A Hybrid Lightning Search Algorithm-Simplex Method for Global Optimization

Table 5

Results of multimodal benchmark functions.

Benchmark function	Result	Algorithms								Rank
		LSA-SM	LSA	BA	FPA	GSA	GWO	WOA	GOA
()	Best	−9825.56	−9351.81	−8496	−7810.43	−4256.89	−7930.68	−9067.96	−8968.99	3
	Worst	−7337.76	−7040.88	−4751.55	−6948.99	−2499.65	−5228.28	−5969.66	−6138.18
	Mean	−8288.62	−7972.7	−6597.79	−7451.38	−2994.2	−6319.63	−7273.86	−7230.55
	Std.	579.2631	634.6361	978.568	225.2153	473.0903	734.5232	940.8279	705.6453
()	Best	0	36.81344	41.99486	110.0765	9.949591	0	0	21.89829	1
	Worst	0	110.4402	133.5967	163.6662	25.86893		0	127.3554
	Mean	0	67.75659	81.00623	132.9833	16.56607		0	66.23884
	Std.	0	17.36836	34.96265	14.67229	3.782151		0	24.06253
()	Best		1.340421	13.28169	4.245114				1.779031	1
	Worst		4.623521	16.48475	7.669989				4.92031
	Mean		2.641427	14.91377	5.537861				2.870023
	Std.		0.890342	0.897401	0.933813				0.679676
()	Best	0		31.60788	3.744125	1.952645	0	0	0.19975	1
	Worst	0	0.041831	308.7602	8.961942	8.369517	0.020272	0.029831	0.535447
	Mean	0	0.006156	97.01063	5.715779	4.129179	0.001419	0.001492	0.380767
	Std.	0	0.010115	60.57474	1.153166	1.834566	0.004793	0.00667	0.110967
()	Best			6.338175	6.64185			0.000202	0.837028	1
	Worst		2.597822	42.24743	17.12305	0.310964	0.079032	0.006291	8.283224
	Mean		0.493764	22.3022	9.904098	0.051832	0.02644	0.001012	4.515233
	Std.		0.721976	9.315506	2.499151	0.078873	0.017096	0.001486	1.725611