Research Article
Dichotomous Binary Differential Evolution for Knapsack Problems
Table 9
Results of mean number of FEs and successful rate on the multidimensional knapsack problems.
| Problem | BPSO | MBPSO | BLDE | BinDE | AQDE | DBDE | MFEs | SR (%) | MFEs | SR (%) | MFEs | SR (%) | MFEs | SR (%) | MFEs | SR (%) | MFEs | SR (%) |
| Sento1 | 6000 | 0 | 6000 | 0 | 5536 | 13 | 6000 | 0 | 6000 | 0 | 5234 | 43 | Sento2 | 6000 | 0 | 6000 | 0 | 6000 | 0 | 6000 | 0 | 6000 | 0 | 6000 | 0 |
| Weing1 | 1471 | 87 | 1951 | 73 | 1401 | 70 | 2789 | 3 | 2724 | 10 | 1642 | 100 | Weing2 | 1047 | 100 | 1819 | 93 | 617 | 100 | 2623 | 17 | 2733 | 13 | 1507 | 97 | Weing3 | 1133 | 90 | 1406 | 90 | 340 | 100 | 1588 | 73 | 2428 | 27 | 1719 | 60 | Weing4 | 888 | 100 | 1396 | 100 | 982 | 93 | 2576 | 23 | 2316 | 63 | 1390 | 100 | Weing5 | 1578 | 87 | 2347 | 60 | 818 | 93 | 2704 | 23 | 2800 | 0 | 2478 | 30 | Weing6 | 1818 | 63 | 1942 | 73 | 1490 | 67 | 2500 | 23 | 2309 | 53 | 1346 | 97 | Weing7 | 10432 | 3 | 10500 | 0 | 10500 | 0 | 10500 | 0 | 10500 | 0 | 10500 | 0 | Weing8 | 10500 | 0 | 10500 | 0 | 7401 | 47 | 10500 | 0 | 10500 | 0 | 10500 | 0 |
| Weish1 | 625 | 100 | 801 | 100 | 579 | 100 | 2077 | 53 | 1269 | 100 | 828 | 100 | Weish2 | 1836 | 60 | 2264 | 53 | 1821 | 53 | 2966 | 13 | 2677 | 33 | 1708 | 100 | Weish3 | 2518 | 43 | 2540 | 47 | 960 | 100 | 2687 | 40 | 3000 | 0 | 1200 | 100 | Weish4 | 1653 | 97 | 2131 | 77 | 874 | 97 | 2651 | 50 | 2728 | 23 | 997 | 100 | Weish5 | 483 | 100 | 610 | 100 | 465 | 100 | 1961 | 63 | 742 | 100 | 714 | 100 | Weish6 | 3455 | 23 | 3915 | 7 | 3650 | 17 | 4000 | 0 | 4000 | 0 | 3649 | 30 | Weish7 | 2202 | 93 | 3703 | 30 | 2555 | 67 | 4000 | 0 | 3943 | 10 | 3629 | 33 | Weish8 | 2677 | 57 | 3457 | 30 | 2755 | 43 | 4000 | 0 | 3808 | 13 | 2928 | 87 | Weish9 | 891 | 100 | 1658 | 100 | 710 | 100 | 3299 | 47 | 3279 | 50 | 1120 | 100 | Weish10 | 3093 | 77 | 4751 | 20 | 2353 | 87 | 5000 | 0 | 5000 | 0 | 2092 | 100 | Weish11 | 2136 | 90 | 3905 | 70 | 4143 | 27 | 4981 | 3 | 4726 | 20 | 3538 | 63 | Weish12 | 2882 | 90 | 4455 | 47 | 1872 | 97 | 5000 | 0 | 5000 | 0 | 2100 | 100 | Weish13 | 3345 | 83 | 4961 | 10 | 2104 | 97 | 5000 | 0 | 5000 | 0 | 2227 | 100 | Weish14 | 5977 | 3 | 6000 | 0 | 4601 | 40 | 6000 | 0 | 6000 | 0 | 3362 | 100 | Weish15 | 3667 | 83 | 5908 | 7 | 2997 | 93 | 6000 | 0 | 6000 | 0 | 2683 | 100 | Weish16 | 4392 | 57 | 6000 | 0 | 4215 | 57 | 6000 | 0 | 6000 | 0 | 3980 | 87 | Weish17 | 4937 | 37 | 5986 | 3 | 5806 | 10 | 6000 | 0 | 5902 | 3 | 5384 | 67 | Weish18 | 4347 | 67 | 7000 | 0 | 6519 | 20 | 7000 | 0 | 7000 | 0 | 4848 | 100 | Weish19 | 4322 | 67 | 6230 | 37 | 4191 | 63 | 7000 | 0 | 7000 | 0 | 3084 | 100 | Weish20 | 5187 | 63 | 7000 | 0 | 5811 | 47 | 7000 | 0 | 7000 | 0 | 3678 | 100 | Weish21 | 4772 | 80 | 6863 | 7 | 4470 | 80 | 7000 | 0 | 7000 | 0 | 3431 | 100 | Weish22 | 6784 | 27 | 8000 | 0 | 5148 | 60 | 8000 | 0 | 8000 | 0 | 3651 | 100 | Weish23 | 7172 | 20 | 8000 | 0 | 7641 | 10 | 8000 | 0 | 8000 | 0 | 7354 | 23 | Weish24 | 3953 | 97 | 8000 | 0 | 7200 | 47 | 8000 | 0 | 8000 | 0 | 5278 | 100 | Weish25 | 7981 | 7 | 8000 | 0 | 7572 | 23 | 8000 | 0 | 8000 | 0 | 5703 | 97 | Weish26 | 3987 | 97 | 8721 | 10 | 6333 | 67 | 9000 | 0 | 9000 | 0 | 4800 | 100 | Weish27 | 3579 | 97 | 8946 | 7 | 6881 | 43 | 9000 | 0 | 9000 | 0 | 5084 | 97 | Weish28 | 4481 | 83 | 8992 | 3 | 3951 | 87 | 9000 | 0 | 9000 | 0 | 3892 | 100 | Weish29 | 3514 | 100 | 8709 | 23 | 4604 | 97 | 9000 | 0 | 9000 | 0 | 4340 | 100 | Weish30 | 8107 | 33 | 9000 | 0 | 8449 | 17 | 9000 | 0 | 9000 | 0 | 7253 | 83 |
| Average | 3896 | 64 | 5259 | 32 | 3908 | 61 | 5610 | 11 | 5560 | 13 | 3671 | 80 |
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