Research Article
A Memetic Lagrangian Heuristic for the 0-1 Multidimensional
Knapsack Problem
Table 2
Results of memetic Lagrangian heuristic on benchmark data.
| Instance | Multistart R-CONS-L1 | Memetic Lagrangian heuristic | Number 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 |
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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.
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