A Crossover Bacterial Foraging Optimization Algorithm

Table 3

Minimum, mean values, and standard deviation for the benchmark function for 𝑓₁−𝑓₇ (represent up to three fractional points).

Function	Statistical measurement	CBFOA			BFOA
		𝑝=50,𝑆=4	𝑝=50,𝑆=20	𝑝=500,𝑆=4	𝑝=50,𝑆=4	𝑝=50,𝑆=20	𝑝=500,𝑆=4
𝑓1	Minimum	1.525	1.319	3.262	1.715	1.456	3.305
	Mean	2.160	1.613	3.392	2.267	1.741	3.437
	Std. Dev.	0.225	0.113	0.048	0.270	0.146	0.052
𝑓2	Minimum	0.136	0.134	0.421	0.151	0.136	0.449
	Mean	0.201	0.166	0.485	0.208	0.172	0.498
	Std. Dev.	0.028	0.013	0.021	0.023	0.016	0.019
𝑓3	Minimum	164.455	152.077	2712.102	172.454	154.242	2895.302
	Mean	197.770	175.040	2908.327	202.866	183.931	2980.910
	Std. Dev.	15.348	11.728	86.705	15.732	11.577	85.742
𝑓4	Minimum	73.536	68.936	5233.215	74.104	70.381	5312.160
	Mean	172.978	112.322	5641.901	163.977	104.736	5806.152
	Std. Dev.	44.929	35.153	218.398	41.819	26.631	219.462
𝑓5	Minimum	0.932	0.811	75.667	0.935	0.850	78.766
	Mean	1.302	1.054	88.812	1.363	1.106	91.327
	Std. Dev.	0.193	0.095	4.865	0.195	0.113	4.838
𝑓6	Minimum	0.838	0.829	75.353	0.998	0.892	81.900
	Mean	1.319	1.053	88.355	1.366	1.096	91.500
	Std. Dev.	0.193	0.091	5.161	0.203	0.111	4.493
𝑓7	Minimum	23.091	19.592	15919.004	23.241	20.682	18340.260
	Mean	33.173	25.865	19284.121	33.991	26.904	20135.431
	Std. Dev.	4.810	2.804	1232.30	6.039	3.076	1050.504
Function	Statistical measurement	ABFOA			GA
		𝑝=50,𝑆=4	𝑝=50,𝑆=20	𝑝=500,𝑆=4	𝑝=50,𝑆=4	𝑝=50,𝑆=20	𝑝=500,𝑆=4
𝑓1	Minimum	3.274	3.182	3.756	3.253	3.334	3.734
	Mean	3.620	3.450	3.837	3.529	3.521	3.797
	Std. Dev.	0.120	0.089	0.030	0.063	0.054	0.015
𝑓2	Minimum	0.299	0.256	0.542	0.248	0.225	0.512
	Mean	0.428	0.363	0.648	0.299	0.273	0.560
	Std. Dev.	0.059	0.039	0.040	0.020	0.019	0.014
𝑓3	Minimum	16.401	16.526	4265.352	337.504	354.976	4616.801
	Mean	27.678	24.500	4559.012	405.755	401.736	4820.149
	Std. Dev.	5.028	3.219	74.756	18.318	15.624	53.202
𝑓4	Minimum	52.703	49.708	8809.955	542.544	486.038	8413.197
	Mean	669.706	233.259	9583.201	615.075	571.955	8814.362
	Std. Dev.	217.473	237.100	318.864	35.159	31.871	139.747
𝑓5	Minimum	7.596	6.305	109.191	10.536	9.701	143.726
	Mean	10.175	8.998	118.319	11.954	11.874	151.972
	Std. Dev.	0.949	0.665	4.176	0.593	0.777	2.242
𝑓6	Minimum	8.270	7.543	104.974	10.350	9.736	142.649
	Mean	10.181	9.086	118.443	12.179	11.957	152.154
	Std. Dev.	0.792	0.576	3.774	0.635	0.684	2.076
𝑓7	Minimum	12.845	11.466	37978.059	230.363	233.034	35713.922
	Mean	18.035	14.753	39957.690	288.583	282.761	37448.482
	Std. Dev.	2.381	1.197	1189.191	20.812	20.009	641.561