本節針對可回溯式門檻接受法之參數，包含起始門檻比率T0、門檻下降比率 r、門檻回溯比率 b、門檻數列長度 K 以及交換法順序等進行測試。
首先針對交換法之順序進行測試。本研究利用Ninsert, N2-opt*, Nchange等三種交換 法，但其組合順序是否會對求解結果造成影響，於是進行測試，測試結果如表 4.
4。
表 4. 4 交換法組合順序之測試
附註：以上以第一階段之最佳求解結果進行測試，T0=3%，K=120，r=0.98，b=0.9
由表 4. 4 知六種組合差異，車輛數在 1~3 輛，總旅行距離在 102.05~820.82 distance units 之間，本研究仍選用首要目標：車輛數最小之 N2-opt*→Ninsert→Nchange
此組合。
從表 4. 6 的數據得知，當 r 越大時，其運算時間會稍微快一些，而求解效果 也有較佳。而在b 值越大時，也會稍微增加運算時間，但求解效果無顯著差異。
求解效果最佳組合為r = 0.98，b = 0.9。
綜合以上測試結果，單一組表現最佳之參數組合為K = 120，T0 =3%，r = 0.98，
b = 0.9。求得之解為車輛為 420 輛，總旅行距離為 59512.93。表 4. 7 為最佳參數 組合的各階段改善效果，可知於(μ,λ)演化策略模組有效地將車輛數減少了 45 輛，而可回溯式門檻接受法模組進一步將車輛數減少了14 輛，並且將總旅行距離 由(μ,λ)演化策略模組的 74932.99 改善至 59512.93，減少了 15420.06 (20.57%)。
表 4. 7 最佳參數組合各階段改善效果
起始解構建 (μ,λ)演化策略 可回溯式門檻接受法
績效項目
例題類型 車輛數 總旅行距離 車輛數 總旅行距離 車輛數 總旅行距離 C1 (9 題) 97 10114.46 90 10084.23 90 7526.21 C2 (8 題) 27 6422.51 24 6268.49 24 4808.83 R1 (12 題) 173 18492.83 155 17939.47 149 15327.39 R2 (11 題) 40 15219.42 36 15135.67 33 10788.47 RC1 (8 題) 110 13850.08 100 12880.32 97 11789.26 RC2 (8 題) 32 13420.82 29 12624.81 27 9272.77 總和 479 77520.12 434 74932.99 420 59512.93
4.5 測試最佳結果
本研究將56 題測試題庫單題最佳結果所對應之參數組合，整理如表 4.8、表 4. 9、
表 4. 10 所示。
表 4. 8 本研究最佳結果與第二階段對應之參數 (群聚分佈題組)
表 4. 10 本研究最佳結果與第二階段對應之參數 (隨機分佈題組)
解題精確度 第二階段之參數
題號 車輛數 總旅行距離 T0 r b K
R101 19 1716.54 4% 0.98 0.9 120 R102 17 1545.06 4% 0.8 0.99 120 R103 13 1347.24 3% 0.8 0.9 120 R104 10 991.27 3% 0.98 0.9 120 R105 14 1398.35 3% 0.98 0.8 120 R106 12 1300.50 3% 0.9 0.9 120 R107 10 1168.95 3% 0.98 0.9 120 R108 9 1000.23 5% 0.9 0.99 120 R109 12 1158.71 3% 0.98 0.9 120 R110 11 1118.24 3% 0.98 0.99 120 R111 11 1111.39 3% 0.98 0.8 120 R112 10 966.13 2% 0.8 0.9 120 R201 4 1330.25 3% 0.98 0.9 120 R202 3 1229.90 2% 0.9 0.8 120 R203 3 975.81 3% 0.98 0.9 120 R204 3 767.96 3% 0.98 0.9 120 R205 3 1049.13 3% 0.98 0.9 120 R206 3 982.18 1% 0.98 0.99 120 R207 2 914.53 3% 0.98 0.9 120 R208 2 739.65 5% 0.98 0.8 120 R209 3 943.71 3% 0.98 0.9 120 R210 3 950.86 4% 0.98 0.9 120 R211 3 814.04 3% 0.98 0.9 120
4.6 測試結果與文獻已知最佳解之比較
本節主要為整理目前文獻已知最佳解，並將測試結果與其比較。
4.6.1 文獻已知最佳解
表 4. 11 為 Solomon (1983)56 題標竿題目之目前文獻已知最佳解。其中第一 目標為車輛數，第二目標為總旅行距離。若有兩篇以上之文獻其求解結果相同，
則僅列出發表時間較早之文獻。
表 4. 11 Solomon 56 題測試題庫文獻已知最佳解
題號 車輛容量/路線時限 車輛數 總旅行距離 最佳解資料來源
