S/N

Datasets

Scale

BKS

Proposed Algorithm (RNN-SA)

Best

Average

Worst

SD

PDbest (%)

PDav (%)

1

eil51

51

426

428.87

429.44

430.24

0.52

0.673709

0.807512

2

berlin52

52

7542

7544.37

7544.37

7544.37

0.00

0.031424

0.031424

3

brazil58

58

25,395

25,395

25,440.40

25,622.00

9.39

0

0.178775

4

st70

70

675

677.11

679.33

682.66

3.04

0.312593

0.641481

5

eil76

76

538

544.37

549.16

555.99

4.40

1.184015

2.074349

6

rat99

99

1211

1219.24

1229.29

1232.68

5.68

0.680429

1.510322

7

kroA100

100

21,282

21,285.44

21,285.44

21,285.44

0.00

0.016164

0.016164

8

kroE100

100

22,068

22,119.90

22,164.92

22,267.17

58.65

0.235182

0.439188

9

eil101

101

629

644.92

652.31

657.71

5.39

2.531002

3.705882

10

bier127

127

118,282

119,331.15

119,849.69

120,061.28

294.00

0.88699

1.325383

11

ch130

130

6110

6171.87

6249.18

6331.14

66.31

1.012602

2.277905

12

pr136

136

96,772

96,922.41

100,335.16

101,924.34

1979.60

0.155427

3.682015

13

ch150

150

6528

6552.30

6553.94

6556.01

1.58

0.372243

0.397365

14

kroA150

150

26,524

26,821.83

27,008.24

27,330.04

194.18

1.12287

1.825667

15

kroB150

150

26,130

26,327.09

26,577.15

26,839.20

232.5

0.754267

1.711251

16

pr152

152

73,682

73,843.09

74,669.58

76,049.93

836.59

0.218629

1.340327

17

u159

159

42,080

42,162.75

42,547.66

42,715.47

90.57

0.196649

1.111359

18

rat195

195

2323

2348.70

2361.50

2375.73

11.49

1.106328

1.65734

19

d198

198

15,780

15,852.33

15,896.40

15,945.10

34.47

0.458365

0.737643

20

kroA200

200

29,368

29,541.83

29,626.42

29,702.88

73.01

0.591903

0.879937

21

kroB200

200

29,437

29,825.16

30,033.03

30,247.70

163.02

1.318613

2.024765

22

pr264

264

49,135

49,197.32

49,375.75

49,779.63

232.85

0.126834

0.489977

23

pr299

299

48,191

48,811.49

49,003.93

49,137.65

154.58

1.287564

1.686892

24

lin318

318

42,029

42,862.50

43,041.10

43,167.09

122.01

1.983154

2.707868

Average

0.71904

1.385866