Statistical Analysis of Tool Switching Problem (ToSP)

 

A non-parametrical statistical test -Wilcoxon ranksum- was executed on the results returned by n the executions performed by HC, TS, SA, GA and MA. Then a comparison between each method with the other was executed but reasons of space we present two essential tables based in the better computational results of methods according to Tables A and B.

 

Tables from 1 to 16 show the results of the comparison n methods vs. n methods for one instance. Each cell in the tables indicates the number of times that the corresponding algorithm is significantly better than the other one with respect to the 5 datasets per instance. For example, a 4 appearing in Table 1 for the instance 4ζ109 in the column of HC means that the GAap behaves significantly better, according to the statistical test, than the HC in 4 of the 5 datasets that were used to solve the specific problem instance. ToSP involves scheduling a number of jobs on a single machine such that the resulting number of tool switches required is kept to a minimum. 

 

Table A. Local Search Methods and Beam Search

 

 

 

HC

HCn

SA

SA*

TS

TSn

TS2

TS2n

TS3

TS3n

1β

2β

3β

4β

5β

Evaluations

4ζ109

Av

8.66

8.3

10.14

10.72

7.94

9.6

7.84

7.8

7.88

7.8

8.4

8.4

8.4

8.4

8.4

3600

 

SD

1.05

0.96

2.08

2.12

0.76

2.42

0.73

0.75

0.74

0.75

0.49

0.49

0.49

0.49

0.49

 

 

B

7

7

8

8

7

7

7

7

7

7

8

8

8

8

8

 

4ζ1010

Av

9.7

9.36

11.26

11.4

8.8

10.4

8.6

8.8

8.6

8.8

10

9.8

9.6

9.6

9.6

4800

 

SD

1.68

1.47

1.89

1.82

1.66

1.36

1.63

1.83

1.63

1.83

2.1

1.83

2.06

2.06

2.06

 

 

B

7

7

8

8

7

8

7

7

7

7

8

8

7

7

7

 

6ζ1015

Av

14.58

14.32

17.06

16.7

13.64

15

13.6

13.8

13.6

13.8

15.2

14.8

14.8

14.8

14.8

10800

 

SD

2.079

2.14

2.37

2.27

2.12

1.67

2.154

2.48

2.15

2.48

1.47

1.47

1.47

1.47

1.47

 

 

B

11

11

13

13

11

13

11

11

11

11

13

13

13

13

13

 

6ζ1512

Av

19.94

18.36

23.38

24.06

17.04

18.2

15.1

15.8

15.18

15.8

18.2

17.6

17.6

17.4

17.4

5760

 

SD

2.51

1.71

3.19

3.21

2.1

2.04

1.85

1.94

1.74

1.94

0.75

1.02

1.02

1.2

1.2

 

 

B

15

16

17

18

13

15

12

13

12

13

17

16

16

16

16

 

6ζ1520

Av

26.42

24.94

30.72

29.62

23.36

28.6

21.64

23

21.76

23

26.2

25.8

25.2

25.2

25.2

22400

 

SD

2.33

2.33

3.04

2.69

1.96

4.36

1.76

2

1.84

2

2.32

2.14

1.6

1.6

1.6

 

 

B

22

21

24

25

20

22

20

20

20

20

23

23

23

23

23

 

8ζ2015

Av

29.8

24.78

34.44

32.76

24.92

29.6

21.32

22

21.9

22

27

26

25.6

25.2

25.2

8400

 

SD

4.46

3.63

4.55

4.28

3.7

7.63

3.49

3.74

3.35

3.74

3.95

4.05

4.27

4.12

4.12

 

 

B

21

20

27

27

20

21

17

17

17

17

21

21

20

20

20

 

8ζ2016

Av

34.1

28.82

39.54

37.42

29.18

30.6

25.6

26.2

25.86

26.2

29.4

29.4

29.4

29.4

29.4

10240

 

SD

2.41

2.04

3.04

3.2

2.09

4.96

1.84

1.33

1.91

1.33

1.63

1.63

1.63

1.63

1.63

 

 

B

28

27

35

30

25

26

22

24

22

24

27

27

27

27

27

 

10ζ2020

Av

37.76

34.24

44.48

42.02

32.42

37.6

28.44

29.6

28.74

29.6

34.2

33.6

33.4

33.4

33.4

16000

 

SD

2.43

1.52

3.306

3.34

2.62

6.83

2.42

1.74

2.38

1.74

3.19

2.87

2.8

2.8

2.8

 

 

B

31

31

36

34

27

32

24

27

24

27

30

30

30

30

30

 

10ζ3025

Av

85.22

69.6

95.28

92.8

73.58

69.6

63.16

63.8

63.56

63.8

73.6

70.8

70.8

70.8

70.6

30000

 

SD

2.41

1.02

4.05

3.49

1.65

1.02

1.12

1.17

1.17

1.17

1.02

1.47

1.47

1.47

1.497

 

 

B

79

68

87

86

69

68

60

62

60

62

72

68

68

68

68

 

15ζ3040

Av

121.18

102.98

133.36

130.84

108.18

110

96.74

96.6

97.66

96.6

111.6

110

109.2

107.8

107.8

80000

 

SD

13.68

14.02

13.5

14.18

13.35

12.36

13.18

14.15

12.71

14.15

15.19

13.55

13.41

13.26

13.26

 

 

B

101

82

111

109

87

93

77

77

79

77

89

89

89

89

89

 

15ζ4030

Av

129.12

100.64

142.92

137.46

111.74

109.8

95.74

95

97.46

95

105.2

103.2

102.8

102.8

102.4

36000

 

SD

9.842

9.715

11.15

10

8.42

18.53

7.86

7.56

7.8

7.56

8.52

9.58

9.75

9.75

9.97

 

 

B

112

88

122

117

97

88

85

88

84

88

96

93

93

93

93

 

20ζ4060

Av

247.5

214.36

270.7

264.1

225.34

241.2

205.54

202.6

208.78

202.6

221.8

220

218.8

218.6

218.6

192000

 

SD

10.39

9.12

12.32

10.48

8.99

26.49

7.94

11.5

8.32

11.5

7.03

6.16

5.71

5.82

5.82

 

