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. 2022 Oct 17;12:17387. doi: 10.1038/s41598-022-22458-9

Table 7.

The results of the scalability analysis of STBO.

m Index GA PSO GSA TLBO MVO GWO WOA TSA MPA RSA AVOA STBO
F1 50 Mean 285.0043 34.26946 6.91E−16 5.57E−68 1.171019 8.13E−44 1.80E−151 9.37E−36 1.87E−46 0 0 0
Std 71.44383 53.81518 4.58E−16 7.14E−68 0.247724 1.43E−43 5.50E−151 2.08E−35 4.78E−46 0 0 0
100 Mean 2782.496 2511.523 673.4191 8.95E−62 18.86453 2.57E−29 3.10E−150 2.63E−25 3.16E−43 0 0 0
Std 322.4319 1007.265 358.3897 1.83E−61 2.305294 2.84E−29 9.10E−150 3.68E−25 5.78E−43 0 0 0
250 Mean 21,206.3 39,344.94 13,078.49 3.85E−58 798.4678 5.56E−18 2.00E−148 1.69E−15 1.31E−40 0 0 0
Std 2180.106 8289.222 1581.329 6.19E−58 80.70753 3.34E−18 8.80E−148 1.96E−15 2.05E−40 0 0 0
500 Mean 69,817.39 165,845 40,569.3 6.55E−56 12,935.45 1.39E−12 1.80E−145 1.00E−10 4.64E−39 0 0 0
Std 3479.445 12,186.53 2491.612 1.55E−55 846.7481 6.09E−13 5.50E−145 1.08E−10 4.39E−39 0 0 0
F2 50 Mean 12.2036 8.359858 0.152633 3.04E−35 35.12252 4.52E−26 2.10E−104 2.23E−22 2.14E−26 0 1.10E−202 0
Std 1.384519 4.660024 0.465052 3.51E−35 69.37835 3.78E−26 4.00E−104 6.44E−22 2.59E−26 0 0 0
100 Mean 46.20699 123.1423 6.597008 2.04E−32 5.90E+15 4.70E−18 1.10E−101 1.53E−16 5.52E−25 0 1.50E−208 0
Std 4.244573 88.20233 2.718062 1.38E−32 2.49E+16 2.32E−18 3.00E−101 1.72E−16 9.87E−25 0 0 0
250 Mean 190.8026 544.4599 77.08794 4.03E−30 6.06E+85 3.31E−11 1.07E−98 2.21E−11 1.03E−23 0 7.90E−211 0
Std 9.96777 20.69241 9.352065 2.34E−30 2.63E+86 1.12E−11 4.63E−98 1.84E−11 2.51E−23 0 0 0
500 Mean 485.2498 1112.286 3.50E+268 3.60E−29 3.10E+211 5.96E−08 1.30E−99 2.02E−08 6.87E−21 0 3.30E−206 0
Std 17.08654 42.27506 65,535 2.37E−29 65,535 1.15E−08 5.90E−99 2.31E−08 3.02E−20 0 0 0
F3 50 Mean 5048.588 6169.914 1821.115 1.29E−19 650.7283 6.38E−06 124,414.6 0.072352 2.50E−07 0 0 0
Std 1078.129 4769.136 448.1044 4.71E−19 154.0739 2.16E−05 29,498.35 0.125204 6.11E−07 0 0 0
100 Mean 18,325.05 50,954.41 7927.23 3.10E−15 29,633.47 11.04603 853,493.7 2220.555 0.004078 0 1.60E−280 0
Std 3075.166 21,471.28 1361.341 5.06E−15 4515.672 19.81332 168,872.8 1432.756 0.011144 0 0 0
250 Mean 136,756.2 336,528 57,829.84 3.66E−10 322,673.6 9257.031 6,878,229 206,030.5 107.5336 0 3.20E−241 0
Std 23,655.14 75,834.61 8985.585 1.56E−09 21,061.8 5349.661 1,098,416 53,625.46 202.0424 0 0 0
500 Mean 668,892.5 1,223,667 275,481.2 1.47E−08 1,317,906 116,541.8 28,062,441 1,035,782 1525.209 0 1.10E−192 0
Std 106,978.1 359,536.2 68,207.09 5.34E−08 103,418.5 59,137.88 9,301,240 165,807.8 1673.877 0 0 0
F4 50 Mean 5.963966 19.53837 8.777958 1.06E−27 4.066982 1.82E−09 66.50783 2.731684 1.24E−17 0 6.70E−196 0
