0, 21, 75, 23, 67, 39, 4, 56, 26, 0 9 0, 52, 7, 82, 48, 8, 83, 89, 0 10 0, 92, 44, 84, 61, 16, 85, 93, 0 11 0, 88, 62, 11, 64, 49, 36, 47, 18, 0 12 0, 1, 70, 9, 35, 34, 78, 77, 28, 0 13 0, 30, 51, 20, 66, 71, 65, 50, 27, 0

例題編號：BHR104C 文獻已知最佳解之車輛數／總旅行距離：11 / 1191.38 本研究之車輛數／總旅行距離：13 / 1297.26

路線編號經過節點順序

1 0, 6, 99, 84, 17, 5, 83, 89, 0 2 0, 43, 15, 53, 72, 74, 75, 73, 40, 0 3 0, 69, 76, 79, 3, 81, 50, 12, 0 4 0, 1, 51, 33, 9, 35, 34, 78, 77, 28, 0 5 0, 7, 62, 48, 8, 47, 10, 31, 27, 0 6 0, 92, 44, 16, 61, 85, 93, 96, 0 7 0, 57, 42, 14, 38, 86, 91, 100, 59, 0 8 0, 41, 22, 23, 67, 39, 56, 4, 21, 58, 0 9 0, 60, 45, 46, 36, 49, 19, 82, 18, 0 10 0, 94, 95, 37, 98, 87, 97, 2, 13, 0 11 0, 64, 11, 63, 90, 32, 30, 0 12 0, 52, 88, 70, 20, 71, 66, 65, 0 13 0, 68, 80, 24, 29, 54, 55, 25, 26, 0

例題編號：BHR105A 文獻已知最佳解之車輛數／總旅行距離：15 / 1561.28 本研究之車輛數／總旅行距離：16 / 1620.64

路線編號經過節點順序

1 0, 95, 2, 84, 8, 48, 0

2 0, 21, 75, 22, 41, 56, 74, 58, 0 3 0, 31, 62, 30, 51, 20, 66, 70, 0

4 0, 59, 92, 98, 16, 61, 85, 37, 91, 100, 93, 0 5 0, 36, 47, 19, 49, 46, 60, 89, 0

6 0, 42, 14, 44, 38, 86, 17, 0 7 0, 15, 73, 40, 26, 54, 24, 80, 0 8 0, 27, 52, 18, 94, 6, 96, 97, 0 9 0, 83, 5, 99, 87, 57, 43, 13, 0 10 0, 63, 64, 11, 90, 10, 0 11 0, 69, 71, 9, 34, 35, 77, 0 12 0, 45, 82, 7, 88, 50, 1, 0 13 0, 28, 12, 78, 79, 3, 68, 0 14 0, 33, 29, 76, 53, 0 15 0, 65, 81, 32, 0

16 0, 72, 39, 23, 67, 55, 4, 25, 0

例題編號：BHR105B 文獻已知最佳解之車輛數／總旅行距離：16 / 1583.3 本研究之車輛數／總旅行距離：16 / 1711.46

路線編號經過節點順序

1 0, 39, 75, 23, 67, 56, 4, 0 2 0, 63, 11, 62, 90, 20, 66, 70, 0 3 0, 2, 15, 40, 54, 74, 0

4 0, 28, 71, 78, 34, 35, 77, 0 5 0, 27, 31, 76, 53, 0

6 0, 47, 36, 64, 49, 1, 0

7 0, 69, 30, 51, 9, 3, 68, 24, 80, 0 8 0, 45, 82, 7, 19, 46, 17, 60, 89, 0 9 0, 52, 88, 6, 94, 97, 37, 93, 0 10 0, 72, 12, 29, 79, 50, 0 11 0, 5, 83, 18, 8, 84, 48, 0

12 0, 42, 14, 38, 86, 43, 91, 100, 0 13 0, 59, 92, 44, 16, 61, 85, 96, 0 14 0, 95, 98, 99, 87, 57, 26, 13, 58, 0 15 0, 21, 73, 22, 41, 55, 25, 0

16 0, 33, 65, 81, 10, 32, 0

例題編號：BHR105C 文獻已知最佳解之車輛數／總旅行距離：16 / 1710.19 本研究之車輛數／總旅行距離：17 / 1811.97

路線編號經過節點順序

1 0, 63, 11, 64, 49, 46, 60, 89, 0 2 0, 27, 12, 29, 79, 3, 54, 0 3 0, 69, 31, 76, 81, 50, 0 4 0, 28, 21, 22, 41, 56, 4, 58, 0 5 0, 95, 99, 87, 57, 74, 0 6 0, 14, 98, 38, 86, 17, 0 7 0, 83, 5, 16, 61, 85, 43, 13, 0 8 0, 59, 92, 44, 84, 8, 48, 0 9 0, 39, 23, 67, 68, 24, 80, 0 10 0, 36, 19, 90, 20, 1, 0

11 0, 45, 82, 7, 6, 94, 37, 91, 100, 93, 0 12 0, 72, 2, 73, 40, 53, 0

13 0, 52, 88, 78, 34, 35, 77, 0 14 0, 33, 71, 51, 9, 66, 70, 0 15 0, 42, 15, 75, 26, 55, 25, 0 16 0, 65, 30, 10, 32, 0

17 0, 47, 62, 18, 96, 97, 0

在文檔中應用時窗離散策略與可回溯式門檻接受法求解VRPBTW問題之研究 (頁 62-83)

建議

參考文獻

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附錄 本研究最佳結果之成本及路線圖

附錄本研究最佳結果之成本及路線圖