A subgradient-based branch-and-bound algorithm for the ...

Table B.4
Detailed results on instances with ratio r = 20
no. Z BB-SG B&C a CPLEX
nodes depth time time nodes time
|I| × |J| = 300 × 300
16 9158.76 65 9 1.89 59.41 76 18.94
17 9171.67 103 9 2.13 144.35 211 24.18
18 9553.60 33 7 2.09 50.83 77 24.18
19 9053.71 93 10 1.95 94.05 326 28.64
20 9046.33 5 2 0.69 7.43 6 9.37
|I| × |J| = 500 × 500
16 12584.49 229 15 10.50 436.20 818 165.68
17 13347.40 569 14 27.67 299.86 636 169.79
18 12831.13 263 10 11.46 193.37 465 119.17
19 13489.62 143 10 7.36 161.94 760 148.87
20 12342.26 117 12 8.67 112.50 389 123.86
|I| × |J| = 700 × 700
16 16000.04 153 13 14.56 313.81 852 387.52
17 16171.67 193 10 24.56 603.38 615 387.81
18 16414.81 205 12 20.42 667.77 684 550.16
19 16366.79 359 10 37.19 577.59 1021 571.46
20 15434.22 195 13 17.44 503.11 2201 890.88
|I| × |J| = 1000 × 1000
16 21331.82 4783 21 707.57 14646.77 4087 4449.72
17 21188.89 305 15 48.82 1747.62 400 604.61
18 20713.43 657 25 111.41 1264.76 780 1098.16
19 20537.45 1317 19 201.27 2427.50 3464 3136.74
20 21560.86 4749 25 574.46 3699.31 10267 10882.98
|I| × |J| = 1500 × 300
16 155489.36 1 0 10.46 146.52 2 31.50
17 156033.33 11 4 24.78 143.59 5 36.87
18 156777.58 1 0 10.71 127.95 4 34.35
19 155946.26 1 0 12.04 158.96 2 31.18
20 156409.40 b 1 0 16.13 157.92 6 34.60
a Computation times reported in Avella and Boccia (2007) divided by 2.
b Avella and Boccia (2007) report on this instance a solution value of 156, 407.23. We could
however not achieve this value.
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