Research Article
A Novel Discrete Global-Best Harmony Search Algorithm for Solving 0-1 Knapsack Problems
Table 4
Comparison among three algorithms on solving 0-1 knapsack problems with small or median sizes.
| No. | Dim. | maxFEs | Approach | Best | Worst | Median | Mean | Std. | SR |
| Kp1 | 10 | | GHS | 295 | 293 | 295 | 294.9 | 0.3136 | 48/50 | NGHS | 295 | 295 | 295 | 295 | 0 | 50/50 | DGHS | 295 | 295 | 295 | 295 | 0 | 50/50 |
| Kp2 | 20 | | GHS | 1024 | 1018 | 1024 | 1023.7 | 1.1876 | 48/50 | NGHS | 1024 | 995 | 1024 | 1018.6 | 8.0585 | 28/50 | DGHS | 1024 | 1024 | 1024 | 1024 | 0 | 50/50 |
| Kp3 | 4 | | GHS | 35 | 35 | 35 | 35 | 0 | 50/50 | NGHS | 35 | 35 | 35 | 35 | 0 | 50/50 | DGHS | 35 | 35 | 35 | 35 | 0 | 50/50 |
| Kp4 | 4 | | GHS | 23 | 23 | 23 | 23 | 0 | 50/50 | NGHS | 23 | 23 | 23 | 23 | 0 | 50/50 | DGHS | 23 | 23 | 23 | 23 | 0 | 50/50 |
| Kp5 | 15 | | GHS | 481.0694 | 466.3380 | 481.0694 | 479.8091 | 3.3263 | 42/50 | NGHS | 481.0694 | 437.9345 | 481.0694 | 479.1293 | 6.5594 | 41/50 | DGHS | 481.0694 | 481.0694 | 481.0694 | 481.0694 | 0 | 50/50 |
| Kp6 | 10 | | GHS | 52 | 52 | 52 | 52 | 0 | 50/50 | NGHS | 52 | 51 | 52 | 51.9400 | 0.2399 | 47/50 | DGHS | 52 | 52 | 52 | 52 | 0 | 50/50 |
| Kp7 | 7 | | GHS | 107 | 105 | 107 | 106.8 | 0.6060 | 45/50 | NGHS | 107 | 107 | 107 | 107 | 0 | 50/50 | DGHS | 107 | 107 | 107 | 107 | 0 | 50/50 |
| Kp8 | 23 | | GHS | 9766 | 9744 | 9756.5 | 9756.2 | 5.3816 | 0/50 | NGHS | 9767 | 9760 | 9765 | 9764.3 | 2.2950 | 15/50 | DGHS | 9767 | 9767 | 9767 | 9767 | 0 | 50/50 |
| Kp9 | 5 | | GHS | 130 | 130 | 130 | 130 | 0 | 50/50 | NGHS | 130 | 130 | 130 | 130 | 0 | 50/50 | DGHS | 130 | 130 | 130 | 130 | 0 | 50/50 |
| Kp10 | 20 | | GHS | 1025 | 1019 | 1025 | 1024.1 | 2.1030 | 43/50 | NGHS | 1025 | 979 | 1025 | 1020.8 | 8.2048 | 31/50 | DGHS | 1025 | 1025 | 1025 | 1025 | 0 | 50/50 |
| Kp11 | 50 | | GHS | 2985 | 2837 | 2935 | 2932.5 | 35.9802 | 0/50 | NGHS | 3087 | 2943 | 3002 | 3006.5 | 29.2779 | 0/50 | DGHS | 3119 | 3114 | 3119 | 3118.7 | 0.9355 | 41/50 | | GHS | 3073 | 2955 | 3022 | 3018.9 | 28.1109 | 0/50 | NGHS | 3104 | 3039 | 3077 | 3076.7 | 16.0329 | 0/50 | DGHS | 3119 | 3119 | 3119 | 3119 | 0 | 50/50 |
| Kp12 | 100 | | GHS | 24551 | 22867 | 23630.5 | 23648.6 | 382.0742 | 0/50 | NGHS | 25817 | 24209 | 24974 | 25028 | 361.3838 | 0/50 | DGHS | 26559 | 26534 | 26541 | 26544 | 10.6246 | 16/50 | | GHS | 25448 | 24343 | 24891 | 24881 | 262.5590 | 0/50 | NGHS | 26418 | 25686 | 26102 | 26102 | 165.5934 | 0/50 | DGHS | 26559 | 26536 | 26559 | 26553 | 8.6175 | 33/50 | | GHS | 26079 | 24806 | 25296 | 25304 | 219.1038 | 0/50 | NGHS | 26428 | 25896 | 26282 | 26264 | 105.0596 | 0/50 | DGHS | 26559 | 26547 | 26559 | 26556 | 5.0214 | 39/50 | | GHS | 26091 | 25151 | 25685 | 25683 | 223.8487 | 0/50 | NGHS | 26489 | 26242 | 26366 | 26367 | 59.8389 | 0/50 | DGHS | 26559 | 26547 | 26559 | 26558 | 3.2886 | 46/50 | | GHS | 26172 | 25379 | 25816 | 25833 | 166.5229 | 0/50 | NGHS | 26559 | 26265 | 26424 | 26420 | 63.9882 | 1/50 | DGHS | 26559 | 26547 | 26559 | 26558.5 | 2.3754 | 48/50 | | GHS | 26326 | 25643 | 25947 | 25954 | 142.3878 | 0/50 | NGHS | 26547 | 26354 | 26441 | 26445 | 46.2120 | 0/50 | DGHS | 26559 | 26559 | 26559 | 26559 | 0 | 50/50 |
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