Table 2: Results of memetic Lagrangian heuristic on benchmark data.

Instance Multistart R-CONS-L1 Memetic Lagrangian heuristicNumber improved/number equalled
Result CPU2 Result CPU2

5.100–0.25 2.40 1435 2.32 1466 0/0
5.100–0.50 1.08 1471 1.08 1500 0/0
5.100–0.75 0.72 1394 0.72 1431 0/0

Average (5.100−*) 1.40 1433 1.37 1466 Total 0/0

5.250–0.25 0.92 3513 0.92 3619 0/0
5.250–0.50 0.49 3606 0.49 3748 0/0
5.250–0.75 0.26 3395 0.25 3529 0/0

Average (5.250−*) 0.56 3505 0.56 3632 Total 0/0

5.500–0.25 0.48 7072 0.48 7124 0/0
5.500–0.50 0.20 7318 0.20 7546 0/0
5.500–0.75 0.14 6846 0.14 6985 0/0

Average (5.500−*) 0.27 7079 0.27 7218 Total 0/0

Average (5.*−*) 0.74 4006 0.73 4105 Total 0/0

10.100–0.25 2.45 2679 2.27 2630 0/0
10.100–0.50 1.46 2717 1.14 2650 0/1
10.100–0.75 0.89 2657 0.69 2598 0/0

Average (10.100−*) 1.60 2684 1.37 2626 Total 0/1

10.250–0.25 1.14 6599 0.88 6441 0/0
10.250–0.50 0.57 6718 0.45 6558 0/0
10.250–0.75 0.35 6535 0.24 6408 0-1

Average (10.250−*) 0.69 6617 0.52 6469 Total 0/1

10.500–0.25 0.58 13196 0.50 12811 0/0
10.500–0.50 0.27 13425 0.24 13057 0/0
10.500–0.75 0.21 13006 0.14 12750 0/0

Average (10.500−*) 0.35 13209 0.29 12873 Total 0/0

Average (10.*−*) 0.88 7504 0.73 7323 Total 0/2

30.100–0.25 4.92 6824 3.19 6796 0/3
30.100–0.50 2.67 6870 1.43 7052 0/3
30.100–0.75 1.56 6817 0.89 6780 0/2

Average (30.100−*) 3.05 6837 1.84 6876 Total 0/8

30.250–0.25 4.24 16819 1.28 16799 2/2
30.250–0.50 2.23 16941 0.59 16958 0/0
30.250–0.75 1.40 16742 0.34 16837 0/0

Average (30.250−*) 2.62 16834 0.74 16865 Total 2/2

30.500–0.25 3.81 33630 0.68 33414 2/0
30.500–0.50 2.13 33802 0.29 33737 1/0
30.500–0.75 1.24 33318 0.19 33440 0/0

Average (30.500−*) 2.39 33583 0.39 33530 Total 3/0

Average (30.*−*) 2.69 19085 0.99 19090 Total 5/10

Total average 1.44 10198 0.82 10173 Total 5/12

1Multistart R-CONS-L returns the best result from 5,000 independent runs of R-CONS-L.
2Average CPU seconds on Pentium III 997 MHz.