Table 4 Average Bin Usage (ABU) obtained by the heuristics and a few selected HHs on the literature testing set (BTS-II).
From: A steady state micro genetic algorithm for hyper-heuristic generation in one-dimensional bin packing
Dataset | Stat | FF | BF | WF | AWF | HHGA\(_{1}\) | HHGA\(_{2}\) | HH\(\mu\)GA\(_{1}\) | HH\(\mu\)GA\(_{2}\) | HHSSGA\(_{1}\) | HHSSGA\(_{2}\) | HHSS\(\mu\)GA\(_{1}\) | HHSS\(\mu\)GA\(_{2}\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
FalkenauerU | Mean | 0.8866 | 0.8951 | 0.7594 | 0.8486 | 0.8949 | 0.8951 | 0.8951 | 0.8948 | 0.8950 | 0.8951 | 0.8548 | 0.8951 |
Stddev | 0.0210 | 0.0204 | 0.0253 | 0.0185 | 0.0205 | 0.0204 | 0.0204 | 0.0204 | 0.0204 | 0.0204 | 0.0603 | 0.0204 | |
Error | 0.7786 | 0.1046 | 10.9561 | 3.8191 | 0.1191 | 0.1058 | 0.1063 | 0.1263 | 0.1062 | 0.1059 | 3.3612 | 0.1055 | |
Worse | 65 | 14 | 80 | 80 | 20 | 15 | 17 | 21 | 16 | 16 | 71 | 15 | |
Equal | 15 | 66 | 0 | 0 | 58 | 65 | 62 | 58 | 64 | 64 | 3 | 65 | |
Better | 0 | 0 | 0 | 0 | 2 | 0 | 1 | 1 | 0 | 0 | 6 | 0 | |
Scholl01 | Mean | 0.8115 | 0.8276 | 0.7092 | 0.7812 | 0.8271 | 0.8273 | 0.8274 | 0.8274 | 0.8275 | 0.8275 | 0.7623 | 0.8276 |
Stddev | 0.0660 | 0.0654 | 0.0486 | 0.0548 | 0.0650 | 0.0652 | 0.0653 | 0.0653 | 0.0653 | 0.0653 | 0.0883 | 0.0654 | |
Error | 11.8965 | 0.3705 | 85.5878 | 33.7754 | 0.6871 | 0.5429 | 0.4582 | 0.4565 | 0.4245 | 0.3752 | 47.3314 | 0.3706 | |
Worse | 676 | 44 | 719 | 710 | 97 | 93 | 54 | 53 | 52 | 46 | 658 | 45 | |
Equal | 44 | 676 | 1 | 10 | 617 | 626 | 666 | 666 | 668 | 674 | 57 | 675 | |
Better | 0 | 0 | 0 | 0 | 6 | 1 | 0 | 1 | 0 | 0 | 5 | 0 | |
Scholl02 | Mean | 0.8877 | 0.8898 | 0.8404 | 0.8817 | 0.8892 | 0.8892 | 0.8892 | 0.8875 | 0.8893 | 0.8892 | 0.8803 | 0.8892 |
Stddev | 0.0507 | 0.0508 | 0.0542 | 0.0499 | 0.0503 | 0.0503 | 0.0503 | 0.0485 | 0.0503 | 0.0503 | 0.0614 | 0.0503 | |
Error | 1.1100 | 0.1259 | 23.8095 | 3.9988 | 0.4066 | 0.3923 | 0.4029 | 1.2083 | 0.3719 | 0.3948 | 4.7693 | 0.3888 | |
Worse | 209 | 77 | 430 | 281 | 122 | 136 | 136 | 153 | 125 | 136 | 185 | 132 | |
Equal | 271 | 403 | 50 | 199 | 356 | 343 | 344 | 321 | 355 | 344 | 285 | 348 | |
Better | 0 | 0 | 0 | 0 | 2 | 1 | 0 | 6 | 0 | 0 | 10 | 0 | |
Scholl03 | Mean | 0.7975 | 0.7975 | 0.7939 | 0.7970 | 0.7975 | 0.7975 | 0.7975 | 0.7975 | 0.7975 | 0.7975 | 0.7975 | 0.7975 |
Stddev | 0.0120 | 0.0120 | 0.0109 | 0.0114 | 0.0120 | 0.0120 | 0.0120 | 0.0120 | 0.0120 | 0.0120 | 0.0120 | 0.0120 | |
Error | 0.0022 | 0.0022 | 0.0385 | 0.0076 | 0.0022 | 0.0022 | 0.0022 | 0.0022 | 0.0022 | 0.0022 | 0.0022 | 0.0022 | |
Worse | 5 | 5 | 7 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | |
Equal | 5 | 5 | 3 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | |
