Table 4 The best, mean and standard deviation of different metaheuristics in dealing with mathematical functions.
From: Energy valley optimizer: a novel metaheuristic algorithm for global and engineering optimization
No. | Alternative metaheuristic algorithms | |||||||
|---|---|---|---|---|---|---|---|---|
ACO | FA | HS | MVO | CSA | ISA | EVO | ||
F1 | Best | 20.70461 | 20.38123 | 3.655346 | 0.069087 | 3.424855 | 1.41E−05 | 0 |
Mean | 20.97241 | 20.50565 | 4.372899 | 3.203908 | 9.174743 | 1.56 | 0.125987 | |
SD | 0.086512 | 0.050224 | 0.313316 | 6.133982 | 3.58599 | 4.09E−01 | 1.25982 | |
F2 | Best | 75.36033 | 5.423342 | 0.408871 | 1.955532 | 9.844303 | 7.06E−07 | 0 |
Mean | 95.46201 | 8.546599 | 0.767617 | 7.655639 | 20.88773 | 4.92E−04 | 5.47E−13 | |
SD | 6.486329 | 1.509117 | 0.150857 | 3.045156 | 4.369272 | 1.16E−03 | 5.47E−12 | |
F3 | Best | 19,933,773 | 1.09E + 09 | 31,448.5 | 0.006724 | 0.044259 | 0 | 0 |
Mean | 75,539,630 | 1.72E + 09 | 67,983.71 | 0.024618 | 6.177559 | 1.28E−08 | 0 | |
SD | 34,603,873 | 3.04E + 08 | 24,225.86 | 0.010664 | 8.326967 | 9.02E−08 | 0 | |
F4 | Best | −0.79993 | −0.99974 | −0.99117 | −1 | −1 | −1 | −1 |
Mean | −0.65791 | −0.99967 | −0.98724 | −0.99999 | −1 | −1 | −1 | |
SD | 0.063929 | 3.13E−05 | 0.002225 | 1.65E−06 | 1.08E−06 | 5.64E−09 | 0 | |
F5 | Best | −4.85263 | −13.5479 | −39.3724 | −13.6182 | −15.0676 | −22.634 | −49 |
Mean | −2.99902 | −10.0326 | −36.6063 | −8.73447 | −11.5189 | −12.5943 | −48.5529 | |
SD | 0.411566 | 1.273413 | 1.04247 | 1.508705 | 1.058497 | 2.991059 | 4.469695 | |
F6 | Best | 15,547.54 | 4403.94 | 651.3584 | 2841.421 | 1009.47 | 0.055643 | 0 |
Mean | 18,151.53 | 5395.454 | 1500.041 | 6914.513 | 3839.607 | 930.2275 | 2.94E−06 | |
SD | 1093.599 | 411.362 | 584.8083 | 2225.258 | 1408.859 | 957.1977 | 2.94E−05 | |
F7 | Best | 511.8067 | 112.6812 | 15.96008 | 110.5245 | 210.6031 | 51.73782 | 0 |
Mean | 587.6085 | 155.6537 | 21.72945 | 211.2711 | 265.203 | 131.404 | 3.64E−07 | |
SD | 25.18078 | 15.83632 | 2.781115 | 42.39096 | 18.5789 | 38.00434 | 3.63E−06 | |
F8 | Best | 10.05457 | 18.11648 | 2.599891 | 0.599873 | 1.399914 | 0.599873 | 0 |
Mean | 12.34569 | 21.19853 | 3.134814 | 0.830873 | 2.029959 | 1.104873 | 0.009265 | |
SD | 0.966472 | 0.822021 | 0.27839 | 0.099184 | 0.226778 | 0.190361 | 0.081186 | |
F9 | Best | 8.49E−07 | 5.35E−11 | 1.08E−09 | 0 | 1.43E−12 | 0 | 0 |
Mean | 2.98E−03 | 2.54E−05 | 1.72E−05 | 9.25E−09 | 1.67E−08 | 0 | 0 | |
SD | 7.70E−03 | 7.88E−05 | 3.90E−05 | 1.75E−08 | 3.39E−08 | 0 | 0 | |
F10 | Best | 77.50366 | 71.56383 | 14.6766 | 0.460693 | 3.379566 | 0.450844 | 0 |
Mean | 91.58769 | 83.56584 | 17.55798 | 1.319453 | 7.234517 | 1.909486 | 0.503791 | |
