Table 7.

Results of fixed-dimension multimodal benchmark functions.

Function	Criteria	COOTCLCO	COOT	PSO	GWO	SSA	BOA	SOA	SCA
F14	avg	0.998	0.998	1.6906	4.1922	0.998	1.0643	1.3948	1.3287
	std	3.0018 × 10−16	2.2395 × 10−16	1.4911	4.4183	1.725 × 10−16	0.36262	0.80721	0.75206
	W	/	≈	+	+	≈	+	+	+
	R	1	2	7	8	3	4	6	5
F15	avg	0.00046961	0.00064839	0.0004961	0.005088	0.00082478	0.00032609	0.0011046	0.00081571
	std	0.00020712	0.00031895	0.00039601	0.0085754	0.00024494	1.7582 × 10−05	0.00031781	0.00030811
	W	/	+	≈	+	+	−	+	+
	R	2	4	3	8	6	1	7	5
F16	avg	−1.0316	−1.0316	−1.0316	−1.0316	−1.0316	−1.0316	−1.0316	−1.0316
	std	6.8377 × 10−16	1.8251 × 10−12	6.7752 × 10−16	2.3368 × 10−09	3.931 × 10−15	1.0339 × 10−05	1.4916 × 10−07	1.4874 × 10−05
	W	/	≈	≈	≈	≈	+	+	+
	R	1	4	2	5	3	8	6	7
F17	avg	0.39789	0.39789	0.39789	0.39789	0.39789	0.39823	0.3979	0.39841
	std	0	1.2974 × 10−15	0	7.2275 × 10−08	2.070 × 10−15	0.00079194	1.0205 × 10−05	0.00052896
	W	/	+	≈	+	≈	+	+	+
	R	1	4	1	5	3	7	6	8
F18	avg	3	3	3	3	3	3.0112	3	3
	std	3.2769 × 10−15	1.5417 × 10−14	1.7916 × 10−15	7.3174 × 10−06	3.959 × 10−14	0.032131	1.9517 × 10−05	4.1425 × 10−05
	W	/	+	≈	+	≈	+	+	+
	R	1	4	2	5	3	8	7	6
F19	avg	−0.30048	−0.30048	−3.8628	−0.30048	−0.30048	−0.30048	−0.30048	−0.30048
	std	2.2584 × 10−16	2.2584 × 10−16	2.7101 × 10−15	2.2584 × 10−16	2.259 × 10−16	2.2584 × 10−16	2.2584 × 10−16	2.2584 × 10−16
	W	/	≈	−	+	≈	+	+	+
	R	2	3	1	7	4	6	5	8
F20	avg	−3.2982	−3.2943	−3.2625	−3.277	−3.2263	−3.1381	−2.7975	−2.8919
	std	0.04837	0.051146	0.060463	0.073544	0.048682	0.14729	0.54644	0.39914
	W	/	≈	+	+	+	+	+	+
	R	1	2	4	3	5	6	8	7
F21	avg	−9.6924	−9.2305	−6.3881	−9.1395	−7.5573	−9.0466	−3.1981	−3.0402
	std	1.3421	2.1365	3.4666	2.0617	3.122	0.94949	3.9074	2.2051
	W	/	+	+	+	+	+	+	+
	R	1	2	6	3	5	4	7	8
F22	avg	−9.5169	−10.2271	−6.578	−10.4027	−9.2863	−9.4478	−6.1925	−3.9181
	std	2.0147	0.96292	3.5147	0.00013733	2.584	1.1399	4.6827	1.9622
	W	/	−	+	−	+	≈	+	+
	R	3	2	6	1	5	4	7	8
F23	avg	−9.7655	−10.3577	−8.1972	−10.5362	−9.4872	−10.0631	−8.1032	−4.9455
	std	1.8698	0.97874	3.6466	0.00010617	2.4332	0.3434	3.9097	1.9771
	W	/	−	+	−	≈	−	+	+
	R	4	2	6	1	5	3	7	8
+/≈/−		/	4/4/2	5/4/1	7/1/2	4/6/0	7/1/2	10/0/0	10/0/0