C101 200/1236 10 827.3 Desrochers et al. (1992) C102 200/1236 10 827.3 Desrochers et al. (1992) C103 200/1236 10 828.06 Rochat and Taillard (1995) C104 200/1236 10 824.78 Rochat and Taillard (1995) C105 200/1236 10 828.94 Rochat and Taillard (1995) C106 200/1236 10 827.3 Desrochers et al. (1992) C107 200/1236 10 827.3 Desrochers et al. (1992) C108 200/1236 10 827.3 Desrochers et al. (1992) C109 200/1236 10 828.94 Rochat and Taillard (1995) C201 700/3390 3 591.56 Rochat and Taillard (1995) RC104 200/240 10 1135.48 Cordeau et al. (2001) RC105 200/240 13 1629.44 Berger and Barkaoui (2004) RC106 200/240 11 1424.73 Berger and Barkaoui (2004) RC107 200/240 11 1230.54 Taillard et al. (1997) RC108 200/240 10 1139.82 Taillard et al. (1997) RC201 1000/960 4 1406.91 Mester et al. (2007) RC202 1000/960 3 1365.645 Debudaj-Grabysz and Czech
(2004)
RC203 1000/960 3 1049.62 Czech and Czarnas (2002) RC204 1000/960 3 798.41 Mester et al. (2007) RC205 1000/960 4 1297.19 Mester et al. (2007) RC206 1000/960 3 1146.32 Homberger and Gering (2005) RC207 1000/960 3 1061.14 Ben and Van Hentenryck (2001) RC208 1000/960 3 828.14 Ibaraki et al. (2002)
表 4. 11(續) Solomon 56 題測試題庫文獻已知最佳解
題號 車輛容量/路線時限 車輛數 總旅行距離 最佳解資料來源 R101 200/230 18 1604.5 Desrochers et al. (1992) R102 200/230 17 1434.0 Desrochers et al. (1992) R103 200/230 13 1207 Thangiah et al. (1994) R104 200/230 9 982.01 Rochat and Taillard (1995) R105 200/230 14 1377.11 Rochat and Taillard (1995) R106 200/230 12 1251.98 Mester et al. (2007) R107 200/230 10 1104.66 Shaw (1997) R108 200/230 9 960.88 Berger and Barkaoui (2004) R109 200/230 11 1194.73 Homberger and Gering (1999) R110 200/230 10 1118.59 Mester et al. (2007) R111 200/230 10 1096.72 Rousseau et al. (2002) R112 200/230 9 953.63 Rochat and Taillard (1995) R201 1000/1000 4 1252.37 Homberger and Gering (1999) R202 1000/1000 3 1191.70 Rousseau et al. (2002) R203 1000/1000 3 939.54 Mester et al. (2007) R204 1000/1000 2 825.52 Bent and Van Hentenryck (2004) R205 1000/1000 3 994.42 Rousseau et al. (2002) R206 1000/1000 3 833 Thangiah et al. (1994) R207 1000/1000 2 890.61 Ropke and Pisinger (2005) R208 1000/1000 2 725.75 Mester et al. (2007) R209 1000/1000 3 855 Thangiah et al. (1994) R210 1000/1000 3 939.34 Mester et al. (2007) R211 1000/1000 2 892.71 Bent and Van Hentenryck (2004)
* 資料來源：本研究整理
4.6.2 測試結果與文獻已知最佳解比較分析