 

B

230

199

251

247

211

213

195

190

198

190

215

215

215

215

215

 

24ζ2030

Av

30.12

25.8

35.06

33

25.66

25.6

22.76

24.2

23

24.2

33

32.6

32.4

32.4

32.4

14400

 

SD

3.56

2.71

4.7

4.5

3.44

2.87

3.13

3.12

3.26

3.12

4.43

4.5

4.63

4.63

4.63

 

 

B

25

23

29

26

21

23

19

21

19

21

28

28

28

28

28

 

24ζ2036

Av

53.32

48.72

61.24

58.44

47.64

51.8

42.62

43.6

43.08

43.6

54

54

53.8

53.8

53.4

23040

 

SD

9.47

8.75

10.5

10.38

8.76

11.48

8.35

6.92

8.32

6.92

8.2

8.2

8.33

8.33

7.61

 

 

B

39

40

46

45

37

40

33

35

33

35

45

45

45

45

45

 

25ζ5040

Av

192.78

167.06

209.98

203.1

168.22

181.8

146.3

143.8

149.74

143.8

167.2

164

162.8

162.8

161.8

48000

 

SD

14.85

16.4

15.98

14.09

12.49

13.96

13.08

13.66

11.88

13.66

12.91

12.55

12.34

12.34

12.16

 

 

B

164

129

179

182

149

163

127

124

133

124

152

147

147

147

147

 

30ζ2040

Av

48.78

44.4

55.6

53.66

43.14

44.4

38.66

38.8

39.18

38.8

52.2

50.2

50.2

50.2

50.2

32000

 

SD

5.24

5.78

6.71

6.25

5.032

5.78

4.36

4.53

4.63

4.53

6.24

7.03

7.03

7.03

7.03

 

 

B

38

35

43

41

33

35

30

31

30

31

42

39

39

39

39

 

 

 

Table B. GA and MA

 

 

 

GAap

GAux

GAucx

maHC

maHCn

maSA

maSA*

maTS

maTSn

maTS2

maTS3

maTSn

maTSn

Evaluations

4ζ109

Av

7.98

8.34

7.86

7.94

7.84

9.1

9.12

9.46

9.48

7.88

7.84

8.24

8.24

3600

 

SD

0.648

0.93

0.749

0.759

0.731

1.36

1.177

1.403

1.33

0.711

0.731

0.907

0.838

 

 

B

7

7

7

7

7

7

7

7

7

7

7

7

7

 

4ζ1010

Av

8.7

9.24

8.64

8.68

8.64

10.1

10.3

10.42

10.46

8.62

8.6

8.98

9.06

4800

 

SD

1.616

1.569

1.634

1.655

1.609

1.578

1.487

1.55

1.7

1.623

1.625

1.556

1.618

 

 

B

7

7

7

7

7

7

7

8

8

7

7

7

7

 

6ζ1015

Av

13.7

14

13.6

13.62

13.6

16.04

15.74

16.3

16.26

13.68

13.64

13.98

14.02

10800

 

SD

2.081

1.908

2.154

2.19

2.154

2.029

2.207

2.156

2.252

2.111

2.133

2.14

2.083

 

 

B

11

11

11

11

11

12

12

13

12

11

11

11

11

 

6ζ1512

Av

16

18.94

15.7

16.12

15.64

20.8

21.48

21.74

21.68

15.26

15.08

16.36

16.26

5760

 

SD

1.887

2.222

1.758

1.693

1.682

2.236

2.343

2.44

2.249

1.741

1.787

1.852

1.753

 

 

B

13

14

12

13

13

17

17

17

18

12

12

13

13

 

6ζ1520

Av

22.98

25.52

22.28

22.44

22.14

27.62

27.16

28.56

28.34

21.92

22.12

23.38

23.48

22400

 

SD

1.871

2.202

1.929

1.941

1.844

2.306

2.641

2.308

2.503

1.831

1.915

2.144

1.921

 

 

B

20

22

20

20

20

24

24

25

23

20

20

20

20

 

8ζ2015

Av

23.86

28.3

22.64

23.36

23.2

31.28

30.34

32.06

32.12

21.58

22.22

24.18

23.58

8400

 

SD

3.262

3.996

3.399

3.404

3.353

4.583

4.598

4.282

4.121

3.589

3.7

3.439

3.293

 

 

B

19

23

17

18

18

24

24

25

27

16

16

18

18

 

8ζ2016

Av

28.08

32.86

26.56

27.32

27.34

35.24

36.16

36.64

36.78

25.58

25.78

27.74

27.82

10240

 

SD

2.305

2.227

2.183

1.891

2.075

2.25

2.477

2.791

2.072

2.089

1.758

2.105

2.085

 

 

B

24

29

22

22

22

30

32

31

33

22

22

22

23

 

10ζ2020

Av

31.02

36.28

29.26

30.1

30.34

38.86

39.82

40.2

40.24

28.54

28.7

31.36

31.34

16000

 

SD

2.649

2.458

2.464

2.184

2.169

2.425

2.439

2.482

2.746

2.326

2.211

2.834

2.495

 

 

B

27

31

24

24

26

34

32

34

35

24

25

25

26

 

10ζ3025

Av

69.38

83.34

65.78

67.72

75.34

87.68

89.56

89.78

90.5

61.82

61.64

66.9

66.7

30000

 

SD

2.884

1.351

1.921

1.709

2.566

1.462

1.824

1.89

2.11

1.211

1.658

2.751

2.766

 

 

B

63

79

63

63

68

84

85

86

83

60

59

62

61

 

15ζ3040

Av

102.26

118.18

98.9

99.96

105.88

122.24

124.4

122.12

123.18

94.53

94.15

100.6

100.8

80000

 

SD

13.204

14.324

12.482

12.9

13.029

14.744

14.358

13.95

13.995

12.305

11.798

11.386

11.975

 

 

B

81

95

79

78

86

98

100

98

104

77

77

81

81

 

15ζ4030

Av

107.52

125.78

99.96

104.8

122.04

128.24

129.32

133.48

134.4

93.2

93.32

97.6

97.78

36000

 