Better | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Waescher | Mean | 0.9093 | 0.9067 | 0.8507 | 0.9006 | 0.9089 | 0.9059 | 0.9060 | 0.9057 | 0.9067 | 0.9059 | 0.9067 | 0.9060 |
Stddev | 0.0178 | 0.0208 | 0.0494 | 0.0217 | 0.0175 | 0.0205 | 0.0205 | 0.0208 | 0.0209 | 0.0204 | 0.0208 | 0.0205 | |
Error | 0.0134 | 0.0570 | 1.0089 | 0.1603 | 0.0188 | 0.0707 | 0.0695 | 0.0737 | 0.0587 | 0.0702 | 0.0579 | 0.0695 | |
Worse | 6 | 1 | 17 | 14 | 4 | 5 | 5 | 8 | 4 | 6 | 3 | 5 | |
Equal | 11 | 16 | 0 | 3 | 13 | 12 | 11 | 9 | 12 | 11 | 13 | 12 | |
Better | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | |
Hard28 | Mean | 0.8679 | 0.8887 | 0.7016 | 0.8049 | 0.8885 | 0.8884 | 0.8886 | 0.8887 | 0.8886 | 0.8887 | 0.8587 | 0.8887 |
Stddev | 0.0315 | 0.0297 | 0.0256 | 0.0246 | 0.0298 | 0.0300 | 0.0298 | 0.0297 | 0.0298 | 0.0297 | 0.0319 | 0.0297 | |
Error | 0.6061 | 0.0237 | 5.2603 | 2.3689 | 0.0287 | 0.0320 | 0.0263 | 0.0240 | 0.0260 | 0.0237 | 0.8632 | 0.0237 | |
Worse | 25 | 3 | 28 | 28 | 12 | 14 | 12 | 4 | 10 | 3 | 28 | 3 | |
Equal | 3 | 25 | 0 | 0 | 15 | 14 | 16 | 24 | 18 | 25 | 0 | 25 | |
Better | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Irnich | Mean | 0.9263 | 0.9326 | 0.7570 | 0.8535 | 0.9325 | 0.9326 | 0.9326 | 0.9326 | 0.9326 | 0.9326 | 0.9134 | 0.9326 |
Stddev | 0.0287 | 0.0292 | 0.0222 | 0.0141 | 0.0291 | 0.0292 | 0.0292 | 0.0292 | 0.0292 | 0.0292 | 0.0643 | 0.0292 | |
Error | 1.5214 | 0.0000 | 42.1449 | 18.9898 | 0.0377 | 0.0051 | 0.0038 | 0.0150 | 0.0031 | 0.0053 | 4.6298 | 0.0048 | |
Worse | 239 | 0 | 240 | 240 | 43 | 23 | 24 | 24 | 20 | 20 | 165 | 16 | |
Equal | 1 | 240 | 0 | 0 | 192 | 216 | 214 | 216 | 219 | 216 | 71 | 221 | |
Better | 0 | 0 | 0 | 0 | 5 | 1 | 2 | 0 | 1 | 4 | 4 | 3 | |
IRUP | Mean | 0.9387 | 0.9590 | 0.7573 | 0.8465 | 0.9400 | 0.9389 | 0.9588 | 0.9588 | 0.9588 | 0.9510 | 0.9584 | 0.9556 |
Stddev | 0.0148 | 0.0153 | 0.0144 | 0.0090 | 0.0157 | 0.0148 | 0.0153 | 0.0152 | 0.0155 | 0.0149 | 0.0157 | 0.0178 | |
Error | 5.0781 | 0.0000 | 50.4265 | 28.1368 | 4.7399 | 5.0209 | 0.0519 | 0.0397 | 0.0941 | 2.0430 | 0.1500 | 0.8502 | |
Worse | 250 | 0 | 250 | 250 | 250 | 250 | 126 | 38 | 55 | 212 | 154 | 147 | |
Equal | 0 | 250 | 0 | 0 | 0 | 0 | 114 | 212 | 160 | 34 | 78 | 100 | |
Better | 0 | 0 | 0 | 0 | 0 | 0 | 10 | 0 | 35 | 4 | 18 | 3 | |
nonIRUP | Mean | 0.9309 | 0.9503 | 0.7523 | 0.8406 | 0.9368 | 0.9318 | 0.9500 | 0.9502 | 0.9501 | 0.9479 | 0.9501 | 0.9488 |
Stddev | 0.0176 | 0.0132 | 0.0215 | 0.0124 | 0.0186 | 0.0174 | 0.0133 | 0.0132 | 0.0132 | 0.0151 | 0.0132 | 0.0145 | |
Error | 4.8406 | 0.0000 | 49.4970 | 27.4095 | 3.3778 | 4.6076 | 0.0625 | 0.0128 | 0.0301 | 0.6022 | 0.0503 | 0.3702 | |
Worse | 250 | 0 | 250 | 250 | 242 | 250 | 93 | 13 | 27 | 186 | 120 | 144 | |
Equal | 0 | 250 | 0 | 0 | 1 | 0 | 157 | 233 | 220 | 54 | 125 | 105 | |
Better | 0 | 0 | 0 | 0 | 7 | 0 | 0 | 4 | 3 | 10 | 5 | 1 |
