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Table 1 The comparative results of G01–G24 benchmark functions using different algorithms

From: Optimal reactive power dispatch using a novel optimization algorithm

Function   PSO BBO DE ABC HTS TLBO JAYA
G01 Best −15 −14.977 −15 −15  − 15 −15 −15
(−15.00) Mean −14.71 −14.7698 −14.555 −15 −15 −10.782 −15
G02 Best −0.669158 −0.7821 −0.472 −0.803598 − 0 .7517 −0.7835 −0.803605
(−0.803619) Mean −0.41996 −0.7642 −0.665 −0.792412 −0.6437 −0.6705 −0.7968
G03 Best 1 −1.0005 −0.99393 −1 −1.0005 −1.0005 −1.005
(−1.0005) Mean 0.764813 −0.3957 −1 −1 −0.9004 −0.8 −1
G04 Best −30,665.539 −30,665.539 −30,665.539 −30,665.539 −30,665.539 −30,665.539 −30,665.539
(−30,665.539) Mean −30,665.539 −30,411.865 −30,665.539 −30,665.539 −30,665.539 −30,665.539 −30,665.539
G05 Best 5126.484 5134.2749 5126.484 5126.484 5126.486 5126.486 5126.486
−5126.486 Mean 5135.973 6130.5289 5264.27 5185.714 5126.5152 5126.6184 5126.5061
G06 Best −6961.814 −6961.8139 −6954.434 −6961.814 −6961.814 −6961.814 −6961.814
(−6961.814) Mean −6961.814 −6181.7461 −6954.434 −6961.813 −6961.814 −6961.814 −6961.814
G07 Best 24.37 25.6645 24.306 24.33 24.3104 24.3101 24.3062
−24.3062 Mean 32.407 29.829 24.31 24.473 24.4945 24.837 24.3092
G08 Best −0.095825 −0.095825 −0.095825 −0.095825 −0.095825 −0.095825 −0.095825
(−0.095825) Mean −0.095825 −0.95824 −0.095825 −0.095825 −0.095825 −0.095825 −0.095825
G09 Best 680.63 680.6301 680.63 680.634 680.6301 680.6301 680.6301
−680.6301 Mean 680.63 692.7162 680.63 680.634 680.6329 680.6336 680.6301
G10 Best 7049.481 7679.0681 7049.548 7053.904 7049.4836 7250.9704 7049.312
−7049.28 Mean 7205.5 8764.9864 7147.334 7224.407 7119.7015 7257.0927 7052.7841
G11 Best 0.749 0.7499 0.752 0.75 0.7499 0.7499 0.7499
−0.7499 Mean 0.749 0.83057 0.901 0.75 0.7499 0.7499 0.7499
G12 Best −1 −1 −1 −1 −1 −1 −1
(−1) Mean −0.998875 −1 −1 −1 −1 −1 −1
G13 Best 0.085655 0.62825 0.385 0.76 0.37319 0.44015 0.003625
(−0.05394) Mean 0.569358 1.09289 0.872 0.968 0.66948 0.69055 0.003627
G14 Best −44.9343 54.6679 −45.7372 −44.6431 −47.7278 −46.5903 −47.7322
(–47.764) Mean −40.871 175.9832 −29.2187 −40.1071 −46.4076 −39.9725 −46.6912
G15 Best 961.715 962.664 961.715 961.7568 961.715 961.715 961.715
−961.715 Mean 965.5154 1001.4367 961.7537 966.2868 961.75 962.8641 961.715
G16 Best −1.9052 −1.9052 −1.9052 −1.9052 −1.9052 −1.9052 −1.9052
(–1.9052) Mean −1.9052 −1.6121 −1.9052 −1.9052 −1.9052 −1.9052 −1.9052
G17 Best 8857.514 9008.5594 8854.6501 8859.713 8853.5396 8853.5396 8853.5396
−8853.5396 Mean 8899.4721 9384.268 8932.0444 8941.9245 8877.9175 8876.5071 8872.5402
G18 Best −0.86603 −0.65734 −0.86531 −0.86603 −0.86603 −0.86603 −0.86603
(–0.86603) Mean −0.8276 −0.56817 −0.86165 −0.86587 −0.77036 −0.86569 −0.86602
G19 Best 33.5358 39.1471 32.6851 33.3325 32.7132 32.7916 32.6803
−32.6555 Mean 36.6172 51.8769 32.768 36.0078 32.7903 34.0792 32.7512
G20 Best 0.24743 1.26181 0.24743 0.24743 0.24743 0.24743 0.24139
−0.204979 Mean 0.97234 1.43488 0.26165 0.80536 0.25519 1.22037 0.24385
G21 Best 193.7311 198.8151 193.7346 193.7343 193.7264 193.7246 193.5841
−193.274 Mean 345.6595 367.2513 366.9193 275.5436 256.6091 264.6092 193.7219
G22 Best −258.74 −267.15 −249.12 −243.43 −272.78 −248.78 −242.45
−236.4309 Mean −255.55 −254.44 −249.46 −251.33 −265.66 −252.56 −239.05
G23 Best −105.9826 2.3163 −72.642 −43.2541 −390.6472 −385.0043 −391.5192
(–400.055) Mean −25.9179 22.1401 −7.2642 −4.3254 −131.2522 −83.7728 −381.2312
G24 Best −5.508 −5.508 −5.508 −5.508 −5.508 −5.508 −5.508
(−5.5080) Mean −5.508 −5.4982 −5.508 −5.508 −5.508 −5.508 −5.508