Table 2.

Comparison of mean fitness and standard deviation between MSCSO and existing optimization algorithms in CEC2005 test function (Bold indicates better data performance).

Function	Measures	MSCSO	SCSO	MFO	SSA	FVIM	AOA	SCA	PSO	DO	SFO
F1	Mean	0	1.6732 × 10−22	6.6835	1.2217 × 10−8	7.8252 × 10−55	1.0115 × 10−18	5.011 × 10−2	8.8258 × 10−7	1.2027 × 10−8	5.9286 × 10−19
	Std	0	0	2.5366	2.8644 × 10−9	2.3666 × 10−54	5.5403 × 10−18	1.2384 × 10−1	1.2243 × 10−6	8.8765 × 10−9	1.2626 × 10−18
F2	Mean	0	1.2274 × 10−11	3.3333	8.7898 × 10−1	6.0333 × 10−32	0	8.8029 × 10−5	3.4267 × 10−1	7.9067 × 10−5	2.9971 × 10−9
	Std	0	6.5811 × 10−11	2.0228	8.4123 × 10−1	7.6058 × 10−32	0	4.1444 × 10−4	1.8244	3.3934 × 10−5	2.3602 × 10−9
F3	Mean	0	7.1882 × 10−19	1.4705	2.6345	2.1786 × 10−6	2.6499 × 10−3	3.3952 × 103	2.5677	1.0250	1.2079 × 10−16
	Std	0	0	1.0837	2.1461	7.2399 × 10−6	7.6668 × 10−3	3.4423 × 103	1.1124	1.2048	2.1024 × 10−16
F4	Mean	0	9.6592 × 10−10	6.8430	8.0524	7.1856 × 10−2	1.6863 × 10−2	1.9320 × 101	3.8051	9.6583 × 10−2	2.0926 × 10−10
	Std	0	4.8151 × 10−10	8.5460	3.5330	3.1181 × 10−2	2.1198 × 10−2	1.3087 × 101	1.3945	5.1918 × 10−2	1.8565 × 10−10
F5	Mean	1.3318	2.8212 × 101	6.8812	1.8062	3.0309 × 101	2.8215 × 101	5.1516 × 102	9.4887	2.8709 × 101	2.8706 × 101
	Std	1.2855	6.9124 × 10−1	2.2651	3.6087	1.1645 × 101	4.3180 × 10−1	1.6177 × 103	1.1385	1.6104 × 101	1.4421 × 10−3
F6	Mean	1.67	1.82	2.3367	1.2538 × 10−8	3.5837	2.7693	4.7484	9.4045 × 10−7	9.1274 × 10−7	3.1592
	Std	6.3222	6.1323 × 10−1	6.8034	2.4312 × 10−9	8.3087 × 10−1	2.4581 × 10−1	8.6016 × 10−1	1.0517 × 10−6	4.1544 × 10−7	2.2552
F7	Mean	6.1529	9.1979 × 10−5	4.0113	1.0180 × 10−1	7.4159 × 10−3	3.9189 × 10−5	2.9036 × 10−2	2.4734 × 10−2	9.3052 × 10−3	8.1435 × 10−5
	Std	6.1166	1.1144 × 10−4	8.6251	3.7415 × 10−2	3.1360 × 10−3	4.5493 × 10−5	2.2559 × 10−2	7.8311 × 10−3	4.9979 × 10−3	6.9022 × 10−5
F8	Mean	−1.203	−6.9303	−8.9559	−7.3619	−5.3718	−5.8265	−3.8623	−7.6221	−8.2970	−3.9342
	Std	1.1679	8.6264 × 102	9.3253	6.9246	1.1014 × 103	3.7253 × 102	2.8576 × 102	7.3327	6.2155 × 102	1.1031 × 103
F9	Mean	0	0	1.7763	5.8006	3.5712 × 101	0	1.6014 × 101	4.8457	1.5862 × 101	0
	Std	0	0	4.3103	2.2665	9.3304	0	1.9496 × 101	1.3825	1.1639 × 101	0
F10	Mean	4.4409 × 10−1	4.4409 × 10−1	1.2452	2.0840	8.1416 × 10−15	4.4409 × 10−1	1.4426 × 101	4.5028 × 10−1	2.4648 × 10−5	5.2770 × 10−10
	Std	0	0	8.5861	8.4850 × 10−1	1.8853 × 10−15	0	8.1441	6.5171 × 10−1	1.1472 × 10−5	5.3965 × 10−10
F11	Mean	0	0	1.5158	1.1401 × 10−2	5.5451 × 10−3	9.9232 × 10−2	2.7640 × 10−1	1.9719 × 10−2	1.5936 × 10−2	0
	Std	0	0	3.4452	1.1605 × 10−2	8.8110 × 10−3	8.2692 × 10−2	2.8250 × 10−1	2.5921 × 10−2	1.6144 × 10−2	0
