Research Article
Deep-Mining Backtracking Search Optimization Algorithm Guided by Collective Wisdom
Table 2
Comparative results of ten algorithms for 10D problems from CEC2005.
| | F | AL | LBSA | BSA | CLPSO | PSOFIPS | TLBO | ETLBO | PSOFDR | BSAISA | OBSA | MBSAgC |
| | F1 | Mean | −450.000 | −450.000 | −450.000 | −450.000 | −450.000 | −450.000 | −439.674 | −450.000 | −450.000 | −450.000 | | Std. | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 32.653 | 0.000 | 1.847E − 11 | 0.000 | | Best | −450.000 | −450.000 | −450.000 | −450.000 | −450.000 | −450.000 | −450.000 | −450.000 | −450.000 | −450.000 | | Rank | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| | F2 | Mean | −450.000 | −449.997 | −449.676 | −450.000 | −450.000 | −450.000 | −450.000 | −449.968 | −446.527 | −450.000 | | Std. | 0.000 | 0.005 | 0.177 | 0.000 | 0.000 | 0.000 | 0.000 | 0.044 | 3.336 | 6.91E − 06 | | Best | −450.000 | −450.000 | −449.906 | −450.000 | −450.000 | −450.000 | −450.000 | −450.000 | −449.791 | −450.000 | | Rank | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 3 | 1 |
| | F3 | Mean | 5652.945 | 21518.124 | 695430.984 | 114431.841 | 70188.530 | 132295.917 | 143065.100 | 31699.067 | 427940.36 | 176254.16 | | Std. | 7686.985 | 18993.641 | 263113.140 | 54898.334 | 47419.217 | 98983.396 | 156627.508 | 17717.113 | 471417.61 | 126171.69 | | Best | 251.786 | 3316.003 | 333184.289 | 48691.653 | 22503.152 | 23119.940 | 6576.186 | 9211.109 | 35974.764 | 39533.675 | | Rank | 1 | 2 | 10 | 9 | 5 | 6 | 3 | 4 | 7 | 8 |
| | F4 | Mean | −450.000 | −449.800 | −445.693 | −450.000 | −450.000 | −450.000 | −438.829 | −444.970 | −430.129 | −449.999 | | Std. | 0.000 | 0.306 | 2.683 | 0.000 | 0.000 | 0.000 | 23.550 | 9.926 | 19.385 | 0.001 | | Best | −450.000 | −449.994 | −449.361 | −450.000 | −450.000 | −450.000 | −450.000 | −449.972 | −448.989 | −450.000 | | Rank | 1 | 2 | 5 | 1 | 1 | 1 | 1 | 4 | 3 | 1 |
| | F5 | Mean | −310.000 | −310.000 | −310.000 | −233.009 | −310.000 | −310.000 | −310.000 | −301.311 | −228.735 | −309.328 | | Std. | 0.000 | 0.000 | 0.000 | 33.727 | 0.000 | 0.000 | 0.000 | 7.416 | 64.078 | 1.034 | | Best | −310.000 | −310.000 | −310.000 | −289.340 | −310.000 | −310.000 | −310.000 | −309.052 | −304.344 | −309.932 | | Rank | 1 | 1 | 1 | 5 | 1 | 1 | 1 | 3 | 4 | 2 |
| | F6 | Mean | 390.548 | 392.105 | 391.599 | 394.658 | 392.592 | 392.167 | 399.415 | 391.651 | 404.196 | 397.153 | | Std. | 1.112 | 2.741 | 1.610 | 0.405 | 3.041 | 2.313 | 18.471 | 2.043 | 11.599 | 7.459 | | Best | 390.001 | 390.091 | 390.348 | 393.841 | 390.000 | 390.000 | 390.002 | 390.005 | 390.000 | 390.000 | | Rank | 2 | 5 | 6 | 8 | 1 | 1 | 3 | 4 | 1 | 1 |
