Research Article
Improving the Bin Packing Heuristic through Grammatical Evolution Based on Swarm Intelligence
Table 4
Results obtained by each heuristic over the instance set.
| Instance | Fitness function | PSO | PESO | Grammar 1 | Grammar 2 | Grammar 3 | Grammar 1 | Grammar 2 | Grammar 3 |
| bin1data | Equation (7) | 316.106020 | 316.106050 | 68.167305 | 316.106020 | 316.106050 | 68.090770 | Bins used | 101097 | 101097 | 101097 | 101097 | 101097 | 78660 | Leftover bins | 22719 | 22719 | 22719 | 22719 | 22719 | 282 |
| bin2data | Equation (7) | 93.388510 | 93.025230 | 44.561455 | 93.388510 | 93.007030 | 44.560112 | Bins used | 23094 | 23156 | 23583 | 23097 | 23156 | 20994 | Leftover bins | 2848 | 2910 | 3337 | 2851 | 2910 | 748 |
| bin3data | Equation (7) | 1.885825 | 1.885825 | 1.390289 | 1.885825 | 1.885825 | 1.390289 | Bins used | 613 | 622 | 650 | 613 | 622 | 596 | Leftover bins | 51 | 60 | 88 | 51 | 60 | 34 |
| binpack1 | Equation (7) | 2.604965 | 2.425894 | 0.914034 | 2.604965 | 2.425894 | 0.913949 | Bins used | 1044 | 1131 | 1372 | 1044 | 1131 | 995 | Leftover bins | 63 | 150 | 391 | 63 | 150 | 14 |
| binpack2 | Equation (7) | 2.396851 | 2.259154 | 0.706004 | 2.396851 | 2.259154 | 0.705970 | Bins used | 2162 | 2342 | 2851 | 2162 | 2342 | 2062 | Leftover bins | 130 | 310 | 819 | 130 | 310 | 30 |
| binpack3 | Equation (7) | 2.133326 | 2.014334 | 0.591543 | 2.133326 | 2.014334 | 0.591541 | Bins used | 4255 | 4614 | 5647 | 4255 | 4614 | 4078 | Leftover bins | 231 | 590 | 1623 | 231 | 590 | 54 |
| binpack4 | Equation (7) | 1.935710 | 1.838669 | 0.495522 | 1.935710 | 1.838669 | 0.495512 | Bins used | 8430 | 9154 | 11253 | 8430 | 9154 | 8108 | Leftover bins | 419 | 1143 | 3242 | 419 | 1143 | 97 |
| binpack5 | Equation (7) | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | Bins used | 400 | 400 | 400 | 400 | 400 | 400 | Leftover bins | 0 | 0 | 0 | 0 | 0 | 0 |
| binpack6 | Equation (7) | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | Bins used | 800 | 800 | 800 | 800 | 800 | 800 | Leftover bins | 0 | 0 | 0 | 0 | 0 | 0 |
| binpack7 | Equation (7) | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | Bins used | 1660 | 1660 | 1660 | 1660 | 1660 | 1660 | Leftover bins | 0 | 0 | 0 | 0 | 0 | 0 |
| binpack8 | Equation (7) | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | Bins used | 3340 | 3340 | 3340 | 3340 | 3340 | 3340 | Leftover bins | 0 | 0 | 0 | 0 | 0 | 0 |
| hard28 | Equation (7) | 0.655350 | 0.655480 | 0.655350 | 0.655350 | 0.655480 | 0.655480 | Bins used | 1995 | 2024 | 2755 | 1995 | 2024 | 1995 | Leftover bins | 23 | 52 | 783 | 23 | 52 | 23 |
| Remaining bins | 26484 | 27934 | 33002 | 26487 | 27934 | 1282 |
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