SD

8.642

9.12

8.433

8.41

9.145

9.444

8.945

9.594

9.863

7.871

7.941

7.552

8.633

 

 

B

91

110

86

91

108

110

115

117

118

82

82

85

85

 

20ζ4060

Av

214

244.48

206.7

208.48

227.16

246.7

250.4

248.2

252.18

201.06

201.48

210.06

209.38

192000

 

SD

10.113

8.823

8.431

8.073

9.098

10.655

10.621

8.693

10.227

7.737

7.918

7.374

8.845

 

 

B

196

232

190

197

213

233

231

235

232

190

191

198

195

 

24ζ2030

Av

25

29.02

23.7

24.14

24.02

30.3

30.3

32

32.26

22.68

22.94

25.32

25.22

14400

 

SD

3.243

3.535

3.145

3.118

3.146

3.651

3.754

3.726

3.676

3.146

3.165

3.301

3.596

 

 

B

20

25

19

20

20

25

24

27

27

19

19

20

20

 

24ζ2036

Av

45.72

51.98

43.64

44.6

44.58

53.62

52.54

56.3

55.84

42.54

42.76

46.38

46.1

23040

 

SD

8.716

9.446

8.214

8.4

8.242

10.006

9.06

10.197

9.886

7.965

7.812

7.902

8.196

 

 

B

35

40

34

34

35

42

41

43

42

33

33

37

35

 

25ζ5040

Av

162.96

188.22

153.84

164.52

190.26

191.14

194.42

198.02

197.32

141.98

144.18

146.54

146.84

48000

 

SD

13.238

13.627

13.167

11.739

15.057

13.358

13.822

14.448

15.185

12.693

12.216

12.939

12.376

 

 

B

143

169

132

146

164

169

165

178

175

122

125

124

129

 

30ζ2040

Av

41.06

46.86

39.8

40.34

40.42

49.8

50.56

51.433

51.66

38.35

38.98

42.06

42.08

32000

 

SD

4.443

5.219

4.271

4.502

4.535

5.337

5.536

5.333

5.348

3.978

4.181

4.953

4.142

 

 

B

32

35

31

31

31

38

40

41

41

30

30

32

33

 

 

 

 

Table 1. Instance  4ζ109

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

2

1

4

0

0

4

4

1

0

1

0

4

5

5

5

0

0

0

0

3

0

GAucx

1

0

3

2

5

0

0

5

5

1

0

1

0

5

5

5

5

0

0

0

0

4

0

GAux

0

0

0

0

1

0

0

4

3

0

0

0

0

4

4

5

4

0

0

0

0

2

0

HCn

0

0

0

0

1

0

0

4

3

0

0

0

0

4

5

5

5

0

0

0

0

2

0

HC

0

0

0

0

0

0

0

1

1

0

0

0

0

3

3

5

4

0

0

0

0

2

0

maHCn

1

0

3

2

5

0

0

5

5

1

0

2

0

5

5

5

5

0

0

0

0

4

0

maHC

1

0

3

1

5

0

0

5

5

1

0

1

0

5

5

5

5

0

0

0

0

4

0

maSA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

4

2

0

0

0

0

2

0

maSA

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

5

1

0

0

0

0

2

0

maTS2n

0

0

0

1

1

0

0

4

3

0

0

0

0

5

5

5

5

0

0

0

0

2

0

maTS2

1

0

3

1

5

0

0

5

5

1

0

2

0

5

5

5

5

0

0

0

0

4

0

maTS3n

0

0

0

0

2

0

0

3

3

0

0

0

0

4

4

5

5

0

0

0

0

2

0

maTS3

1

0

3

2

5

0

0

5

5

1

0

2

0

5

5

5

5

0

0

0

0

4

0

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

3

1

0

0

0

0

1

0

maTS

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

3

1

0

0

0

0

1

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

TS2n

1

0

3

2

5

0

0

5

5

2

0

2

0

5

5

5

5

0

0

0

0

4

0

TS2

1

0

3

2

5

0

0

5

5

1

0

2

0

5

5

5

5

0

0

0

0

4

0

TS3n

1

0

3

2

5

0

0

5

5

2

0

2

0

5

5

5

5

0

0

0

0

4

0

TS3

1

0

3

1

5

0

0

5

5

1

0

1

0

5

5

5

5

0

0

0

0

4

0

TSn

0

0

0

0

1

0

0

2

1

0

0

0

0

2

2

3

2

0

0

0

0

0

0

TS

1

0

3

1

5

0

0

5

5

1

0

1

0

5

5

5

5

0

0

0

0

4

0

 

Table 2. Instance  4ζ1010

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

3

4

5

0

0

5

5

0

0

0

0

5

5

5

5

1

0

1

0

4

0

GAucx

1

0

3

4

5

0

0

5

5

0

0

1

0

5

5

5

5

1

0

1

0

4

0

GAux

0

0

0

1

3

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

0

HCn

0

0

0

0

1

0

0

4

4

0

0

0

0

5

5

5

5

0

0

0

0

3

0

HC

0

0

0

0

0

0

0

2

2

0

0

0

0

5

3

5

5

0

0

0

0

2

0

maHCn

0

0

3

4

5

0

0

5

5

0

0

1

0

5

5

5

5

1

0

1

0

4

0

maHC

0

0

3

4

5

0

0

5

5

0

0

0

0

5

5

5

5

1

0

1

0

4

0

maSA*

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

3

2

0

0

0

0

2

0

maSA

0

0

0

0

0

0

0

1

0

0

0

0

0

2

0

4

3

0

0

0

0

2

0

maTS2n

0

0

1

2

3

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

0

maTS2

0

0

3

4

5

0

0

5

5

1

0

2

0

5

5

5

5

1

0

1

0

4

0

maTS3n

0

0

0

0

2

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

0

maTS3

0

0

3

4

5

0

0

5

5

1

0

3

0

5

5

5

5

1

0

1

0

4

0

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

3

2

0

0

0

0

1

0

maTS

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

3

2

0

0

0

0

1

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

TS2n

0

0

2

3

4

0

0

5

5

2

0

3

0

5

5

5

5

0

0

0

0

3

0

TS2

0

0

3

4

5

0

0

5

5

1

0

3

0

5

5

5

5

1

0

1

0

4

0

TS3n

0

0

2

3

4

0

0

5

5

2

0

3

0

5

5

5

5

0

0

0

0

3

0

TS3

0

0

3

4

5

0

0

5

5

1

0

3

0

5

5

5

5

1

0

1

0

4

0

TSn

0

0

0

0

1

0

0

1

1

0

0

0

0

2

1

3

4

0

0

0

0

0

0

TS

0

0

2

4

5

0

0

5

5

1

0

0

0

5

5

5

5

0

0

0

0

4

0

 

