Table A4.

The Detailed Comparison Of Various Algorithms On Various Dimensions Of CEC05 Benchmark Functions(b).

		DE [6]				GWO [18]				HHO [83]
		ave	best	worst	std	ave	best	worst	std	ave	best	worst	std
F1	50	$1.72\times {10}^1$	$9.23$	$2.65\times {10}^1$	$5.98$	$1.36\times {10}^{-43}$	$7.04\times {10}^{-46}$	$6.63\times {10}^{-43}$	$2.63\times {10}^{-43}$	$5.35\times {10}^{-76}$	$3.87\times {10}^{-86}$	$2.64\times {10}^{-75}$	$1.05\times {10}^{-75}$
	100	$3.35\times {10}^3$	$2.85\times {10}^3$	$4.58\times {10}^3$	$6.33\times {10}^2$	$1.37\times {10}^{-40}$	$6.06\times {10}^{-42}$	$5.70\times {10}^{-40}$	$2.17\times {10}^{-40}$	$6.46\times {10}^{-74}$	$1.16\times {10}^{-77}$	$3.21\times {10}^{-73}$	$1.28\times {10}^{-73}$
	200	$4.44\times {10}^4$	$3.81\times {10}^4$	$5.24\times {10}^4$	$4.89\times {10}^3$	$2.66\times {10}^{-39}$	$2.64\times {10}^{-40}$	$4.90\times {10}^{-39}$	$1.71\times {10}^{-39}$	$1.77\times {10}^{-73}$	$3.81\times {10}^{-89}$	$8.38\times {10}^{-73}$	$3.31\times {10}^{-73}$
	500	$3.32\times {10}^5$	$3.12\times {10}^5$	$3.62\times {10}^5$	$1.83\times {10}^4$	$9.00\times {10}^{-37}$	$1.61\times {10}^{-38}$	$2.35\times {10}^{-36}$	$8.68\times {10}^{-37}$	$5.92\times {10}^{-71}$	$6.29\times {10}^{-80}$	$2.96\times {10}^{-70}$	$1.18\times {10}^{-70}$
	1000	$9.89\times {10}^5$	$9.61\times {10}^5$	$1.03\times {10}^6$	$2.37\times {10}^4$	$7.99\times {10}^{-36}$	$1.28\times {10}^{-37}$	$2.89\times {10}^{-35}$	$1.05\times {10}^{-35}$	$1.73\times {10}^{-69}$	$1.61\times {10}^{-79}$	$7.96\times {10}^{-69}$	$3.12\times {10}^{-69}$
F2	50	$5.86$	$2.43$	$1.02\times {10}^1$	$2.85$	$6.47\times {10}^{-28}$	$1.69\times {10}^{-28}$	$1.56\times {10}^{-27}$	$5.14\times {10}^{-28}$	$3.71\times {10}^{-37}$	$1.93\times {10}^{-39}$	$1.13\times {10}^{-36}$	$4.49\times {10}^{-37}$
	100	$1.64\times {10}^2$	$1.42\times {10}^2$	$1.75\times {10}^2$	$1.16\times {10}^1$	$6.78\times {10}^{-26}$	$5.15\times {10}^{-26}$	$9.05\times {10}^{-26}$	$1.60\times {10}^{-26}$	$7.65\times {10}^{-39}$	$3.14\times {10}^{-43}$	$3.62\times {10}^{-38}$	$1.43\times {10}^{-38}$
	200	$4.61\times {10}^2$	$4.34\times {10}^2$	$4.98\times {10}^2$	$2.47\times {10}^1$	$3.59\times {10}^{-24}$	$6.36\times {10}^{-25}$	$7.94\times {10}^{-24}$	$2.62\times {10}^{-24}$	$1.33\times {10}^{-36}$	$4.44\times {10}^{-42}$	$6.65\times {10}^{-36}$	$2.66\times {10}^{-36}$
