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Table 3 Comparison between the best-known results and Modified ABC

From: Modified artificial bee colony for the vehicle routing problems with time windows

No

Instance

Best-known result

Source

Modified ABC

Percentage difference between Modified ABC with the best known solutions (%)

N.V

Distance

N.V

Distance

0

R1-01

18

1607.70

Desrochers et al. (1992)

20

1643.18

2.21

1

R1-02

17

1434.00

Desrochers et al. (1992)

18

1480.73

3.26

2

R1-03

13

1175.67

Lau et al. (2001)

14

1240.87

5.55

3

R1-04

10

982.01

Rochat and Tailard (1995)

12

1047.06

6.62

4

R1-05

15

1346.12

Kallehauge et al. (2001)

16

1369.52

1.74

5

R1-06

13

1234.6

Cook and Rich (1999)

13

1271.13

2.96

6

R1-07

11

1051.84

Kallehauge et al. (2001)

12

1129.99

7.43

7

R1-08

9

960.88

Berger and Barkaoui (2004)

11

1004.11

4.50

8

R1-09

12

1013.2

Chiang and Russel (1997)

13

1170.5

15.53

9

R1-10

12

1068.00

Cook and Rich (1999)

12

1123.36

5.18

10

R1-11

12

1048.70

Cook and Rich (1999)

12

1101.59

5.04

11

R1-12

10

953.63

Rochat and Tailard (1995)

11

1019.84

6.94

12

R2-01

4

1252.37

Homberger and Gehring (1999)

8

1185.57

−5.33

13

R2-02

3

1158.98

Lau et al. (2003)

7

1103.15

−4.82

14

R2-03

3

939.50

Woch and Lebkowski (2009)

6

958.94

2.07

15

R2-04

2

825.52

Bent and Van Hentenryck (2004)

4

818.44

−0.86

16

R2-05

3

994.42

Rousseau et al. (2002)

6

1020.53

2.63

17

R2-06

3

833.00

Thangiah et al. (1994)

5

960.29

15.28

18

R2-07

3

814.78

Rochat and Tailard (1995)

5

905.7

11.16

19

R2-08

2

726.75

Mester et al. (2007)

4

764.9

5.25

20

R2-09

3

855.00

Thangiah et al. (1994)

6

943.16

10.31

21

R2-10

3

939.34

Mester et al. (2007)

6

1003.91

6.87

22

R2-11

2

877.55

Yu et al. (2009)

5

837.66

−4.55

23

C1-01

10

827.30

Desrochers et al. (1992)

10

828.94

0.20

24

C1-02

10

827.30

Desrochers et al. (1992)

10

828.94

0.20

25

C1-03

10

826.30

Tavares et al. (2003)

10

828.94

0.32

26

C1-04

10

822.90

Tavares et al. (2003)

10

858.9

4.37

27

C1-05

10

827.30

Tavares et al. (2003)

10

828.94

0.20

28

C1-06

10

827.30

Desrochers et al. (1992)

10

828.94

0.20

29

C1-07

10

827.30

Tavares et al. (2003)

10

828.94

0.20

30

C1-08

10

827.30

Tavares et al. (2003)

10

828.94

0.20

31

C1-09

10

827.30

Tavares et al. (2003)

10

828.94

0.20

32

C2-01

3

589.10

Cook and Rich (1999)

3

591.56

0.42

33

C2-02

3

589.10

Cook and Rich (1999)

3

591.56

0.42

34

C2-03

3

591.17

Li and Lim (2002)

3

600.54

1.58

35

C2-04

3

590.60

Potvin and Bengio (1996)

3

610.01

3.29

36

C2-05

3

588.88

De Backer et al. (2000)

3

588.88

0.00

37

C2-06

3

588.49

Lau et al. (2003)

3

588.88

0.07

38

C2-07

3

588.29

Rochat and Tailard (1995)

3

589.58

0.22

39

C2-08

3

588.32

Rochat and Tailard (1995)

3

591.65

0.57

40

RC1-01

15

1619.8

Kohl et al. (1999)

16

1634.52

0.91

41

RC1-02

13

1530.86

Cordone and Calvo (2001)

15

1492.89

−2.48

42

RC1-03

11

1261.67

Shaw (1998)

13

1334.57

5.78

43

RC1-04

10

1135.48

Cordeau et al. (2001)

11

1215.62

7.06

44

RC1-05

13

1589.91

Tan et al. (2006)

15

1546.43

−2.73

45

RC1-06

12

1371.69

Tan et al. (2006)

14

1423.1

3.75

46

RC1-07

11

1222.16

Tan et al. (2006)

12

1300

6.37

47

RC1-08

10

1133.90

Tan et al. (2006)

12

1193.68

5.27

48

RC2-01

4

1134.91

Tan et al. (2006)

8

1308.76

15.32

49

RC2-02

4

1130.53

Tan et al. (2006)

8

1167

3.23

50

RC2-03

3

1026.61

Tan et al. (2006)

6

1014.79

−1.15

51

RC2-04

3

798.41

Mester et al. (2007)

4

881.88

10.45

52

RC2-05

4

1297.19

Mester et al. (2007)

7

1210.68

−6.67

53

RC2-06

3

1112.20

Yu et al. (2009)

6

1112.38

0.02

54

RC2-07

3

1040.67

Yu et al. (2009)

7

1059.62

1.82

55

RC2-08

3

828.14

Ibaraki et al. (2001)

5

882.06

6.51

  1. NV number of vehicles