| | F7 | Mean | 1087.046 | 1087.082 | 1087.208 | −179.810 | 1087.046 | 1087.046 | 1087.288 | −179.935 | −179.816 | −179.816 | | Std. | 0.000 | 0.076 | 0.045 | 0.098 | 0.000 | 0.000 | 0.197 | 0.043 | 0.078 | 0.086 | | Best | 1087.046 | 1087.046 | 1087.046 | −179.949 | 1087.046 | 1087.046 | 1087.266 | −179.986 | −179.933 | −179.958 | | Rank | 5 | 5 | 5 | 3 | 5 | 5 | 6 | 1 | 4 | 2 |
| | F8 | Mean | −119.643 | −119.681 | −119.624 | −119.640 | −119.628 | −119.648 | −119.714 | −119.616 | −119.607 | −119.796 | | Std. | 0.053 | 0.085 | 0.081 | 0.090 | 0.087 | 0.066 | 0.075 | 0.070 | 0.072 | 0.070 | | Best | −119.728 | −119.812 | −119.792 | −119.851 | −119.831 | −119.628 | −119.800 | −119.747 | −119.722 | −119.741 | | Rank | 8 | 3 | 6 | 1 | 2 | 10 | 4 | 7 | 9 | 5 |
| | F9 | Mean | −330.000 | −330.000 | −330.000 | −329.333 | −322.342 | −322.737 | −327.314 | −330.000 | −329.343 | −329.877 | | Std. | 0.000 | 0.000 | 0.000 | 0.723 | 2.928 | 2.696 | 1.487 | 0.000 | 0.844 | 0.312 | | Best | −330.000 | −330.000 | −330.000 | −330.000 | −326.020 | −327.015 | −329.005 | −330.000 | −330.000 | −330.000 | | Rank | 1 | 1 | 1 | 1 | 4 | 3 | 2 | 1 | 1 | 1 |
| | F10 | Mean | −323.493 | −320.479 | −316.698 | −317.409 | −319.885 | −321.513 | −319.259 | −319.005 | −310.290 | −317.531 | | Std. | 1.987 | 3.542 | 3.125 | 5.428 | 4.132 | 3.593 | 6.612 | 3.914 | 9.254 | 6.979 | | Best | −325.724 | −324.562 | −322.465 | −324.188 | −325.025 | −327.015 | −328.010 | −325.505 | −323.468 | −324.812 | | Rank | 3 | 7 | 10 | 8 | 5 | 2 | 1 | 4 | 9 | 6 |
| | F11 | Mean | 95.188 | 94.889 | 95.319 | 93.633 | 94.002 | 94.632 | 91.962 | 94.957 | 95.001 | 94.381 | | Std. | 0.746 | 1.196 | 0.572 | 0.536 | 1.652 | 0.997 | 1.023 | 0.848 | 1.271 | 1.627 | | Best | 93.737 | 92.408 | 94.425 | 92.922 | 91.059 | 92.619 | 90.702 | 92.744 | 92.209 | 91.286 | | Rank | 9 | 5 | 10 | 8 | 2 | 6 | 1 | 7 | 4 | 3 |
| | F12 | Mean | −444.398 | −438.290 | −363.666 | −422.531 | 1445.385 | 794.693 | −203.253 | −448.681 | −197.091 | −294.114 | | Std. | 16.545 | 16.021 | 65.389 | 47.468 | 5027.194 | 2860.501 | 507.838 | 13.907 | 645.215 | 421.269 | | Best | −459.985 | −455.477 | −431.128 | −455.719 | −460.000 | −460.000 | −459.496 | −460.000 | −458.383 | −460.000 | | Rank | 2 | 6 | 7 | 5 | 1 | 1 | 3 | 1 | 4 | 1 |