Std 0.978908 3.071924 1.928206 7.94E−28 1.385832 2.88E−09 27.76152 2.912462 8.45E−18 0 0 0
100 Mean 13.80378 37.51555 16.06594 1.35E−25 41.92272 0.003378 77.59964 34.24477 4.35E−16 0 9.20E−193 0
Std 1.359287 3.83295 1.503749 1.33E−25 6.774704 0.003706 23.46463 12.32771 2.17E−16 0 0 0
250 Mean 26.5063 53.88201 22.08527 6.02E−24 80.66538 21.2961 77.16777 96.01481 3.04E−14 0 1.80E−204 0
Std 1.60905 5.368787 1.848865 1.18E−23 3.341441 7.816487 22.70411 3.384094 2.07E−14 0 0 0
500 Mean 36.97724 67.43914 26.76013 3.20E−23 92.43218 57.82163 78.34497 99.24345 5.46E−13 0 1.80E−201 0
Std 1.911597 4.690484 1.645312 2.84E−23 1.646392 6.138673 20.24963 0.22398 8.70E−13 0 0 0
F5 50 Mean 2713.719 1085.306 131.5463 47.42296 603.6723 47.40183 47.43972 48.32421 44.03808 46.49249 0.000162 0
Std 1305.112 1169.986 73.26552 0.9332 920.3005 0.79805 0.54216 0.656619 0.590632 10.94366 0.000166 0
100 Mean 125,110.4 287,904.9 17,204.66 97.81196 1237.219 97.63697 97.80163 98.29339 95.135 98.96354 0.00046 0
Std 43,089.33 264,617.7 10,886.6 0.677834 844.555 0.636675 0.37934 0.488629 0.843997 0.066664 0.000509 0
250 Mean 4,083,468 21,300,786 1,044,548 248.0782 35,979.2 247.8359 247.1009 247.9578 245.7841 248.9852 0.007509 0
Std 1,041,684 5,177,053 294,478.5 0.299102 14,532.75 0.42663 0.319189 0.561326 0.706112 0.015649 0.018946 0
500 Mean 21,818,155 1.66E+08 5,695,001 498.0625 3,316,483 497.6689 495.7569 498.2494 495.6662 498.9886 0.005212 0
Std 2,517,887 25,976,011 825,086.1 0.269248 471,390.8 0.173736 0.442375 0.48665 0.528731 0.003021 0.006083 0
F6 50 Mean 305.615 42.04067 0.003316 3.660992 1.073896 2.243901 0.378736 6.441274 0.003395 11.46592 4.58E−05 0
Std 77.1288 53.90269 0.014831 0.597425 0.212681 0.481915 0.230127 0.957914 0.015141 1.656754 2.24E−05 0
100 Mean 2716.183 3158.425 649.5424 12.34831 18.44157 9.286886 1.937719 13.80242 0.815919 24.70658 0.014634 0
Std 493.7557 2883.38 352.0708 0.75096 2.245434 0.787782 0.928162 1.00861 0.362987 0.166974 0.055799 0
250 Mean 21,479.14 40,123.4 12,867.19 44.38734 782.2298 38.47129 8.908795 41.33491 13.65313 62.19509 0.101121 0
Std 1771.678 6381.723 1821.69 1.271032 65.41419 1.275285 2.236528 1.601417 1.08496 0.120169 0.183189 0
500 Mean 68,512.54 166,510.4 40,708.14 102.2647 13,141.71 92.61489 18.32255 95.38288 52.989 124.7206 0.11678 0
Std 4438.758 14,455.79 3093.243 1.840089 725.7806 1.57135 5.184106 1.850498 1.997287 0.06375 0.234366 0
F7 50 Mean 0.029469 0.563845 0.192132 0.002251 0.039289 0.001623 0.003268 0.009127 0.000786 8.80E−05 0.00012 1.21E−05
Std 0.006066 0.245682 0.070887 0.001521 0.012198 0.00081 0.004275 0.004542 0.000395 9.50E−05 0.000122 1.39E−05
100 Mean 0.277241 6.359927 2.081773 0.002365 0.197949 0.002509 0.001804 0.022533 0.00069 4.95E−05 0.000128 1.04E−05
