Research Article

A Heuristic Approach Based on Clarke-Wright Algorithm for Open Vehicle Routing Problem

Table 3

Computational results between the proposed CW and CW for data sets A, B, P, E, C, and F.

Number InstanceSolutionPercentage improvementCPU time (seconds)
CWCW-1 CW-2CW-3CW-1CW-2CW-3

1A-n32-k5612.99535.921.7493.18487.3112.57119.54420.5034.819
2A-n33-k5496.61458.521.5425.54424.547.66914.31114.5125.493
3A-n33-k6566.16546.181.7464.10462.433.52818.02618.3215.289
4A-n34-k5547.27 520.09 1.1519.51508.174.9665.0717.1435.675
5A-n36-k5689.48571.701.8535.23519.4617.08322.37324.6606.134
6A-n37-k5579.74541.641.9511.12486.246.57211.83616.1286.689
7A-n37-k6712.86 612.76 1.9616.26581.0714.04113.55118.4876.825
8A-n38-k5552.83 520.78 1.6531.49498.005.7963.8599.9187.092
9A-n39-k5704.55590.71 1.2554.80549.6816.15821.25421.9807.568
10A-n39-k6720.55558.861.9547.57533.0722.43924.00726.0197.494
11A-n44-k6757.90 724.33 1.1641.77617.394.43015.32318.54010.323
12A-n45-k6734.97 643.56 2.0716.52648.6712.4372.51111.74210.414
13A-n45-k7829.44759.401.6699.86685.168.44415.62217.39510.754
14A-n46-k7738.00645.241.1593.57583.5412.56919.57020.93011.259
15A-n48-k7789.39756.581.1726.54669.834.1567.96215.14612.534
16A-n53-k7816.38 702.85 1.5665.39655.1813.90718.49519.74615.624
17A-n54-k7951.51808.42 1.5723.60709.2715.03823.95225.45816.224
18A-n55-k9802.06 736.91 1.9696.52669.068.12313.15816.58217.324
19A-n62-k8979.51 851.151.3815.21783.1813.10516.77420.04422.959
20A-n65-k9844.35 800.41 1.2783.42728.595.2057.21713.71024.524
21A-n69-k9942.87 798.64 2.0773.17757.7615.29617.99819.63228.600

Average percentage improvement of data set A10.64414.87717.93311.601

1B-n31-k5383.68367.000.9364.80362.734.3474.9235.4634.365
2B-n34-k5541.34 506.260.9459.59458.766.48015.10315.2545.556
3B-n35-k5599.16595.151.4567.34557.330.6695.3116.9825.981
4B-n38-k6500.64483.14 1.4450.72445.633.4959.97210.9897.109
5B-n39-k5382.11 354.03 1.4334.70322.547.35012.40915.5907.602
6B-n41-k6539.15 507.25 1.8493.34483.075.9178.49610.4028.549
7B-n43-k6483.21481.57 1.6432.30428.170.34010.53611.3919.422
8B-n44-k7575.52560.541.9512.64501.312.60310.92712.89510.244
9B-n45-k5601.71512.73 1.9509.56488.0714.78815.31518.88710.357
10B-n45-k6459.90 430.83 1.1431.54403.816.3236.16812.19710.573
11B-n50-k7537.23491.93 1.9446.07437.158.43316.96918.62913.265
12B-n51-k7703.81 683.31 2.0656.01625.142.9136.79211.17813.509
13B-n52-k7482.90465.171.8450.07441.193.6726.7988.63714.586
14B-n56-k7497.15474.13 1.5463.06420.484.6296.85615.42017.409
15B-n63-k10950.48950.481.0857.90837.070.0009.74011.93123.724
16B-n64-k9572.41 541.70 1.2581.72520.475.364−1.6279.07423.764
17B-n68-k9830.48777.68 1.1758.69701.726.3578.64415.50427.874

Average percentage improvement of data set B4.9229.02012.37812.582

1P-n16-k8235.89235.890.3235.06235.060.0000.3520.3521.173
2P-n19-k2198.25 172.93 1.9168.57168.5712.77114.97214.9721.565
3P-n20-k2210.01184.50 1.9170.28170.2812.14718.91818.9181.712
4P-n21-k2209.92180.271.8168.15163.8814.12419.89721.9331.729
5P-n22-k2206.00183.581.8171.46167.1910.88316.76518.8401.888
6P-n22-k8370.26 345.53 1.6352.14345.876.6794.8926.5882.330
7P-n23-k8309.74 307.28 1.7304.83302.870.7941.5862.2192.608
8P-n40-k5420.65395.731.5370.64349.555.92411.88916.9027.749
9P-n45-k5459.29 442.231.5396.64391.813.71413.64114.69210.159
10P-n50-k7468.42447.691.5440.56397.384.4265.94815.16713.237
11P-n55-k7513.45464.901.4452.69411.589.45511.83319.84016.627
12P-n55-k8505.72476.431.8442.21412.555.79312.55818.42316.349
13P-n55-k10555.25502.56 1.6488.65444.319.49011.99519.98117.387
14P-n60-k10584.40 539.43 1.8503.38482.097.69413.86417.50720.499
15P-n65-k10649.31 592.351.6531.57522.508.77218.13319.52929.626

Average percentage improvement of data set P7.51111.81615.0589.642

1E-n22-k4286.91260.611.3252.61252.619.16911.95511.9553.753
2E-n23-k3497.18456.861.2444.29442.988.11110.63810.9014.156
3E-n33-k4633.04576.291.4518.04511.268.96518.16519.23612.223
4E-n51-k5493.02 477.78 2.0452.67416.063.0918.18515.61036.154
5E-n76-k10697.03 641.48 1.9587.35567.147.97115.73618.63568.917
6E-n101-k8807.33724.482.0694.88642.3610.26213.92920.43382.387

Average percentage improvement of data set E7.92813.10116.12834.598

1F-n45-k4615.12 535.852.0478.40463.9012.88622.22724.58410.365
2F-n72-k4208.29 191.18 2.0187.67177.008.2129.89915.02142.554
3F-n135-k71033.24 856.33 1.9816.30775.8017.12220.99624.916112.258

Average percentage improvement of data set F12.74017.70721.50755.059

Italic number indicates the infeasible solution (the number of vehicles used is inadequate).