| | F13 | Mean | −129.666 | −129.697 | −129.564 | −128.810 | −129.196 | −129.044 | −129.352 | −129.577 | −129.353 | −129.342 | | Std. | 0.073 | 0.118 | 0.118 | 0.146 | 0.165 | 0.256 | 0.271 | 0.067 | 0.151 | 0.175 | | Best | −129.830 | −129.932 | −129.769 | −129.109 | −129.447 | −129.384 | −129.745 | −129.728 | −129.663 | −129.625 | | Rank | 2 | 1 | 3 | 10 | 8 | 9 | 4 | 5 | 6 | 7 |
| | F14 | Mean | −296.902 | −296.694 | −296.591 | −297.170 | −297.215 | −297.081 | −297.241 | −296.757 | −296.517 | −296.627 | | Std. | 0.207 | 0.205 | 0.151 | 0.306 | 0.249 | 0.459 | 0.685 | 0.215 | 0.253 | 0.276 | | Best | −297.288 | −297.108 | −296.948 | −297.642 | −297.566 | −297.701 | −298.570 | −297.395 | −297.095 | −297.545 | | Rank | 7 | 8 | 10 | 3 | 4 | 2 | 1 | 6 | 9 | 5 | | F15 | Mean | 120.030 | 124.232 | 140.582 | 209.829 | 450.644 | 401.382 | 387.275 | 123.356 | 170.949 | 3.654 | | Std. | 0.089 | 12.918 | 28.900 | 99.415 | 141.887 | 156.564 | 203.967 | 11.180 | 99.357 | 200.365 | | Best | 120.000 | 120.000 | 120.002 | 120.460 | 195.411 | 197.129 | 176.891 | 120.000 | 120.003 | 120.000 | | Rank | 1 | 1 | 2 | 4 | 6 | 7 | 5 | 1 | 3 | 1 |
| | F16 | Mean | 223.754 | 231.537 | 257.700 | 232.105 | 228.617 | 230.096 | 254.799 | 228.345 | 245.791 | 235.776 | | Std. | 3.450 | 10.701 | 14.508 | 10.777 | 9.831 | 9.972 | 29.896 | 5.584 | 10.049 | 9.911 | | Best | 218.507 | 209.614 | 223.542 | 221.355 | 219.015 | 217.668 | 222.865 | 215.613 | 221.217 | 218.609 | | Rank | 4 | 1 | 10 | 8 | 6 | 3 | 9 | 2 | 7 | 5 |
| | F17 | Mean | 241.073 | 249.588 | 269.953 | 251.164 | 246.701 | 228.562 | 247.905 | 242.396 | 272.287 | 261.650 | | Std. | 11.036 | 10.448 | 16.875 | 19.976 | 19.773 | 5.540 | 21.479 | 10.483 | 29.610 | 18.040 | | Best | 227.764 | 237.089 | 252.680 | 216.798 | 218.722 | 222.809 | 219.166 | 227.236 | 230.774 | 230.880 | | Rank | 6 | 9 | 10 | 1 | 2 | 4 | 3 | 5 | 7 | 8 |
| | F18 | Mean | 603.702 | 393.335 | 702.404 | 580.649 | 709.009 | 715.153 | 864.345 | 735.541 | 831.072 | 861.593 | | Std. | 253.504 | 155.192 | 86.522 | 277.920 | 237.366 | 240.232 | 96.241 | 202.699 | 157.059 | 121.229 | | Best | 310.000 | 310.000 | 559.128 | 310.000 | 310.000 | 393.632 | 700.558 | 310.075 | 310.000 | 310.000 | | Rank | 1 | 1 | 4 | 1 | 1 | 3 | 5 | 2 | 1 | 1 |
| | F19 | Mean | 572.111 | 404.878 | 752.056 | 442.020 | 756.348 | 716.366 | 864.003 | 688.951 | 711.459 | 842.334 | | Std. | 278.437 | 162.270 | 46.800 | 214.463 | 201.804 | 227.717 | 131.102 | 190.598 | 241.647 | 160.075 | | Best | 310.000 | 310.000 | 656.476 | 310.000 | 417.269 | 366.021 | 698.725 | 312.483 | 310.009 | 310.000 | | Rank | 1 | 1 | 6 | 1 | 5 | 4 | 7 | 3 | 2 | 1 |