Table 3. Instance  6ζ1015

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

1

3

5

0

0

5

5

0

0

0

0

5

5

5

5

1

0

1

0

3

0

GAucx

0

0

2

3

5

0

0

5

5

1

0

2

0

5

5

5

5

1

0

1

0

3

0

GAux

0

0

0

1

3

0

0

5

5

0

0

0

0

5

5

5

5

1

0

1

0

3

0

HCn

0

0

0

0

1

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

0

HC

0

0

0

0

0

0

0

4

5

0

0

0

0

5

5

5

5

0

0

0

0

3

0

maHCn

0

0

2

3

5

0

0

5

5

1

0

2

0

5

5

5

5

1

0

1

0

3

0

maHC

0

0

2

3

5

0

0

5

5

1

0

2

0

5

5

5

5

1

0

1

0

3

0

maSA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

2

0

0

0

0

0

0

maSA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

1

0

0

0

0

0

0

maTS2n

0

0

0

1

3

0

0

5

5

0

0

0

0

5

5

5

5

1

0

1

0

3

0

maTS2

0

0

2

3

5

0

0

5

5

0

0

1

0

5

5

5

5

1

0

1

0

3

0

maTS3n

0

0

0

0

2

0

0

5

5

0

0

0

0

5

5

5

5

1

0

1

0

3

0

maTS3

0

0

2

3

5

0

0

5

5

0

0

1

0

5

5

5

5

1

0

1

0

3

0

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

maTS

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

TS2n

0

0

2

2

4

0

0

5

5

1

0

2

0

5

5

5

5

0

0

0

0

3

0

TS2

0

0

2

3

5

0

0

5

5

1

0

2

0

5

5

5

5

1

0

1

0

3

0

TS3n

0

0

2

2

4

0

0

5

5

1

0

2

0

5

5

5

5

0

0

0

0

3

0

TS3

0

0

2

3

5

0

0

5

5

1

0

2

0

5

5

5

5

1

0

1

0

3

0

TSn

0

0

0

1

1

0

0

2

4

0

0

0

0

4

4

4

4

1

0

1

0

0

0

TS

0

0

2

3

5

0

0

5

5

0

0

2

0

5

5

5

5

1

0

1

0

3

0

 

Table 4. Instance  6ζ1512

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

5

4

5

0

1

5

5

0

0

0

0

5

5

5

5

1

0

1

0

4

2

GAucx

0

0

5

5

5

0

0

5

5

2

0

1

0

5

5

5

5

1

0

1

0

5

5

GAux

0

0

0

2

3

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

0

HCn

0

0

3

0

3

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

0

0

HC

0

0

0

0

0

0

0

4

1

0

0

0

0

3

5

5

5

0

0

0

0

0

0

maHCn

0

0

5

5

5

0

2

5

5

2

0

0

0

5

5

5

5

1

0

1

0

5

4

maHC

0

0

5

5

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

4

maSA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

3

3

0

0

0

0

0

0

maSA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

5

4

0

0

0

0

0

0

maTS2n

0

0

5

5

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

3

maTS2

2

1

5

5

5

2

4

5

5

5

0

4

0

5

5

5

5

2

0

2

0

5

5

maTS3n

0

0

5

5

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

3

maTS3

2

2

5

5

5

1

5

5

5

5

0

4

0

5

5

5

5

4

0

4

0

5

5

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

3

2

0

0

0

0

0

0

maTS

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

2

0

0

0

0

0

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

TS2n

1

1

5

5

5

0

2

5

5

3

0

2

0

5

5

5

5

0

0

0

0

5

5

TS2

3

3

5

5

5

3

4

5

5

5

0

3

0

5

5

5

5

3

0

3

0

5

5

TS3n

1

1

5

5

5

0

2

5

5

3

0

2

0

5

5

5

5

0

0

0

0

5

5

TS3

3

2

5

5

5

2

5

5

5

5

0

3

0

5

5

5

5

2

0

2

0

5

5

TSn

0

0

3

1

3

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

0

0

TS

0

0

5

3

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

0

 