Std 0.109251 6.051414 0.959512 0.001368 0.028032 0.001204 0.001604 0.008074 0.000271 7.53E−05 0.000109 1.01E−05
250 Mean 14.51263 127.255 69.68376 0.003042 2.268139 0.00645 0.003257 0.093088 0.000885 8.38E−05 0.000157 1.36E−05
Std 2.095997 48.34713 15.68223 0.001392 0.343546 0.00241 0.003305 0.035296 0.000421 7.11E−05 0.000179 1.18E−05
500 Mean 152.9307 1238.266 685.4945 0.003431 41.51178 0.010719 0.002206 0.535833 0.000924 7.47E−05 0.000171 1.67E−05
Std 26.25327 198.34 99.68845 0.002319 6.351142 0.003335 0.002982 0.122946 0.000412 7.07E−05 0.00015 1.53E−05
F8 50 Mean − 12,272.8 − 10,802.7 − 3403.91 − 7204.86 − 12,793.7 − 9338.85 − 19,090.3 − 8745.76 − 14,938.1 − 9022.4 − 20,353.6 − 20,413
Std 1103.911 1130.198 507.9481 852.2193 1008.764 1287.406 2667.391 807.3113 715.9989 202.8098 524.94 1176.142
100 Mean − 18,876.3 − 18,284.3 − 4539.53 − 9438.36 − 24,721 − 16,403.4 − 38,730.4 − 14,103.8 − 28,018.7 − 17,227.2 − 40,235 − 41,150
Std 1754.896 2043.847 746.9655 961.5354 1632.216 2974.611 4599.436 889.5166 861.137 1182.774 1140.119 1847.596
250 Mean − 31,100.3 − 36,587.6 − 7604.78 − 15,364.1 − 55,415.3 − 35,384.6 − 87,802.5 − 23,017.4 − 57,688.4 − 37,088.8 − 96,183.8 − 100,730
Std 3266.845 2315.238 1353.598 1984.653 2685.69 2404.494 14,060.16 1501.685 1813.612 2064.086 6413.815 4650.807
500 Mean − 45,608.7 − 55,847.5 − 10,442.3 − 22,573 − 96,126.1 − 61,887.1 − 188,510 − 32,328.1 − 96,995.4 − 66,008.1 − 176,969 − 201,718
Std 3441.277 3362.234 2117.996 2518.76 2539.443 5243.808 26,903.39 1972.414 2350.496 4893.541 14,449.97 7420.386
F9 50 Mean 187.09 116.6431 54.67295 0 242.2961 0.49703 0 359.0799 0 0 0 0
Std 25.47509 30.12197 9.988632 0 49.28747 1.530593 0 59.85311 0 0 0 0
100 Mean 591.5714 340.1137 133.9363 0 572.9428 0.189209 0 897.1359 0 0 0 0
Std 39.8328 40.68969 18.74462 0 96.95193 0.84617 0 115.5391 0 0 0 0
250 Mean 2086.163 1457.558 693.863 0 2156.602 1.952586 2.27E−14 2711.363 0 0 0 0
Std 64.22998 85.31377 76.61462 0 112.0258 3.110418 1.02E−13 271.96 0 0 0 0
500 Mean 4646.933 3828.066 2231.817 0 5422.097 3.544948 0 5356.486 0 0 0 0
Std 112.9087 150.4184 112.0155 0 163.6803 4.402665 0 486.9464 0 0 0 0
F10 50 Mean 5.389597 5.507252 0.286075 4.44E−15 1.754842 3.27E−14 3.91E−15 1.013365 4.44E−15 8.88E−16 8.88E−16 8.88E−16
Std 0.379123 0.949512 0.449919 0 0.479574 3.15E−15 2.09E−15 1.424865 0 0 0 0
100 Mean 7.96934 10.84341 3.155674 4.44E−15 5.028315 1.11E−13 4.62E−15 7.55E−10 4.44E−15 8.88E−16 8.88E−16 8.88E−16
Std 0.3831 1.36695 0.870762 0 4.973398 6.71E−15 2.15E−15 3.37E−09 0 0 0 0
250 Mean 10.74289 15.85386 7.168624 4.44E−15 18.97748 1.40E−10 4.62E−15 4.47E−09 4.44E−15 8.88E−16 8.88E−16 8.88E−16
