Table 1: Results of local search heuristics on benchmark data.

Instance CONS [10] R-CONS [13, 19] R-CONS-L
Result1 Best2 Ave2 CPU3 Best2 Ave2 CPU3

5.100–0.25 13.70 9.71 22.32 2.20 2.47 3.20 286
5.100–0.50 7.25 5.73 14.00 1.57 1.10 1.35 292
5.100–0.75 5.14 3.70 7.98 0.87 0.72 0.83 278

Average (5.100−*) 8.70 6.38 14.77 1.55 1.43 1.79 285

5.250–0.25 6.77 7.62 17.65 13.23 0.92 1.03 703
5.250–0.50 5.27 4.94 11.27 9.24 0.49 0.56 722
5.250–0.75 3.55 3.02 6.26 5.06 0.26 0.29 679

Average (5.250−*) 5.20 5.19 11.73 9.18 0.56 0.63 701

5.500–0.25 4.93 7.80 15.27 53.00 0.48 0.50 1414
5.500–0.50 2.65 4.18 9.45 36.56 0.20 0.22 1464
5.500–0.75 2.22 2.63 5.43 19.75 0.14 0.15 1367

Average (5.500−*) 3.27 4.87 10.05 36.44 0.27 0.29 1415

Average (5.*−*) 5.72 5.48 12.18 15.72 0.75 0.91 800

10.100–0.25 15.88 11.49 22.93 3.66 2.75 6.30 536
10.100–0.50 10.01 7.75 14.76 2.63 1.47 3.68 543
10.100–0.75 6.57 3.61 8.05 1.42 0.91 2.02 532

Average (10.100−*) 10.82 7.62 15.25 2.57 1.71 4.00 537

10.250–0.25 11.26 10.32 17.26 22.19 1.22 3.87 1321
10.250–0.50 6.49 6.46 11.51 15.65 0.58 2.07 1344
10.250–0.75 4.16 3.43 6.05 8.40 0.36 1.23 1306

Average (10.250−*) 7.30 6.74 11.61 15.41 0.72 2.39 1323

10.500–0.25 8.27 9.59 14.91 88.30 0.64 2.89 2641
10.500–0.50 5.26 5.56 9.28 67.33 0.27 1.39 2686
10.500–0.75 3.49 3.28 5.24 32.50 0.22 0.90 2601

Average (10.500−*) 5.67 6.14 9.81 62.71 0.37 1.73 2642

Average (10.*−*) 7.93 6.83 12.22 26.90 0.93 2.71 1501

30.100–0.25 16.63 11.75 22.02 9.55 5.06 9.17 1365
30.100–0.50 10.31 7.51 14.57 6.80 2.80 5.52 1374
30.100–0.75 6.60 4.20 7.97 3.79 1.64 3.22 1363

Average (30.100−*) 11.18 7.82 14.85 6.71 3.17 5.97 1367

30.250–0.25 13.32 11.36 17.01 58.46 4.42 6.84 3364
30.250–0.50 8.19 6.71 10.87 40.51 2.36 4.11 3388
30.250–0.75 4.45 3.56 5.86 21.73 1.44 2.39 3348

Average (30.250−*) 8.65 7.21 11.25 40.23 2.74 4.45 3366

30.500–0.25 10.34 9.39 14.02 228.56 4.00 5.94 6726
30.500–0.50 6.80 6.17 9.20 157.49 2.23 3.69 6755
30.500–0.75 3.82 3.34 4.90 83.43 1.27 2.14 6659

Average (30.500−*) 6.99 6.30 9.37 156.49 2.50 3.92 6713

Average (30.*−*) 8.94 7.11 11.82 67.81 2.80 4.78 3815

Total average 7.53 6.47 12.08 36.81 1.50 2.80 2039

1Since CONS is a deterministic algorithm, each run always outputs the same result.
2Results from 1,000 runs.
3Total CPU seconds on Pentium III 997 MHz.