表 4. 12、表 4. 13、表 4. 為本研究測試結果與目前文獻已知最佳解之比較分 析。表中字體加粗表示本研究所求得之解至少與目前已知最佳解相同，其中與已 知最佳解相同的有C103、C105、C109、C201、C202、C203、C205、C206、C207、
C208 等十題。若從第一目標：車輛數來看的話，已有 44 題與已知最佳解相同。
表 4. 12 測試結果與文獻最佳解之比較 (群聚分佈題組)
表 4. 13(續) 測試結果與文獻最佳解之比較 (混合分佈題組)
文獻已知最佳解 本研究最佳結果
題號 車輛數 總旅行距離 車輛數 誤差(輛) 總旅行距離 誤差(%)
運算時間 (CPU min) RC201 4 1406.91 4 0 1457.00 3.56% 8.88 RC202 3 1365.645 4 1 1236.56 -9.45% 9.18 RC203 3 1049.62 3 0 1091.66 4.01% 9.44 RC204 3 798.41 3 0 833.01 4.33% 9.11 RC205 4 1297.19 4 0 1346.25 3.78% 9.07 RC206 3 1146.32 3 0 1189.23 3.74% 9.06 RC207 3 1061.14 3 0 1096.38 3.32% 9.16 RC208 3 828.14 3 0 837.99 1.19% 9.25 RC2 總和 26 8953.375 27 1 9088.08 1.50% 73.15
表 4. 14 測試結果與文獻最佳解之比較 (隨機分佈群組)
文獻已知最佳解 本研究最佳結果
題號 車輛數 總旅行距離 車輛數 誤差(輛) 總旅行距離 誤差(%)
運算時間 (CPU min) R101 18 1604.5 19 1 1716.54 6.98% 8.25 R102 17 1434.0 17 0 1545.06 7.74% 8.23 R103 13 1207 13 0 1347.24 11.62% 8.33 R104 9 982.01 10 1 991.27 0.94% 8.46 R105 14 1377.11 14 0 1398.35 1.54% 8.32 R106 12 1251.98 12 0 1300.50 3.88% 8.35 R107 10 1104.66 10 0 1168.95 5.82% 8.36 R108 9 960.88 9 0 1000.23 4.10% 8.39 R109 11 1194.73 12 1 1158.71 -3.01% 8.35 R110 10 1118.59 11 1 1118.24 -0.03% 8.43 R111 10 1096.72 11 1 1111.39 1.34% 8.42 R112 9 953.63 10 1 966.13 1.31% 8.34 R1 總和 142 14285.81 148 6 14822.60 3.76% 100.23
表 4. 14(續) 測試結果與文獻最佳解之比較 (隨機分佈群組)
總旅行距離方面，本研究之總和為58001.90，較文獻最佳解之 56638.94 多出了 2.41%。而在六類測試例題中，以群聚類型的題組表現最佳，C1 與 C2 類型的車輛
第五章 結論與建議
本研究以Homberger and Gehring (2005)所提出之混合巨集啟發式解法為基 礎，結合Tarantilis et al. (2001)所提出之可回溯式門檻接受法，發展出一個混合 演化巨集啟發式解法來求解VRPTW，並以 Solomon (1983)提出之 56 題分為六大 類型之國際標竿題庫測試其求解效果。在本研究提出之混合演化巨集啟發式解法
以供接下來之演化策略進行演化改善之用，但由於本研究僅利用Solomon I1 插入法之策略，雖然可以利用種子點選擇策略以及時間與空間混合成本之觀 念構建多個起始解，但可能其構建之起始解，差異性仍然不夠明顯。往後之 研究可以考慮使用多個不同的起始解構建方法，增加起始解之間的差異程 度，以期有不錯的成果。
2. 在(μ,λ)演化策略的部份，本研究之鄰域結構僅採用 Ninsert、N2-opt*,、Nchange
此三種交換改善模組，而此三種鄰域結構僅N2-opt*對於解之擾動較大，但可 能仍略嫌不足。因此可以考慮新增其他擾動較大之交換改善模組，如 Gendreau et al. 所提出之一般化插入法與解繫法(Generalized Insertion / Unstring and String, GENIUS)，使其演化過程更為劇烈，以期能從中得到更 好的結果。
3. 在可回溯式門檻接受法的部份，於廖昱傑(2007)的研究中指出，適當地調整 門檻回溯值b，將有很大的空間可以更進一步地改善。而本研究因為時間上 的因素，未能針對b 值進行廣泛的測試分析，但未來仍可針對此一參數或是 門檻回溯方式，在求解的過程中適當地調整回溯幅度，進行更進一步的研究 分析。另外由於本研究僅採用距離成本來評斷是否在門檻可接受範圍之內，
但若能將車輛數或者是車容量使用等因素混合考量，進一步加強縮減車輛數 之功能，可能也會有相當不錯之成效。
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