Std 0.334866 0.676188 0.371374 0 4.076866 5.24E−11 2.44E−15 3.19E−09 0 0 0 0
500 Mean 12.25589 17.35226 9.145829 4.44E−15 20.70852 5.21E−08 3.38E−15 5.11E−07 4.44E−15 8.88E−16 8.88E−16 8.88E−16
Std 0.174913 0.215727 0.303231 0 0.070891 1.22E−08 2.33E−15 3.81E−07 0 0 0 0
F11 50 Mean 4.052498 1.457349 30.33821 0 0.761331 0.000976 0 0.00581 0 0 0 0
Std 0.803584 0.648617 7.427283 0 0.061095 0.004365 0 0.007483 0 0 0 0
100 Mean 26.35897 21.79932 97.63246 0 1.169893 0.001514 0 0.004743 0 0 0 0
Std 4.094358 9.647885 10.20711 0 0.024039 0.004755 0 0.007544 0 0 0 0
250 Mean 193.6629 353.5776 1104.15 0 7.894967 0.001375 5.55E−18 0.012257 0 0 0 0
Std 12.63072 43.8592 47.3678 0 0.713036 0.006151 2.48E−17 0.017872 0 0 0 0
500 Mean 627.7852 1540.037 4647.865 0 121.6026 0.001047 0 0.010433 0 0 0 0
Std 32.5443 104.1384 113.7393 0 9.110349 0.004683 0 0.02146 0 0 0 0
F12 50 Mean 1.794942 7.930916 1.742268 0.147094 2.719225 0.082447 0.013583 6.888216 8.49E−09 1.254882 5.36E−07 9.42E−33
Std 0.711264 3.528295 0.894647 0.036661 0.841177 0.031664 0.014297 4.282754 1.17E−08 0.229805 3.80E−07 2.81E−48
100 Mean 8.188648 32.71512 5.133908 0.36174 8.276208 0.24133 0.021398 10.24539 0.009444 1.258981 0.000198 4.71E−33
Std 1.640979 24.67439 1.363192 0.040864 1.843543 0.04763 0.022961 4.540495 0.0039 0.103201 0.000879 1.40E−48
250 Mean 47,652.44 4,716,917 21.88649 0.633515 42.14883 0.542416 0.027522 65.1672 0.072691 1.225052 9.41E−05 1.88E−33
Std 65,626.15 2,935,210 6.096715 0.040427 7.225588 0.04906 0.010868 115.8512 0.011464 0.007345 0.000284 3.51E−49
500 Mean 2,535,944 90,916,183 884.6464 0.824569 116,501.9 0.747753 0.039326 46,754 0.203489 1.20229 9.54E−05 9.42E−34
Std 1,052,760 25,963,807 986.5159 0.016698 67,940.08 0.033203 0.018023 54,125.95 0.019065 0.002856 0.000205 1.76E−49
F13 50 Mean 12.08077 39.25416 14.53883 3.017419 0.184215 1.774649 0.585467 5.23522 0.083563 1.693285 1.48E−07 1.35E−32
Std 3.219958 8.195503 11.08645 0.444856 0.054379 0.335202 0.263984 0.716397 0.068924 1.979402 2.09E−07 2.81E−48
100 Mean 199.7021 29,222.48 125.1532 8.164988 80.09712 6.324213 1.986033 12.01446 6.040318 9.890124 2.54E−07 1.35E−32
Std 225.0718 43,015.76 44.23044 0.381571 34.61998 0.424363 0.960595 1.093216 2.587355 0.03041 2.16E−07 2.81E−48
250 Mean 1,881,794 29,219,357 98,379.96 24.24311 546.7537 21.06385 5.335894 137.2253 22.9728 24.90092 0.005026 1.35E−32
Std 1,046,952 8,331,513 103,971.4 0.375005 71.90737 0.419527 1.264721 102.9533 0.398369 0.029412 0.022476 2.81E−48
500 Mean 24,409,101 4.10E+08 1,078,726 49.81733 2,251,206 45.92283 11.08914 3764.666 47.63375 49.89766 0.018481 1.35E−32
Std 5,989,248 1.06E+08 392,617.9 0.067117 781,787.8 0.540198 3.486242 3208.632 0.475035 0.011192 0.046167 2.81E−48