	500	$1.44\times {10}^3$	$1.37\times {10}^3$	$1.50\times {10}^3$	$5.27\times {10}^1$	$3.02\times {10}^{-23}$	$2.07\times {10}^{-23}$	$3.84\times {10}^{-23}$	$6.20\times {10}^{-24}$	$1.00\times {10}^{-38}$	$1.25\times {10}^{-42}$	$4.96\times {10}^{-38}$	$1.97\times {10}^{-38}$
	1000	N/A	N/A	N/A	N/A	$5.10\times {10}^{-23}$	$3.14\times {10}^{-23}$	$7.40\times {10}^{-23}$	$1.37\times {10}^{-23}$	$3.14\times {10}^{-36}$	$2.63\times {10}^{-46}$	$1.55\times {10}^{-35}$	$6.21\times {10}^{-36}$
F3	50	$9.96\times {10}^4$	$8.80\times {10}^4$	$1.13\times {10}^5$	$8.75\times {10}^3$	$1.49\times {10}^1$	$7.67\times {10}^{-1}$	$5.56\times {10}^1$	$2.11\times {10}^1$	$3.82\times {10}^{-49}$	$2.22\times {10}^{-74}$	$1.91\times {10}^{-48}$	$7.65\times {10}^{-49}$
	100	$4.75\times {10}^5$	$4.27\times {10}^5$	$5.38\times {10}^5$	$3.93\times {10}^4$	$2.83\times {10}^3$	$2.90\times {10}^2$	$8.03\times {10}^3$	$2.77\times {10}^3$	$1.49\times {10}^{-52}$	$8.99\times {10}^{-61}$	$7.48\times {10}^{-52}$	$2.99\times {10}^{-52}$
	200	$1.76\times {10}^6$	$1.64\times {10}^6$	$1.87\times {10}^6$	$8.77\times {10}^4$	$3.52\times {10}^4$	$1.20\times {10}^4$	$9.74\times {10}^4$	$3.15\times {10}^4$	$2.95\times {10}^{-50}$	$1.61\times {10}^{-60}$	$1.47\times {10}^{-49}$	$5.89\times {10}^{-50}$
	500	$1.05\times {10}^7$	$8.72\times {10}^6$	$1.15\times {10}^7$	$1.00\times {10}^6$	$4.49\times {10}^5$	$2.48\times {10}^5$	$6.42\times {10}^5$	$1.40\times {10}^5$	$1.78\times {10}^{-45}$	$2.04\times {10}^{-57}$	$8.92\times {10}^{-45}$	$3.57\times {10}^{-45}$
	1000	$4.31\times {10}^7$	$4.12\times {10}^7$	$4.54\times {10}^7$	$1.41\times {10}^6$	$4.04\times {10}^6$	$2.77\times {10}^6$	$5.44\times {10}^6$	$9.94\times {10}^5$	$1.57\times {10}^{-19}$	$2.63\times {10}^{-60}$	$7.87\times {10}^{-19}$	$3.15\times {10}^{-19}$
F4	50	$9.11\times {10}^1$	$8.85\times {10}^1$	$9.35\times {10}^1$	$1.62$	$8.10\times {10}^{-8}$	$9.67\times {10}^{-9}$	$2.83\times {10}^{-7}$	$1.03\times {10}^{-7}$	$5.25\times {10}^{-36}$	$1.20\times {10}^{-41}$	$2.62\times {10}^{-35}$	$1.04\times {10}^{-35}$
	100	$9.56\times {10}^1$	$9.46\times {10}^1$	$9.68\times {10}^1$	$7.61\times {10}^{-1}$	$2.21\times {10}^{-6}$	$1.22\times {10}^{-7}$	$5.87\times {10}^{-6}$	$1.94\times {10}^{-6}$	$4.69\times {10}^{-38}$	$1.96\times {10}^{-40}$	$1.54\times {10}^{-37}$	$5.89\times {10}^{-38}$
