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

Table 4

Results of unimodal benchmark functions.

Benchmark function	Result	Algorithm
		ABC	BA	GGSA	DA	PSOGSA	MFO	LMFO
()	Best	19896.78	365717.3	16278.78	1513.435	34835.45	140219.4	1.2921E − 234
	Worst	36049.23	456284	24262.84	52511.62	142227.4	240000.7	3.3309E − 183
	Mean	26677.04	414807.8	19224.04	24716.82	94735.12	185588.4	1.1103E − 184
	Std	4640.383	20515.24	1852.355	11046.55	25051.92	24177.67	0
()	Best	108.0735	1.83E + 84	149.7263	26.27986	637.56	420.5512	8.5E − 129
	Worst	186.4672	3.9E + 99	189.8577	255.79923	8.06E + 40	722.4955	7.3E − 99
	Mean	140.2811	1.45E + 98	165.8829	137.88594	2.69E + 39	560.1173	2.4E − 100
	Std	14.5252	7.06E + 98	9.599018	56.674292	1.47E + 40	61.66749	1.3E − 99
()	Best	582404	823783.5	160277.3	69110.62	344077.3	462517.7	1.6E − 215
	Worst	920006.2	4617625	1020727	906356.8	891332.5	1094366	6.4E − 167
	Mean	757278.3	1572330	434895.9	342508.6	541491.3	772538.3	3.3E − 168
	Std	72837.78	837152.1	190865.2	203490.9	142131.3	170946.5	0
()	Best	94.265	87.48997	20.44273	27.0486	76.25401	95.26014	6.1E − 117
	Worst	97.40102	92.12282	31.30115	59.69617	98.74303	98.15999	6.18E − 82
	Mean	95.8655	90.09865	27.12328	41.97914	95.69831	97.03653	2.06E − 83
	Std	0.778229	1.330154	2.551274	7.80909	5.90858	0.687621	1.13E − 82
()	Best	16111660	88328339	2399953	4717141	2565682	3.61E + 08	196.9121
	Worst	94041761	1.59E + 08	5103632	47976603	4.82E + 08	8.92E + 08	198.6685
	Mean	41344878	1.33E + 08	3740872	18257995	1.35E + 08	6.14E + 08	198.2609
	Std	17567952	18028179	643192.1	10933433	1.24E + 08	1.41E + 08	0.459128
()	Best	17165.43	384155.3	14899	4422.437	33665.58	136678.5	39.65709
	Worst	30743.79	453905.5	24873	63473.4	109123.6	228511.5	42.92694
	Mean	23922.99	417903	19220.47	24167.16	76561.32	180669.8	41.49763
	Std	3074.406	17001.78	2314.721	12441.1	19018.55	24671.19	0.632867
()	Best	51.88092	0.400252	6.492429	9.23801	11.89278	1181.991	2.3E − 06
	Worst	299.2207	0.744656	14.77883	181.7351	71.66514	2686.255	0.000427
	Mean	157.1676	0.551746	9.090199	52.06488	19.83666	1908.788	8.56E − 05
	Std	58.73575	0.072809	1.742479	39.34587	10.47516	360.7708	0.000108
()	Best	181.8735	172.1645	28.45978	14.59629	130.6204	168.6843	1.62807
	Worst	198.3101	200.1905	40.21054	80.16251	169.9275	202.2427	1.840634
	Mean	190.2888	188.036	33.67195	43.38706	153.398	187.9161	1.752264
	Std	4.168661	6.867959	2.232835	13.6498	10.91374	7.601635	0.06096