Table 5. Instance  6ζ1520

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

5

5

5

0

0

5

5

1

0

1

0

5

5

5

5

1

0

1

0

5

1

GAucx

2

0

5

5

5

0

0

5

5

1

0

3

0

5

5

5

5

3

0

3

0

5

5

GAux

0

0

0

0

1

0

0

4

5

0

0

0

0

5

5

5

5

0

0

0

0

3

0

HCn

0

0

2

0

3

0

0

4

5

0

0

0

0

5

5

5

5

0

0

0

0

3

0

HC

0

0

0

0

0

0

0

0

3

0

0

0

0

4

5

5

5

0

0

0

0

3

0

maHCn

2

0

5

5

5

0

0

5

5

3

0

5

0

5

5

5

5

4

0

4

0

5

5

maHC

1

0

5

5

5

0

0

5

5

2

0

3

0

5

5

5

5

2

0

2

0

5

5

maSA*

0

0

0

0

0

0

0

0

0

0

0

0

0

1

3

4

5

0

0

0

0

3

0

maSA

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

3

5

0

0

0

0

3

0

maTS2n

0

0

5

4

5

0

0

5

5

0

0

0

0

5

5

5

5

1

0

1

0

4

0

maTS2

5

2

5

5

5

1

2

5

5

5

0

5

0

5

5

5

5

4

0

4

0

5

5

maTS3n

0

0

4

4

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

5

0

maTS3

2

0

5

5

5

0

0

5

5

3

0

5

0

5

5

5

5

3

0

3

0

5

5

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

3

0

0

0

0

3

0

maTS

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

3

0

0

0

0

2

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

TS2n

1

0

5

4

5

0

0

5

5

1

0

3

0

5

5

5

5

0

0

0

0

5

3

TS2

5

3

5

5

5

3

4

5

5

5

0

5

3

5

5

5

5

4

0

4

0

5

5

TS3n

1

0

5

4

5

0

0

5

5

1

0

3

0

5

5

5

5

0

0

0

0

5

3

TS3

5

2

5

5

5

1

3

5

5

5

0

5

1

5

5

5

5

4

0

4

0

5

5

TSn

0

0

2

0

2

0

0

2

2

0

0

0

0

2

2

3

2

0

0

0

0

0

0

TS

0

0

5

5

5

0

0

5

5

0

0

1

0

5

5

5

5

1

0

1

0

5

0

 

Table 6. Instance  8ζ2015

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

5

0

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

2

GAucx

2

0

5

4

5

0

2

5

5

3

0

3

0

5

5

5

5

0

0

0

0

4

5

GAux

0

0

0

0

3

0

0

4

5

0

0

0

0

5

5

5

5

0

0

0

0

3

0

HCn

0

0

4

0

5

0

0

5

5

1

0

0

0

5

5

5

5

0

0

0

0

2

2

HC

0

0

0

0

0

0

0

0

2

0

0

0

0

4

4

4

4

0

0

0

0

2

0

maHCn

2

0

5

3

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

5

maHC

1

0

5

3

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

5

maSA*

0

0

0

0

0

0

0

0

0

0

0

0

0

3

2

4

4

0

0

0

0

2

0

maSA

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

2

3

0

0

0

0

2

0

maTS2n

0

0

5

1

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

1

maTS2

5

4

5

5

5

5

5

5

5

5

0

4

2

5

5

5

5

2

0

2

0

5

5

maTS3n

0

0

5

3

5

0

0

5

5

1

0

0

0

5

5

5

5

0

0

0

0

4

2

maTS3

4

1

5

5

5

3

4

5

5

4

0

4

0

5

5

5

5

0

0

0

0

5

5

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

0

0

0

0

2

0

maTS

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

0

0

0

0

2

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

0

0

0

0

2

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

0

TS2n

4

3

5

5

5

5

4

5

5

5

0

4

1

5

5

5

5

0

0

0

0

5

5

TS2

5

5

5

5

5

5

5

5

5

5

1

4

3

5

5

5

5

4

0

4

2

5

5

TS3n

4

3

5

5

5

5

4

5

5

5

0

4

1

5

5

5

5

0

0

0

0

5

5

TS3

5

4

5

5

5

5

5

5

5

5

0

4

2

5

5

5

5

2

0

2

0

5

5

TSn

0

0

2

0

3

0

0

3

3

1

0

0

0

3

3

3

3

0

0

0

0

0

2

TS

0

0

5

0

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

0

 

Table 7. Instance  8ζ2016

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

5

2

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

3

GAucx

4

0

5

4

5

1

1

5

5

2

0

1

0

5

5

5

5

1

0

1

0

4

5

GAux

0

0

0

0

0

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

1

0

HCn

1

0

5

0

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

1

2

HC

0

0

0

0

0

0

0

4

0

0

0

0

0

5

4

4

5

0

0

0

0

1

0

maHCn

0

0

5

3

5

0

0

5

5

1

0

0

0

5

5

5

5

0

0

0

0

3

4

maHC

2

0

5

3

5

0

0

5

5

1

0

0

0

5

5

5

5

0

0

0

0

3

4

maSA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

5

0

0

0

0

1

0

maSA

0

0

0

0

0

0

0

1

0

0

0

0

0

5

2

4

5

0

0

0

0

1

0

maTS2n

0

0

5

3

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

3

maTS2

5

2

5

5

5

5

5

5

5

4

0

5

0

5

5

5

5

3

0

3

0

5

5

maTS3n

0

0

5

2

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

4

maTS3

5

2

5

5

5

5

5

5

5

5

0

5

0

5

5

5

5

2

0

2

0

5

5

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

4

0

0

0

0

1

0

maTS

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

4

0

0

0

0

1

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

TS2n

4

2

5

5

5

5

5

5

5

5

1

4

0

5

5

5

5

0

0

0

1

5

5

TS2

5

3

5

5

5

5

5

5

5

5

0

5

0

5

5

5

5

3

0

3

0

5

5

TS3n

4

2

5

5

5

5

5

5

5

5

1

4

0

5

5

5

5

0

0

0

1

5

5

TS3

4

2

5

5

5

5

5

5

5

5

0

5

0

5

5

5

5

1

0

1

0

5

5

TSn

1

0

4

1

4

0

0

4

4

0

0

0

0

4

4

4

4

0

0

0

0

0

2

TS

0

0

5

0

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

0

 