	200	$9.76\times {10}^1$	$9.71\times {10}^1$	$9.84\times {10}^1$	$4.48\times {10}^{-1}$	$8.10\times {10}^{-4}$	$1.42\times {10}^{-5}$	$3.43\times {10}^{-3}$	$1.31\times {10}^{-3}$	$9.14\times {10}^{-34}$	$1.20\times {10}^{-43}$	$4.55\times {10}^{-33}$	$1.82\times {10}^{-33}$
	500	$9.88\times {10}^1$	$9.80\times {10}^1$	$9.93\times {10}^1$	$4.83\times {10}^{-1}$	$4.07\times {10}^{-1}$	$8.65\times {10}^{-2}$	$6.77\times {10}^{-1}$	$2.44\times {10}^{-1}$	$1.19\times {10}^{-37}$	$8.57\times {10}^{-44}$	$5.93\times {10}^{-37}$	$2.37\times {10}^{-37}$
	1000	$9.95\times {10}^1$	$9.93\times {10}^1$	$9.97\times {10}^1$	$1.13\times {10}^{-1}$	$7.84$	$1.37$	$2.75\times {10}^1$	$9.97$	$8.51\times {10}^{-38}$	$9.46\times {10}^{-42}$	$4.19\times {10}^{-37}$	$1.67\times {10}^{-37}$
F5	50	$3.65\times {10}^3$	$2.82\times {10}^3$	$4.09\times {10}^3$	$4.48\times {10}^2$	$4.67\times {10}^1$	$4.55\times {10}^1$	$4.83\times {10}^1$	$9.89\times {10}^{-1}$	$1.94\times {10}^{-2}$	$2.66\times {10}^{-3}$	$6.93\times {10}^{-2}$	$2.50\times {10}^{-2}$
	100	$2.76\times {10}^6$	$1.24\times {10}^6$	$3.38\times {10}^6$	$7.74\times {10}^5$	$9.76\times {10}^1$	$9.73\times {10}^1$	$9.81\times {10}^1$	$2.66\times {10}^{-1}$	$1.01\times {10}^{-2}$	$2.34\times {10}^{-3}$	$2.94\times {10}^{-2}$	$1.02\times {10}^{-2}$
	200	$5.41\times {10}^7$	$4.13\times {10}^7$	$6.31\times {10}^7$	$8.00\times {10}^6$	$1.96\times {10}^2$	$1.95\times {10}^2$	$1.97\times {10}^2$	$9.89\times {10}^{-1}$	$3.27\times {10}^{-2}$	$3.09\times {10}^{-3}$	$7.82\times {10}^{-2}$	$2.47\times {10}^{-2}$
	500	$6.95\times {10}^8$	$5.87\times {10}^8$	$8.68\times {10}^8$	$1.01\times {10}^8$	$4.95\times {10}^2$	$4.95\times {10}^2$	$4.96\times {10}^2$	$4.04\times {10}^{-1}$	$1.01\times {10}^{-1}$	$8.89\times {10}^{-3}$	$3.33\times {10}^{-1}$	$1.21\times {10}^{-1}$
	1000	$2.44\times {10}^9$	$2.17\times {10}^9$	$2.63\times {10}^9$	$1.56\times {10}^8$	$9.94\times {10}^2$	$9.94\times {10}^2$	$9.94\times {10}^2$	$1.76\times {10}^{-1}$	$8.92\times {10}^{-2}$	$2.61\times {10}^{-2}$	$2.16\times {10}^{-1}$	$6.81\times {10}^{-2}$
F6	50	$1.44\times {10}^1$	$8.31$	$2.42\times {10}^1$	$5.49$	$1.10$	$5.12\times {10}^{-1}$	$2.01$	$5.13\times {10}^{-1}$	$1.80\times {10}^{-4}$	$5.87\times {10}^{-6}$	$5.09\times {10}^{-4}$	$2.06\times {10}^{-4}$
