Table 13.

Comparison of results of the classical benchmark functions between DA, PSO, DE, and FA.

F	Meas.	DA	PSO	DE	FA
F1	Mean	2.85E − 18	4.2E − 18	2.23e − 19	1.72e − 10
	Std.	7.16E − 18	1.31E − 18	1.75e − 19	9.43e − 10
F2	Mean	1.49E − 05	0.003154	6.24e − 12	6.01e − 07
	Std.	3.76E − 05	0.009811	2.2e − 12	3.29e − 06
F3	Mean	1.29E − 06	0.001891	27.882386	1.58e − 10
	Std.	2.1E − 06	0.003311	12.845742	8.66e − 10
F4	Mean	0.000988	0.001748	0.002883	5.913 − 03
	Std.	0.002776	0.002515	0.000577	0.029813
F5	Mean	7.600558	63.45331	9.50058	2.383765
	Std.	6.786473	80.12726	3.204155	1.350716
F6	Mean	4.17E − 16	4.36E − 17	2.22e − 19	1.9e − 10
	Std.	1.32E − 15	1.38E − 16	1.47e − 19	1.04e − 09
F7	Mean	0.010293	0.005973	0.005256	1.57e − 04
	Std.	0.004691	0.003583	0.001649	1.01e − 04
F8	Mean	−2857.58	−7.1E + 11	−4181.932984	−3566.452419
	Std.	383.6466	1.2E + 12	30.0487686	239.113661
F9	Mean	16.01883	10.44724	7.31e − 11	7.462188
	Std.	9.479113	7.879807	1.04e − 10	4.41686
F10	Mean	0.23103	0.280137	2.1e − 10	8.47e − 07
	Std.	0.487053	0.601817	9.14e − 11	4.64e − 06
F11	Mean	0.193354	0.083463	0.001259	0.053309
	Std.	0.073495	0.035067	0.002957	0.053615
F12	Mean	0.031101	8.57E − 11	2.32e − 20	1.92e − 12
	Std.	0.098349	2.71E − 10	3.1e − 20	1.05e − 11
F13	Mean	0.002197	0.002197	4.25e − 20	8.21e − 12
	Std.	0.004633	0.004633	4.52e − 20	4.5e − 11
F14	Mean	103.742	150	0.99800	0.99800
	Std.	91.24364	135.4006	0	1.700065e − 16
F15	Mean	193.0171	188.1951	0.000698	3.77e − 04
	Std.	80.6332	157.2834	1.546e − 04	1.853–04
F16	Mean	458.2962	263.0948	−1.031628	−1.031628
	Std.	165.3724	187.1352	6.77e − 16	1.06e − 15
F17	Mean	596.6629	466.5429	0.3978873	3.0
	Std.	171.0631	180.9493	0	6.05e − 15
F18	Mean	229.9515	136.1759	2.9999999	−3.862782
	Std.	184.6095	160.0187	1.27e − 15	2.79e − 15
F19	Mean	679.588	741.6341	−3.862782	−3.259273
	Std.	199.4014	206.7296	2.71e − 15	0.059789
F20	Mean	−3.32199	−3.27047	−3.321797	−9.316829
	Std.	−3.38E − 06	0.059923	0.001054	2.21393
F21	Mean	−10.1532	−7.3874	−9.867489	−10.147907
	Std.	6.60E − 15	3.11458	0.722834	1.396876
F22	Mean	−10.4029	−8.5305	−10.381587	−9.398946
	Std.	1.51E − 06	3.038572	0.075194	1.99413
F23	Mean	−10.5364	−9.1328	−10.530836	−10.2809
	Std.	2.97E − 07	2.640148	0.02909	1.39948

For each test function, the result of the algorithm that has shown its superiority comparing to the other algorithms for solving a specific function is shown in bold.