Table 8. Instance  10ζ2020

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

5

5

5

0

0

5

5

1

0

0

0

5

5

5

5

0

0

0

0

5

2

GAucx

3

0

5

5

5

1

1

5

5

3

0

4

0

5

5

5

5

2

0

2

0

5

5

GAux

0

0

0

1

2

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

0

HCn

0

0

3

0

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

1

0

HC

0

0

0

0

0

0

0

2

1

0

0

0

0

5

5

5

5

0

0

0

0

1

0

maHCn

1

0

5

5

5

0

0

5

5

2

0

0

0

5

5

5

5

1

0

1

0

5

5

maHC

1

0

5

5

5

1

0

5

5

2

0

1

0

5

5

5

5

1

0

1

0

5

5

maSA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

5

0

0

0

0

1

0

maSA

0

0

0

0

0

0

0

0

0

0

0

0

0

1

1

4

5

0

0

0

0

1

0

maTS2n

0

0

5

2

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

1

maTS2

5

1

5

5

5

5

5

5

5

5

0

5

0

5

5

5

5

3

0

3

0

5

5

maTS3n

0

0

5

3

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

2

maTS3

5

2

5

5

5

5

5

5

5

5

0

5

0

5

5

5

5

2

0

2

0

5

5

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

5

0

0

0

0

1

0

maTS

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

5

0

0

0

0

1

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

1

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

TS2n

2

1

5

5

5

3

3

5

5

3

0

3

0

5

5

5

5

0

1

0

0

5

4

TS2

5

2

5

5

5

5

5

5

5

5

0

5

1

5

5

5

5

3

0

3

0

5

5

TS3n

2

1

5

5

5

3

3

5

5

3

0

3

0

5

5

5

5

0

1

0

0

5

4

TS3

4

1

5

5

5

5

4

5

5

5

0

5

0

5

5

5

5

2

0

2

0

5

5

TSn

0

0

1

0

3

0

0

4

4

0

0

0

0

4

4

4

4

0

0

0

0

0

0

TS

0

0

5

3

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

0

 

Table 9. Instance  10ζ3025

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

5

0

5

4

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

0

4

GAucx

4

0

5

5

5

5

2

5

5

0

0

0

0

5

5

5

5

0

0

0

0

5

5

GAux

0

0

0

0

1

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

0

0

HCn

0

0

5

0

5

5

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

0

5

HC

0

0

0

0

0

0

0

5

2

0

0

0

0

4

5

5

5

0

0

0

0

0

0

maHCn

0

0

5

0

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

0

0

maHC

1

0

5

4

5

5

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

5

maSA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

5

0

0

0

0

0

0

maSA

0

0

0

0

0

0

0

3

0

0

0

0

0

4

3

4

5

0

0

0

0

0

0

maTS2n

1

0

5

3

5

5

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

5

maTS2

5

5

5

5

5

5

5

5

5

5

0

5

0

5

5

5

5

5

4

5

4

5

5

maTS3n

1

0

5

4

5

5

1

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

5

maTS3

5

5

5

5

5

5

5

5

5

5

0

5

0

5

5

5

5

4

2

4

4

5

5

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

4

0

0

0

0

0

0

maTS

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

4

0

0

0

0

0

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

0

0

0

0

0

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

TS2n

5

3

5

5

5

5

5

5

5

5

0

4

0

5

5

5

5

0

1

0

2

5

5

TS2

5

5

5

5

5

5

5

5

5

4

0

5

0

5

5

5

5

3

0

3

1

5

5

TS3n

5

3

5

5

5

5

5

5

5

5

0

4

0

5

5

5

5

0

1

0

2

5

5

TS3

5

4

5

5

5

5

5

5

5

4

0

4

0

5

5

5

5

2

0

2

0

5

5

TSn

0

0

5

0

5

5

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

0

5

TS

0

0

5

0

5

2

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

0

0

 

Table 10. Instance  15ζ3040

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

5

1

5

4

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

5

GAucx

4

0

5

4

5

5

1

5

5

3

0

4

0

5

5

5

5

0

0

0

0

4

5

GAux

0

0

0

0

3

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

1

0

HCn

0

0

5

0

5

4

0

5

5

0

0

1

0

5

5

5

5

0

0

0

0

1

5

HC

0

0

0

0

0

0

0

4

1

0

0

0

0

5

2

5

5

0

0

0

0

1

0

maHCn

0

0

5

0

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

1

4

maHC

4

0

5

3

5

5

0

5

5

2

0

2

0

5

5

5

5

0

0

0

0

3

5

maSA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

5

5

0

0

0

0

1

0

maSA

0

0

0

0

0

0

0

3

0

0

0

0

0

4

3

5

5

0

0

0

0

1

0

maTS2n

0

0

5

2

5

4

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

5

maTS2

5

4

5

5

5

5

5

5

5

5

0

5

0

5

5

5

5

3

2

3

3

5

5

maTS3n

0

0

5

1

5

3

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

5

maTS3

5

5

5

5

5

5

5

5

5

5

0

5

0

5

5

5

5

3

2

3

3

5

5

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

5

5

0

0

0

0

1

0

maTS

0

0

0

0

0

0

0

1

0

0

0

0

0

1

0

5

5

0

0

0

0

1

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

1

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

TS2n

5

3

5

5

5

5

5

5

5

4

2

5

1

5

5

5

5

0

2

0

2

5

5

TS2

5

3

5

5

5

5

5

5

5

4

0

5

0

5

5

5

5

1

0

1

3

5

5

TS3n

5

3

5

5

5

5

5

5

5

4

2

5

1

5

5

5

5

0

2

0

2

5

5

TS3

5

1

5

5

5

5

4

5

5

4

0

5

0

5

5

5

5

0

0

0

0

5

5

TSn

0

0

4

0

4

3

0

4

4

0

0

1

0

4

4

4

4

0

0

0

0

0

3

TS

0

0

5

0

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

0

 

Table 11. Instance  15ζ4030

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

5

0

5

5

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

5

GAucx

5

0

5

2

5

5

5

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

5

GAux

0

0

0

0

3

0

0

5

4

0

0

0

0

5

5

5

5

0

0

0

0

1

0

HCn

4

1

5

0

5

5

4

5

5

0

0

0

0

5

5

5

5

0

0

0

0

1

5

HC

0

0

0

0

0

0

0

0

0

0

0

0

0

5

5

5

5

0

0

0

0

1

0

maHCn

0

0

5

0

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

1

0

maHC

2

0

5

1

5

5

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

5

maSA*

0

0

0

0

0

0

0

0

0

0

0

0

0

5

5

5

5

0

0

0

0

1

0

maSA

0

0

0

0

0

0

0

0

0

0

0

0

0

5

5

5

5

0

0

0

0

1

0

maTS2n

5

1

5

3

5

5

5

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

5

maTS2

5

5

5

5

5

5

5

5

5

3

0

4

0

5

5

5

5

4

3

4

5

5

5

maTS3n

5

1

5

1

5

5

5

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

5

maTS3

5

5

5

5

5

5

5

5

5

4

0

5

0

5

5

5

5

2

3

2

5

5

5

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

5

0

0

0

0

1

0

maTS

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

4

5

0

0

0

0

1

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

3

0

0

0

0

1

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

TS2n

5

3

5

4

5

5

5

5

5

2

1

2

1

5

5

5

5

0

2

0

3

4

5

TS2

5

5

5

4

5

5

5

5

5

1

0

2

0

5

5

5

5

1

0

1

2

4

5

TS3n

5

3

5

4

5

5

5

5

5

2

1

2

1

5

5

5

5

0

2

0

3

4

5

TS3

5

2

5

1

5

5

5

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

5

TSn

2

1

4

0

4

4

2

4

4

0

0

0

0

4

4

4

4

0

0

0

0

0

4

TS

0

0

5

0

5

5

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

1

0

 