	100	$3.04\times {10}^3$	$1.96\times {10}^3$	$3.50\times {10}^3$	$5.65\times {10}^2$	$4.47$	$3.52$	$6.26$	$9.89\times {10}^{-1}$	$4.52\times {10}^{-5}$	$1.81\times {10}^{-5}$	$9.08\times {10}^{-5}$	$2.46\times {10}^{-5}$
	200	$4.80\times {10}^4$	$3.98\times {10}^4$	$5.98\times {10}^4$	$6.85\times {10}^3$	$1.25\times {10}^1$	$1.12\times {10}^1$	$1.35\times {10}^1$	$7.27\times {10}^{-1}$	$2.28\times {10}^{-4}$	$2.05\times {10}^{-5}$	$5.23\times {10}^{-4}$	$2.18\times {10}^{-4}$
	500	$3.24\times {10}^5$	$3.16\times {10}^5$	$3.30\times {10}^5$	$6.24\times {10}^3$	$4.89\times {10}^1$	$4.45\times {10}^1$	$5.23\times {10}^1$	$2.65$	$6.46\times {10}^{-4}$	$1.08\times {10}^{-4}$	$1.25\times {10}^{-3}$	$4.79\times {10}^{-4}$
	1000	$1.01\times {10}^6$	$9.75\times {10}^5$	$1.07\times {10}^6$	$3.42\times {10}^4$	$1.27\times {10}^2$	$1.22\times {10}^2$	$1.31\times {10}^2$	$3.64$	$2.59\times {10}^{-3}$	$3.34\times {10}^{-5}$	$5.59\times {10}^{-3}$	$2.16\times {10}^{-3}$
F7	50	$1.82\times {10}^{-1}$	$1.66\times {10}^{-1}$	$2.13\times {10}^{-1}$	$1.68\times {10}^{-2}$	$1.94\times {10}^{-3}$	$4.96\times {10}^{-4}$	$4.81\times {10}^{-3}$	$1.60\times {10}^{-3}$	$3.66\times {10}^{-5}$	$9.47\times {10}^{-6}$	$5.53\times {10}^{-5}$	$1.80\times {10}^{-5}$
	100	$4.65$	$1.75$	$8.58$	$2.42$	$2.16\times {10}^{-3}$	$9.59\times {10}^{-4}$	$3.69\times {10}^{-3}$	$8.86\times {10}^{-4}$	$5.71\times {10}^{-5}$	$4.17\times {10}^{-5}$	$8.90\times {10}^{-5}$	$1.78\times {10}^{-5}$
	200	$1.51\times {10}^2$	$1.23\times {10}^2$	$1.68\times {10}^2$	$1.56\times {10}^1$	$1.27\times {10}^{-3}$	$4.17\times {10}^{-4}$	$2.46\times {10}^{-3}$	$7.70\times {10}^{-4}$	$1.26\times {10}^{-4}$	$1.28\times {10}^{-5}$	$2.46\times {10}^{-4}$	$9.17\times {10}^{-5}$
	500	$5.26\times {10}^3$	$4.66\times {10}^3$	$5.85\times {10}^3$	$4.08\times {10}^2$	$3.81\times {10}^{-3}$	$1.78\times {10}^{-3}$	$5.06\times {10}^{-3}$	$1.17\times {10}^{-3}$	$3.05\times {10}^{-4}$	$2.18\times {10}^{-5}$	$8.95\times {10}^{-4}$	$3.16\times {10}^{-4}$
	1000	$3.57\times {10}^4$	$3.11\times {10}^4$	$3.91\times {10}^4$	$3.26\times {10}^3$	$2.75\times {10}^{-3}$	$1.28\times {10}^{-3}$	$4.36\times {10}^{-3}$	$1.21\times {10}^{-3}$	$1.44\times {10}^{-4}$	$4.37\times {10}^{-5}$	$5.09\times {10}^{-4}$	$1.82\times {10}^{-4}$