Lévy-Flight Moth-Flame Algorithm for Function Optimization and Engineering Design Problems

Table 5

Results of multimodal benchmark functions.

Benchmark function	Result	Algorithm
		ABC	BA	GGSA	DA	PSOGSA	MFO	LMFO
()	Best	575.1608	1363.369	1563.422	730.92416	922.1832	1769.441	0
	Worst	709.019	1810.465	1867.616	1890.9545	1476.272	2125.69	0
	Mean	653.9316	1630.768	1752.838	1367.3899	1231.578	1951.426	0
	Std	36.46425	100.7203	81.02372	280.04565	117.1903	79.01827	0
()	Best	12.54258	19.20527	10.52907	8.666612	19.23309	19.92131	8.88E − 16
	Worst	14.8045	19.9564	11.89042	14.75436	19.96677	20.01897	8.88E − 16
	Mean	13.82113	19.73614	11.21024	11.88909	19.69719	19.95433	8.88E − 16
	Std	0.554162	0.260154	0.383654	1.453704	0.31107	0.019396	0
()	Best	142.2548	4290.404	137.6285	61.43179	654.9388	1229.64	0
	Worst	316.036	5283.435	221.9276	600.151	1631.547	2048.454	0
	Mean	225.3103	4997.492	171.5404	224.0744	1251.695	1543.04	0
	Std	51.75854	184.8135	16.55978	104.4042	204.6207	197.6001	0
()	Best	7393398	3.86E + 08	28.17774	1662.384	7043398	7.03E + 08	8.88E − 16
	Worst	1.67E + 08	6.85E + 08	77685.77	23172033	2.05E + 09	1.92E + 09	8.88E − 16
	Mean	58731093	5.59E + 08	11043.76	2516012	7.28E + 08	1.3E + 09	8.88E − 16
	Std	37177591	81914079	20355.03	4641204	5.15E + 08	3.01E + 08	0
()	Best	19464968	1.25E + 09	646700.5	2620391	26666517	1.68E + 09	19.4713
	Worst	3.4E + 08	2.09E + 09	3319003	1.83E + 08	2.47E + 09	4.04E + 09	19.79025
	Mean	1.53E + 08	1.72E + 09	1684844	27183053	9.73E + 08	2.62E + 09	19.62771
	Std	82296565	1.89E + 08	724732.9	34759974	7.07E + 08	5.46E + 08	0.072549
()	Best	47.28706	90.66079	103.3283	15.38694	58.10706	129.0595	1.1E − 125
	Worst	62.0743	168.7346	139.0044	197.7987	107.5327	216.9578	1.1E − 103
	Mean	53.55967	119.4603	118.7804	116.3619	80.96392	171.3074	3.9E − 105
	Std	3.438082	19.18661	8.52589	43.5411	12.93695	23.18654	2E − 104
()	Best	5373.354	4315.808	461.6698	1142.924	4411.244	5741.417	5E − 168
	Worst	6101.204	10167.76	3585.345	4914.844	9429.568	11241.25	2.6E − 117
	Mean	5810.789	5283	1327.234	3451.42	6873.222	8566.525	8.6E − 119
	Std	207.7704	1065.437	640.8766	1139.356	1451.294	1527.992	4.7E − 118