SD | 2.434241 | 4.747136 | 1.236382 | 0.505237 | 1.954402 | 0.958307 | 4.897183 | |
F11 | Best | 56.83658 | 34.3526 | 3.065453 | 0.088745 | 0.023951 | 0.000271 | 0 |
Mean | 68.01628 | 38.76511 | 3.687095 | 0.148389 | 0.111745 | 0.074045 | 1.10E−06 | |
SD | 3.374358 | 1.686266 | 0.247853 | 0.023546 | 0.058802 | 0.114694 | 1.10E−05 | |
F12 | Best | 333,012.9 | 284.4142 | 3805.585 | 0.424549 | 53.86077 | 0.013213 | 0 |
Mean | 474,307.6 | 471.6474 | 5370.455 | 0.904045 | 113.9655 | 2.278516 | 0.259769 | |
SD | 44,714.95 | 90.6102 | 635.0582 | 0.30938 | 29.47293 | 5.882736 | 2.597688 | |
F13 | Best | 1.05E + 09 | 5.38E + 08 | 8,042,041 | 0.188584 | 3122.341 | 0.018164 | 0 |
Mean | 1.42E + 09 | 6.99E + 08 | 12,104,315 | 0.501756 | 18,977.06 | 340.8279 | 0.001432 | |
SD | 1.12E + 08 | 58,432,546 | 1,604,566 | 0.160563 | 8842.065 | 457.0865 | 0.01432 | |
F14 | Best | 71,819.64 | 15.43768 | 954.7067 | 0.132864 | 10.13445 | 12.38795 | 46.96118 |
Mean | 97,864.79 | 19.82098 | 1262.973 | 0.269682 | 49.44706 | 22.25387 | 73.26776 | |
SD | 11,197 | 1.451369 | 142.6338 | 0.075034 | 40.36055 | 4.672117 | 10.17666 | |
F15 | Best | 70,339.89 | 16.00331 | 888.4887 | 0.130584 | 12.04421 | 16.55338 | 26.27337 |
Mean | 97,836.47 | 19.52131 | 1240.962 | 0.279098 | 54.91552 | 24.86934 | 72.60386 | |
SD | 10,159.17 | 1.460158 | 139.9793 | 0.072831 | 56.50644 | 4.299523 | 11.2144 | |
F16 | Best | 1872.414 | 0.527636 | 85.29447 | 0.008924 | 0.171064 | 3.42E−12 | 0 |
Mean | 2199.699 | 0.668883 | 108.5625 | 0.013944 | 0.89789 | 2.23E−09 | 0 | |
SD | 134.2236 | 0.058032 | 10.19812 | 0.002377 | 0.567639 | 1.20E−08 | 0 | |
F17 | Best | 223,877 | 130,660 | 8707 | 36 | 173 | 166 | 22 |
Mean | 268,117.9 | 148,673.9 | 10,812.77 | 84.51 | 299.23 | 559.02 | 32.41 | |
SD | 13,451.02 | 7049.15 | 969.7187 | 31.88759 | 65.20935 | 160.5713 | 4.878514 | |
F18 | Best | 5,588,993 | 5,588,993 | 195,795.3 | 867.3468 | 3839.556 | 1924.694 | 262.1536 |
Mean | 6,702,584 | 6,702,584 | 267,328.7 | 1195.725 | 6439.726 | 5520.177 | 420.8609 | |
SD | 337,357.7 | 337,357.7 | 25,817.66 | 140.2667 | 1114.555 | 2013.876 | 839.9876 | |
F19 | Best | 0.857868 | 0.47082 | 0.083849 | 0.504413 | 0.401207 | 0.318924 | 0 |
Mean | 0.892505 | 0.541511 | 0.106005 | 0.580524 | 0.494181 | 0.5283 | 0.002477 | |
SD | 0.009596 | 0.024226 | 0.008691 | 0.031767 | 0.027936 | 0.047698 | 0.023212 | |
F20 | Best | 0.000205 | 2.35E−05 | 2.79E−06 | 1.99E−05 | 1.28E−06 | 7.16E−06 | 9.65E−06 |
Mean | 0.018252 | 1.44E−03 | 1.85E−03 | 2.03E−03 | 1.73E−03 | 1.15E−03 | 1.13E−03 | |
SD | 0.021241 | 1.14E−03 | 2.03E−03 | 1.80E−03 | 1.51E−03 | 1.02E−03 | 1.37E−03 | |
