Discrete Dynamics in Nature and Society / 2013 / Article / Tab 1 / Research Article
A Memetic Lagrangian Heuristic for the 0-1 Multidimensional
Knapsack Problem 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
1 Since CONS is a deterministic algorithm, each run always outputs the same result.
2 Results from 1,000 runs.
3 Total CPU seconds on Pentium III 997 MHz.
