Research Article
An Accelerated Fixed-Point Algorithm Applied to Quadratic Convex Separable Knapsack Problems
Table 4
Flow test for state-of-the-art algorithms.
| Dimension | Iterations | Time (sec) | Error | | Avg | Max | Min | Avg | Max | Min | ā |
| FPA2 | 500000 | 6.2 | 8 | 5 | 0.010 | 0.018 | 0.008 | 0 | 1000000 | 6.5 | 9 | 5 | 0.021 | 0.040 | 0.017 | 0 | 10000000 | 6.4 | 11 | 4 | 0.372 | 0.446 | 0.311 | 0 | 50000000 | 6.5 | 9 | 5 | 1.813 | 2.027 | 1.628 | 0 |
| Newton | 500000 | 6.1 | 8 | 4 | 0.017 | 0.022 | 0.010 | 0 | 1000000 | 6.5 | 9 | 5 | 0.036 | 0.048 | 0.025 | 0 | 10000000 | 6.1 | 10 | 4 | 0.403 | 0.507 | 0.258 | 0 | 50000000 | 6.2 | 9 | 5 | 1.978 | 2.604 | 1.542 | 0 |
| Variable fixing | 500000 | 6.2 | 8 | 5 | 0.015 | 0.021 | 0.010 | 0 | 1000000 | 6.5 | 9 | 5 | 0.033 | 0.044 | 0.022 | 0 | 10000000 | 6.5 | 11 | 4 | 0.376 | 0.467 | 0.223 | 0 | 50000000 | 6.6 | 9 | 5 | 1.860 | 2.395 | 1.340 | 0 |
| FPA | 500000 | 6.2 | 8 | 5 | 0.011 | 0.021 | 0.009 | 0 | 1000000 | 6.5 | 9 | 5 | 0.024 | 0.046 | 0.020 | 0 | 10000000 | 6.4 | 11 | 4 | 0.438 | 0.531 | 0.369 | 0 | 50000000 | 6.5 | 9 | 5 | 2.135 | 2.351 | 1.925 | 0 |
| Secant | 500000 | 14.4 | 16 | 9 | 0.018 | 0.022 | 0.013 | 0 | 1000000 | 14.6 | 19 | 11 | 0.040 | 0.052 | 0.029 | 0 | 10000000 | 14.3 | 21 | 10 | 0.425 | 0.791 | 0.283 | 0 | 50000000 | 14.2 | 17 | 9 | 2.026 | 3.088 | 1.511 | 0 |
| Median search | 500000 | 20.0 | 20 | 19 | 0.030 | 0.034 | 0.028 | 0 | 1000000 | 20.9 | 21 | 20 | 0.061 | 0.068 | 0.057 | 0 | 10000000 | 24.3 | 25 | 24 | 0.750 | 0.825 | 0.715 | 0 | 50000000 | 26.6 | 27 | 26 | 3.657 | 4.012 | 3.507 | 0 |
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