F12	Mean	2.6045	7.3425 × 10−2	1.5387	4.8849 × 101	8.1274 × 10−1	4.0717 × 10−1	6.5974 × 102	8.5519 × 10−2	6.9630 × 10−8	2.7687 × 10−1
	Std	1.3674	2.9459 × 10−2	4.6668	3.0881	6.0639 × 10−1	4.6520 × 10−2	3.5664 × 103	2.0937 × 10−1	3.6371 × 10−8	3.8328 × 10−1
F13	Mean	4.7895	2.4395	1.3669	1.6889	2.2887	2.7819	4.5932 × 102	6.2330 × 10−3	1.0343 × 10−6	1.0019 × 10−2
	Std	1.0445	4.2140 × 10−1	7.4867	6.2236	3.9923 × 10−1	1.2718 × 10−1	2.4504 × 103	1.1425 × 10−2	3.7267 × 10−7	3.2748 × 10−2
F14	Mean	1.0311	6.0842	2.3483	9.98 × 10−1	9.1841	1.0218 × 101	1.4618	9.98 × 10−1	9.98 × 10−1	8.1515
	Std	1.8148	4.5054	1.9251	2.6562 × 10−16	4.6576	3.1487	8.5309 × 10−1	4.1233 × 10−17	4.9736 × 10−16	4.8078
F15	Mean	3.1987	4.0878 × 10−4	1.7980 × 10−3	8.3495 × 10−4	5.0951 × 10−3	2.2018 × 10−2	8.5939 × 10−4	3.6175 × 10−3	1.1016 × 10−3	1.8113 × 10−2
	Std	3.9231	2.7855 × 10−4	3.5397 × 10−3	2.8094 × 10−4	8.6189 × 10−3	3.5493 × 10−2	3.5571 × 10−4	1.1204 × 10−2	3.6516 × 10−3	3.0145 × 10−2
F16	Mean	−1.031628	−1.0316284	−1.0316284	−1.0316284	−1.0316282	−1.0316283	−1.0316002	−1.0316284	−1.0316284	−1.0316282
	Std	4.0375 × 10−1	2.4429 × 10−10	6.7752 × 10−16	7.2408 × 10−15	8.8799 × 10−7	1.0438 × 10−7	2.7392 × 10−5	6.7752 × 10−16	8.2357 × 10−14	1.0214 × 10−6
F17	Mean	0.3978873	0.39788737	0.39788736	0.39788736	0.39788755	0.40560883	0.39892979	0.39788736	0.39788736	0.39791132
	Std	5.1770	2.0828 × 10−8	0	5.2723 × 10−15	4.3609 × 10−7	7.5248 × 10−3	9.4806 × 10−4	0	3.4351 × 10−12	1.0370 × 10−4
F18	Mean	3.0000007	3.00000123	3	3	3.00003310	10.9652648	3.00003931	3	3.00000000	12.0000119
	Std	1.5252	1.8880 × 10−6	1.3297 × 10−15	1.3386 × 10−13	5.1040 × 10−5	1.2387 × 101	8.7638 × 10−5	8.8049 × 10−16	2.2231 × 10−9	2.4901 × 101
F19	Mean	3.8627805	−3.8616140	−3.8627821	−3.8627821	−3.8627257	−3.8536551	−3.8550555	−3.8627821	−3.8627821	−3.8035099
	Std	2.3680 × 10−6	2.7517 × 10−3	2.7101 × 10−15	5.2138 × 10−14	6.4765 × 10−5	2.6938 × 10−3	1.8405 × 10−3	2.6823 × 10−15	2.3382 × 10−8	1.9563 × 10−1
F20	Mean	−3.322	−3.2477	−3.1982	−3.2238	−3.2821	−3.0976	−2.8989	−3.2679	−3.2744	−2.9596
	Std	2.1588 × 10−6	1.1059 × 10−1	5.7419 × 10−2	5.0081 × 10−2	5.7438 × 10−2	7.5351 × 10−2	3.0548 × 10−1	6.9818 × 10−2	5.9241 × 10−2	1.9696 × 10−1
F21	Mean	−9.983	−5.0860	−6.3886	−7.3946	−7.1978	−3.7087	−2.2721	−5.7286	−6.0454	−5.7652
	Std	9.3075 × 10−1	1.2230	3.4639	3.3091	3.2043	1.1244	1.9682	3.3243	3.3225	2.8908
F22	Mean	−9.694	−6.8608	−8.7772	−9.5422	−9.5982	−4.2464	−3.1372	−6.5563	−7.3459	−5.8515
	Std	1.8377	2.5475	3.0521	2.2747	2.2776	1.6229	1.7211	3.5019	3.6572	2.9746
F23	Mean	−9.996	−6.4471	−7.4247	−8.2498	−9.7547	−4.2953	−3.8125	−7.6379	−6.7571	−6.0959
	Std	1.6501	3.1867	3.6601	3.5821	2.3855	1.1388	1.9384	3.6788	3.7216	3.1840
Avg. rank		1.57	3.61	6.22	4.52	4.48	5.65	7.70	4.65	3.61	5.39