Research Article
An Accelerated Fixed-Point Algorithm Applied to Quadratic Convex Separable Knapsack Problems
Table 3
Correlated test for state-of-the-art algorithms.
| Dimension | Iterations | Time (sec) | Error | | Avg | Max | Min | Avg | Max | Min | ā |
| FPA2 | 500000 | 4.9 | 8 | 3 | 0.010 | 0.017 | 0.008 | 0 | 1000000 | 5.2 | 8 | 4 | 0.020 | 0.036 | 0.018 | 0 | 10000000 | 5.2 | 10 | 4 | 0.356 | 0.421 | 0.329 | 0 | 50000000 | 5.0 | 9 | 4 | 1.730 | 1.968 | 1.617 | 0 |
| Newton | 500000 | 4.9 | 8 | 3 | 0.017 | 0.021 | 0.013 | 0 | 1000000 | 5.1 | 8 | 4 | 0.036 | 0.045 | 0.031 | 0 | 10000000 | 5.0 | 10 | 4 | 0.407 | 0.494 | 0.359 | 0 | 50000000 | 4.9 | 9 | 4 | 1.961 | 2.345 | 1.757 | 0 |
| Variable fixing | 500000 | 8.2 | 10 | 7 | 0.021 | 0.024 | 0.019 | 0 | 1000000 | 8.4 | 10 | 7 | 0.045 | 0.049 | 0.040 | 0 | 10000000 | 8.9 | 12 | 8 | 0.517 | 0.573 | 0.482 | 0 | 50000000 | 9.0 | 12 | 8 | 2.542 | 2.695 | 2.338 | 0 |
| FPA | 500000 | 4.9 | 8 | 3 | 0.011 | 0.020 | 0.009 | 0 | 1000000 | 5.2 | 8 | 4 | 0.023 | 0.041 | 0.020 | 0 | 10000000 | 5.2 | 10 | 4 | 0.418 | 0.507 | 0.383 | 0 | 50000000 | 5.0 | 9 | 4 | 2.016 | 2.305 | 1.883 | 0 |
| Secant | 500000 | 8.1 | 12 | 6 | 0.018 | 0.032 | 0.012 | 0 | 1000000 | 8.5 | 11 | 7 | 0.037 | 0.064 | 0.025 | 0 | 10000000 | 8.3 | 12 | 6 | 0.382 | 0.637 | 0.239 | 0 | 50000000 | 7.9 | 11 | 6 | 1.927 | 3.082 | 1.016 | 0 |
| Median search | 500000 | 19.9 | 20 | 19 | 0.037 | 0.040 | 0.034 | 0 | 1000000 | 21.0 | 21 | 20 | 0.075 | 0.082 | 0.068 | 0 | 10000000 | 24.3 | 25 | 24 | 0.896 | 1.042 | 0.790 | 0 | 50000000 | 26.7 | 27 | 26 | 4.375 | 4.570 | 3.893 | 0 |
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