| | F20 | Mean | 442.654 | 410.210 | 666.374 | 748.635 | 791.997 | 896.631 | 681.122 | 807.355 | 595.677 | 863.810 | | Std. | 211.159 | 177.868 | 75.428 | 251.178 | 186.662 | 164.780 | 117.945 | 208.837 | 102.402 | 162.465 | | Best | 310.000 | 310.000 | 566.636 | 310.000 | 310.000 | 486.451 | 693.240 | 310.000 | 314.640 | 310.000 | | Rank | 1 | 1 | 4 | 1 | 1 | 3 | 5 | 1 | 2 | 1 |
| | F21 | Mean | 910.002 | 832.592 | 846.708 | 830.619 | 1110.454 | 931.239 | 1212.545 | 944.930 | 1002.404 | 1028.386 | | Std. | 171.591 | 86.672 | 28.555 | 222.507 | 367.780 | 360.290 | 400.425 | 196.868 | 269.495 | 302.654 | | Best | 660.019 | 585.919 | 790.540 | 660.000 | 660.000 | 660.000 | 660.000 | 613.723 | 660.000 | 660.000 | | Rank | 4 | 1 | 5 | 3 | 3 | 3 | 3 | 2 | 3 | 3 |
| | F22 | Mean | 1074.270 | 1079.861 | 1141.724 | 1131.082 | 1150.209 | 1135.155 | 1177.217 | 924.494 | 961.467 | 1075.162 | | Std. | 145.718 | 148.046 | 7.787 | 3.327 | 29.625 | 24.736 | 79.315 | 232.730 | 231.505 | 170.075 | | Best | 660.000 | 660.000 | 1131.022 | 1125.586 | 1116.253 | 1110.458 | 1109.829 | 660.000 | 660.000 | 660.000 | | Rank | 1 | 1 | 6 | 5 | 4 | 3 | 2 | 1 | 1 | 1 |
| | F23 | Mean | 829.609 | 918.677 | 906.039 | 1069.522 | 1178.115 | 1237.380 | 1431.577 | 998.441 | 1275.131 | 1176.097 | | Std. | 56.624 | 1.797 | 42.468 | 179.455 | 232.518 | 257.118 | 315.479 | 149.953 | 146.070 | 188.499 | | Best | 785.173 | 914.095 | 785.173 | 919.468 | 919.468 | 919.468 | 919.468 | 785.173 | 919.468 | 919.468 | | Rank | 1 | 2 | 1 | 3 | 3 | 3 | 3 | 1 | 3 | 3 |
| | F24 | Mean | 460.000 | 460.000 | 696.247 | 588.505 | 460.000 | 460.000 | 1126.804 | 460.000 | 500.000 | 460.000 | | Std. | 0.000 | 0.000 | 252.248 | 86.471 | 0.000 | 0.000 | 239.476 | 0.000 | 103.723 | 000.000 | | Best | 460.000 | 460.000 | 460.211 | 460.001 | 460.000 | 460.000 | 760.000 | 460.000 | 460.000 | 460.000 | | Rank | 1 | 1 | 3 | 2 | 1 | 1 | 4 | 1 | 1 | 1 |
| | F25 | Mean | 1079.394 | 1080.375 | 1079.655 | 612.785 | 1078.221 | 1076.067 | 1339.389 | 460.000 | 660.000 | 460.000 | | Std. | 2.258 | 2.634 | 2.151 | 80.691 | 2.460 | 20650 | 217.394 | 0.000 | 164.002 | 000.000 | | Best | 1075.267 | 1074.953 | 1077.376 | 460.000 | 1074.200 | 1071.563 | 1071.868 | 460.000 | 460.000 | 460.000 | | Rank | 6 | 5 | 7 | 1 | 4 | 2 | 3 | 1 | 1 | 1 |
| | Average rank | | 2.84 | 2.88 | 5.4 | 3.76 | 3.08 | 3.4 | 3.24 | 2.76 | 3.84 | 2.76 |
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