Research Article
Binary Equilibrium Optimization Algorithm for Computing Connected Domination Metric Dimension Problem
| Cycle graph | N | M | | BEOA | BGWO | BPSO | BWO | BSMO | BGO | BAEO | BEHO |
| 4 | 4 | γcr | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | t(sec) | 32.1 | 48.8 | 39.8 | 56.3 | 35.2 | 51.7 | 63.9 | 54.6 | Iteration | 1 | 1 | 1 | 2 | 1 | 2 | 1 | 3 |
| 5 | 5 | γcr | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | t(sec) | 91.1 | 85.2 | 72.1 | 103.9 | 52.8 | 125.7 | 149.5 | 111.3 | Iteration | 1 | 4 | 24 | 21 | 8 | 17 | 13 | 29 |
| 6 | 6 | γcr | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | t(sec) | 127.7 | 156.5 | 191.4 | 215.9 | 144.3 | 203.6 | 227.1 | 219.7 | Iteration | 6 | 16 | 32 | 35 | 11 | 37 | 53 | 48 |
| 7 | 7 | γcr | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | t(sec) | 191.6 | 125.03 | 234.2 | 302.4 | 203.5 | 319.3 | 337.8 | 326.2 | Iteration | 19 | 54 | 45 | 82 | 29 | 64 | 56 | 70 |
| 8 | 8 | γcr | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | t(sec) | 115.9 | 284.2 | 301.1 | 396.8 | 281.6 | 381.4 | 413.2 | 397.9 | Iteration | 3 | 20 | 23 | 38 | 16 | 31 | 47 | 63 |
| 9 | 9 | γcr | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | t(sec) | 183.2 | 317.8 | 369.5 | 443.7 | 325.1 | 465.7 | 499.4 | 482.8 | Iteration | 17 | 39 | 16 | 49 | 32 | 61 | 47 | 63 |
| 10 | 10 | γcr | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | t(sec) | 248.6 | 386.9 | 412.1 | 506.03 | 212.4 | 536.8 | 574.9 | 601.3 | Iteration | 29 | 53 | 59 | 78 | 42 | 92 | 85 | 109 |
| 11 | 11 | γcr | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | t(sec) | 347.8 | 439.3 | 490.03 | 589.7 | 434.9 | 592.5 | 687.1 | 694.7 | Iteration | 52 | 64 | 72 | 126 | 69 | 87 | 123 | 95 |
| 12 | 12 | γcr | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | t(sec) | 381.2 | 472.6 | 596.8 | 654.7 | 509.4 | 671.4 | 756.9 | 741.2 | Iteration | 11 | 142 | 50 | 94 | 42 | 63 | 38 | 116 |
| 13 | 13 | γcr | 11 | 11 | 11 | 11 | 11 | 11 | 11 | 11 | t(sec) | 226.9 | 585.9 | 503.5 | 728.4 | 564.1 | 745.3 | 819.2 | 804.9 | Iteration | 9 | 38 | 184 | 146 | 19 | 88 | 72 | 61 |
| 14 | 14 | γcr | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | t(sec) | 295.7 | 703.5 | 756.99 | 801.7 | 638.4 | 815.1 | 910.3 | 895.6 | Iteration | 43 | 95 | 132 | 161 | 57 | 115 | 96 | 158 |
| 15 | 15 | γcr | 13 | 13 | 13 | 13 | 13 | 13 | 13 | 13 | t(sec) | 312.6 | 872.8 | 845.1 | 879.6 | 717.3 | 897.4 | 1067.5 | 980.3 | Iteration | 16 | 27 | 71 | 109 | 26 | 147 | 65 | 106 |
| 16 | 16 | γcr | 14 | 14 | 14 | 14 | 14 | 14 | 14 | 14 | t(sec) | 266.2 | 924.4 | 908.7 | 955.3 | 802.6 | 980.2 | 1206.7 | 1096.1 | Iteration | 12 | 32 | 39 | 67 | 50 | 135 | 46 | 83 |
| 17 | 17 | γcr | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | t(sec) | 231.9 | 1165.3 | 1013.1 | 1168.5 | 854.3 | 1091.8 | 1315.7 | 1289.6 | Iteration | 5 | 11 | 57 | 73 | 42 | 90 | 81 | 65 |
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