Table 12. Instance  20ζ4060

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

5

1

5

5

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

5

GAucx

5

0

5

4

5

5

1

5

5

1

0

1

0

5

5

5

5

1

0

1

1

5

5

GAux

0

0

0

0

3

0

0

4

2

0

0

0

0

5

4

5

5

0

0

0

0

1

0

HCn

1

0

5

0

5

4

1

5

5

0

0

0

0

5

5

5

5

0

0

0

1

2

4

HC

0

0

0

0

0

0

0

2

0

0

0

0

0

4

0

5

5

0

0

0

0

1

0

maHCn

0

0

5

1

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

0

maHC

3

0

5

2

5

5

0

5

5

1

0

0

0

5

5

5

5

1

0

1

1

4

5

maSA*

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

5

5

0

0

0

0

1

0

maSA

0

0

0

0

0

0

0

3

0

0

0

0

0

5

2

5

5

0

0

0

0

1

0

maTS2n

1

0

5

1

5

5

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

5

maTS2

5

5

5

5

5

5

5

5

5

5

0

5

0

5

5

5

5

3

5

3

5

5

5

maTS3n

3

0

5

1

5

5

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

5

maTS3

5

4

5

5

5

5

5

5

5

5

0

5

0

5

5

5

5

3

5

3

5

5

5

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

5

5

0

0

0

0

1

0

maTS

0

0

0

0

0

0

0

2

0

0

0

0

0

3

0

5

5

0

0

0

0

1

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

0

0

0

0

1

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

TS2n

4

3

5

4

5

5

4

5

5

3

1

3

1

5

5

5

5

0

3

0

4

4

5

TS2

5

0

5

5

5

5

4

5

5

4

0

4

0

5

5

5

5

2

0

2

5

5

5

TS3n

4

3

5

4

5

5

4

5

5

3

1

3

1

5

5

5

5

0

3

0

4

4

5

TS3

3

0

5

4

5

5

0

5

5

1

0

0

0

5

5

5

5

0

0

0

0

4

5

TSn

1

0

4

0

4

2

1

4

4

0

0

0

0

4

4

4

3

0

0

0

1

0

2

TS

0

0

5

1

5

2

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

0

 

Tabla 13. Instance  24ζ2030

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

5

2

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

1

GAucx

4

0

5

4

5

1

0

5

5

4

0

4

0

5

5

5

5

3

0

3

0

4

5

GAux

0

0

0

0

3

0

0

3

5

0

0

0

0

5

5

5

5

0

0

0

0

0

0

HCn

1

0

5

0

5

0

0

5

5

0

0

1

0

5

5

5

5

0

0

0

0

0

2

HC

0

0

0

0

0

0

0

0

0

0

0

0

0

5

4

4

5

0

0

0

0

0

0

maHCn

2

0

5

3

5

0

0

5

5

4

0

3

0

5

5

5

5

1

0

1

0

3

5

maHC

2

0

5

3

5

0

0

5

5

3

0

3

0

5

5

5

5

1

0

1

0

3

3

maSA*

0

0

0

0

0

0

0

0

1

0

0

0

0

4

4

4

5

0

0

0

0

0

0

maSA

0

0

0

0

0

0

0

0

0

0

0

0

0

5

4

4

5

0

0

0

0

0

0

maTS2n

0

0

5

3

5

0

0

5

5

0

0

0

0

5

5

5

5

1

0

1

0

3

0

maTS2

5

3

5

5

5

5

5

5

5

5

0

5

0

5

5

5

5

4

0

4

0

5

5

maTS3n

0

0

5

2

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

0

maTS3

5

2

5

5

5

3

4

5

5

5

0

5

0

5

5

5

5

4

0

4

0

5

5

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

4

0

0

0

0

0

0

maTS

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

5

0

0

0

0

0

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

TS2n

3

1

5

3

5

1

1

5

5

3

0

3

0

5

5

5

5

0

0

0

0

3

4

TS2

5

4

5

5

5

5

5

5

5

5

0

5

0

5

5

5

5

4

0

4

0

5

5

TS3n

3

1

5

3

5

1

1

5

5

3

0

3

0

5

5

5

5

0

0

0

0

3

4

TS3

5

1

5

5

5

4

4

5

5

5

0

5

0

5

5

5

5

4

0

4

0

5

5

TSn

1

0

5

1

5

0

0

5

5

0

0

1

0

5

5

5

5

0

0

0

0

0

2

TS

0

0

5

3

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

2

0

 

