A Hybrid Algorithm Framework with Learning and Complementary Fusion Features for Whale Optimization Algorithm

Table 4

Comparison of optimization results obtained for the unimodal benchmark functions.

AL	Runs = 30, N = 30, and T = 1000
		DE	BBO	BSA	PSO	HS	GSA	WOA	WOA-DE	WOA-BSA
F1	Best	2.90E − 12	0.454643	0.000908	1.04E − 11	0.042385	4.64E − 17	2.76E − 167	6.92E − 190	1.62E − 187
	Mean	1.33E − 11	1.013223	0.006257	9.73E − 09	0.063236	1.01E − 16	1.46E − 153	1.07E − 168	1.45E − 172
	Std	9.98E − 12	0.311571	0.010917	4.23E − 08	0.010899	3.76E − 17	7.91E − 153	0	0
F2	Best	3.99E − 08	0.271733	0.006726	1.00E − 05	0.575724	3.50E − 08	3.31E − 114	2.46E − 124	2.01E − 124
	Mean	6.80E − 08	0.324236	0.020418	0.001313	0.727765	5.20E − 08	9.88E − 105	8.47E − 113	1.27E − 112
	Std	1.95E − 08	0.041092	0.014974	0.004947	0.05865	1.17E − 08	4.94E − 104	4.21E − 112	5.75E − 112
F3	Best	10808.03597	83.765444	394.952176	3.208562	3084.50285	195.538197	1677.30974	175.10162	532.871248
	Mean	15723.1259	135.934273	878.22206	14.904551	5228.201445	409.456876	9735.512836	10045.18144	7621.728202
	Std	2683.155994	34.026326	315.589252	7.677907	1591.552755	129.83509	3898.890192	5986.48178	4199.058749
F4	Best	1.080885	0.742244	3.262876	0.311111	4.216935	1.35E − 08	0.019063	5.68E − 10	4.30E − 19
	Mean	1.575045	0.972736	5.969996	0.563087	6.113542	1.264362	17.704825	14.259819	1.562263
	Std	0.38751	0.123737	1.57968	0.153909	1.246667	1.284382	14.58112	17.566092	6.519626
F5	Best	25.398273	39.474199	43.67835	11.716823	91.050677	25.861836	26.607341	25.886812	26.835697
	Mean	38.31135	149.884822	114.032052	60.388778	342.973593	37.244874	27.1471	27.512334	27.496506
	Std	21.417578	181.590232	35.216402	43.241123	492.144758	24.882941	0.485147	0.547347	0.539586
F6	Best	2.88E − 12	0.6227	0.00076	2.51E − 11	0.048128	4.50E − 17	0.007148	0.012986	0.015406
	Mean	8.90E − 12	1.071114	0.00788	9.68E − 09	0.070002	1.03E − 16	0.057661	0.263633	0.20125
	Std	5.67E − 12	0.279422	0.008319	3.00E − 08	0.011199	4.46E − 17	0.078559	0.224346	0.192754
F7	Best	0.016252	0.002011	0.012074	0.037104	0.035229	0.016733	0.000115	0.00016	0.0001
	Mean	0.027322	0.006396	0.030674	0.078177	0.055369	0.049762	0.001935	0.0015	0.001579
	Std	0.005743	0.002154	0.012799	0.023769	0.011801	0.021587	0.001959	0.001692	0.001761
Rank	Best	6	8	7	5	9	3	4	1	2
	Mean	5	7	6	4	8	2	3	3	1
	Std	1	5	6	4	7	1	2	3	1