A Modified Dragonfly Optimization Algorithm for Single- and Multiobjective Problems Using Brownian Motion

Table 3

Comparative results of the single-objective benchmark functions.

Benchmark functions	Performance results			Percentage of success rate
	LFM	SSCBM	Brownian motion	SSCBM	Brownian motion
F1 (min.)	5.56E − 06	4.89E − 07	2.29E − 06	91.20	58.72
F1 (avg.)	4.59E + 00	5.03E + 00	4.93E + 00	−9.71	−7.52
F2 (min.)	1.29E − 02	7.24E − 03	1.80E − 03	43.99	86.05
F2 (avg.)	1.46E + 00	1.26E + 00	8.68E − 01	13.59	40.69
F3 (min.)	8.39E − 02	3.03E − 02	1.02E − 01	63.88	−21.02
F3 (avg.)	1.38E + 02	1.63E + 02	8.40E + 01	−17.42	39.30
F4 (min.)	3.45E − 02	2.63E − 02	3.02E − 02	23.84	12.35
F4 (avg.)	1.91E + 00	2.08E + 00	1.78E + 00	−8.87	6.58
F5 (min.)	5.56E + 00	4.03E + 00	5.44E + 00	27.53	2.16
F5 (avg.)	1.74E + 03	1.45E + 03	5.74E + 02	16.97	67.06
F6 (min.)	4.10E − 07	3.04E − 09	1.65E − 07	99.26	59.69
F6 (avg.)	5.49E + 00	4.30E + 00	5.58E + 00	21.55	−1.65
F7 (min.)	1.41E − 03	1.01E − 03	1.09E − 03	28.48	23.27
F7 (avg.)	1.95E − 01	2.18E − 02	2.22E − 02	88.80	88.62
F8 (min.)	−3.89E + 03	−3.94E + 03	−3.92E + 03	1.26	0.63
F8 (avg.)	−2.82E + 03	−2.84E + 03	−2.93E + 03	1.05	4.22
F9 (min.)	2.99E + 00	2.61E + 00	2.46E + 00	12.83	17.89
F9 (avg.)	3.06E + 01	2.44E + 01	2.47E + 01	20.39	19.47
F10 (min.)	4.44E − 15	8.88E − 16	8.88E − 16	80.00	80.00
F10 (avg.)	2.28E + 00	2.26E + 00	2.32E + 00	0.63	−1.79
F11 (min.)	3.94E − 03	8.59E − 07	4.10E − 03	99.98	−4.07
F11 (avg.)	4.70E − 01	4.38E − 01	4.34E − 01	6.81	7.71
F12 (min.)	1.63E − 04	3.07E − 04	2.85E − 04	−88.69	−75.08
F12 (avg.)	1.29E + 00	1.20E + 00	1.29E + 00	7.11	0.50
F13 (min.)	6.70E − 05	4.23E − 05	3.08E − 05	36.80	54.05
F13 (avg.)	8.35E − 01	6.90E − 01	6.71E − 01	17.38	19.72
F14 (min.)	9.98E − 01	9.98E − 01	9.98E − 01	0.00	0.00
F14 (avg.)	1.25E + 00	1.23E + 00	1.20E + 00	1.97	3.97
F15 (min.)	3.41E − 04	3.08E − 04	3.13E − 04	9.83	8.09
F15 (avg.)	2.45E − 03	2.12E − 03	2.04E − 03	13.45	16.70

Note: min. = minimum; avg. = average.