Tabla 14. Instance  24ζ2036

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

5

5

5

0

0

5

5

1

0

1

0

5

5

5

5

1

0

1

0

5

5

GAucx

3

0

5

5

5

0

0

5

5

4

0

5

0

5

5

5

5

1

0

1

0

5

5

GAux

0

0

0

0

2

0

0

2

4

0

0

0

0

5

5

5

5

0

0

0

0

0

0

HCn

0

0

5

0

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

1

0

HC

0

0

0

0

0

0

0

0

0

0

0

0

0

4

4

5

5

0

0

0

0

0

0

maHCn

1

0

5

5

5

0

0

5

5

3

0

2

0

5

5

5

5

1

0

1

0

5

5

maHC

2

0

5

5

5

0

0

5

5

3

0

2

0

5

5

5

5

1

0

1

0

5

5

maSA*

0

0

0

0

1

0

0

0

1

0

0

0

0

5

5

5

5

0

0

0

0

0

0

maSA

0

0

0

0

0

0

0

0

0

0

0

0

0

4

5

5

5

0

0

0

0

0

0

maTS2n

0

0

5

3

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

2

maTS2

5

3

5

5

5

5

5

5

5

5

0

5

0

5

5

5

5

2

0

2

0

5

5

maTS3n

0

0

5

5

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

5

3

maTS3

5

1

5

5

5

4

4

5

5

5

0

5

0

5

5

5

5

2

1

2

1

5

5

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

5

0

0

0

0

0

0

maTS

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

3

5

0

0

0

0

0

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

0

0

0

0

0

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

TS2n

4

1

5

5

5

3

3

5

5

4

1

4

1

5

5

5

5

0

1

0

1

5

4

TS2

5

3

5

5

5

5

5

5

5

5

0

5

1

5

5

5

5

4

0

4

0

5

5

TS3n

4

1

5

5

5

3

3

5

5

4

1

4

1

5

5

5

5

0

1

0

1

5

4

TS3

5

0

5

5

5

5

5

5

5

5

0

5

0

5

5

5

5

2

0

2

0

5

5

TSn

0

0

4

0

5

0

0

5

5

0

0

0

0

5

5

5

4

0

0

0

0

0

0

TS

0

0

5

3

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

0

 

Table 15. Instance  25ζ5040

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

5

2

5

5

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

3

GAucx

5

0

5

3

5

5

5

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

5

GAux

0

0

0

0

3

1

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

1

0

HCn

1

1

4

0

4

4

1

4

4

0

0

0

0

4

4

5

5

0

0

0

0

2

3

HC

0

0

0

0

0

0

0

0

0

0

0

0

0

3

3

5

5

0

0

0

0

1

0

maHCn

0

0

0

0

1

0

0

3

0

0

0

0

0

5

5

5

5

0

0

0

0

1

0

maHC

0

0

5

2

5

5

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

3

maSA*

0

0

0

0

0

0

0

0

0

0

0

0

0

1

4

5

5

0

0

0

0

1

0

maSA

0

0

0

0

0

0

0

3

0

0

0

0

0

5

5

5

5

0

0

0

0

1

0

maTS2n

5

4

5

4

5

5

5

5

5

0

0

0

0

5

5

5

5

0

0

0

3

4

5

maTS2

5

5

5

5

5

5

5

5

5

4

0

3

1

5

5

5

5

4

5

4

5

5

5

maTS3n

5

4

5

5

5

5

5

5

5

0

0

0

0

5

5

5

5

1

0

1

2

5

5

maTS3

5

5

5

5

5

5

5

5

5

0

0

0

0

5

5

5

5

2

2

2

5

5

5

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

4

5

0

0

0

0

1

0

maTS

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

4

5

0

0

0

0

1

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

0

0

0

0

1

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

TS2n

5

4

5

5

5

5

5

5

5

2

1

2

1

5

5

5

5

0

4

0

5

5

5

TS2

5

5

5

4

5

5

5

5

5

0

0

0

0

5

5

5

5

1

0

1

5

4

5

TS3n

5

4

5

5

5

5

5

5

5

2

1

2

1

5

5

5

5

0

4

0

5

5

5

TS3

5

3

5

3

5

5

5

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

5

TSn

1

1

4

0

4

4

1

4

4

0

0

0

0

4

4

4

4

0

0

0

0

0

2

TS

0

0

5

1

5

5

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

0

 

Table 16. Instance  30ζ2040

 

 

GAap

GAucx

GAux

HCn

HC

maHCn

maHC

maSA*

maSA

maTS2n

maTS2

maTS3n

maTS3

maTSn

maTS

SA*

SA

TS2n

TS2

TS3n

TS3

TSn

TS

GAap

0

0

5

4

5

0

0

5

5

1

0

2

0

5

5

5

5

0

0

0

0

4

4

GAucx

2

0

5

4

5

2

2

5

5

3

0

3

0

5

5

5

5

1

0

1

0

4

5

GAux

0

0

0

1

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

1

0

HCn

1

0

4

0

5

1

0

5

5

1

0

1

0

5

5

5

5

1

0

1

0

0

1

HC

0

0

0

0

0

0

0

4

0

0

0

0

0

5

5

5

5

0

0

0

0

0

0

maHCn

1

0

5

4

5

0

0

5

5

4

0

3

0

5

5

5

5

0

0

0

0

4

5

maHC

1

0

5

4

5

0

0

5

5

3

0

3

0

5

5

5

5

1

0

1

0

4

5

maSA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

2

5

0

0

0

0

0

0

maSA

0

0

0

0

0

0

0

0

0

0

0

0

0

5

4

4

5

0

0

0

0

0

0

maTS2n

0

0

5

4

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

4

1

maTS2

5

4

5

5

5

5

5

5

5

5

0

5

2

5

5

5

5

1

0

1

2

5

5

maTS3n

0

0

5

3

5

0

0

5

5

0

0

0

0

5

5

5

5

0

0

0

0

3

2

maTS3

4

1

5

5

5

4

4

5

5

5

0

5

0

5

5

5

5

1

0

1

0

5

5

maTSn

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

5

0

0

0

0

0

0

maTS

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

4

0

0

0

0

0

0

SA*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

0

0

0

0

0

0

SA

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

TS2n

4

4

5

4

5

4

4

5

5

5

2

5

2

5

5

5

5

0

1

0

3

4

5

TS2

5

4

5

5

5

5

5

5

5

5

0

5

1

5

5

5

5

1

0

1

2

5

5

TS3n

4

4

5

4

5

4

4

5

5

5

2

5

2

5

5

5

5

0

1

0

3

4

5

TS3

4

1

5

5

5

3

4

5

5

5

0

5

0

5

5

5

5

1

0

1

0

5

5

TSn

1

0

4

0

5

1

0

5

5

1

0

1

0

5

5

5

5

1

0

1

0

0

1

TS

0

0

5

4

5

0

0

5

5

0

0

1

0

5

5

5

5

0

0

0

0

4

0

 

 

 

 

 

Last update: 9 November 2008                                              Comments: jedgar@unet.edu.ve