MEEF: A Minimum-Elimination-Escape Function Method for Multimodal Optimization Problems

Table 4

Results obtained by the MEEF method starting from different initial points.

		Initial point	Obtained solution	Function value	FE
	2	(−2, −2)	(−0.089842004424893, 0.712656395105758)	−1.031628453489877	89
	2	(8, 8)	(9.424776894809153, 2.474997849423675)	0.397887357736760	30
	2	(−2, −2)	(0.000000010826836, −0.999999992529544)	3.000000000000036	97
	2	(−0.7, −0.6)	(0.836906625737857, −0.650879325753485)	−1.999999999999982	74
	2	(−2, −2)	(0.999999408887528, 0.999998918185347)	3.544550322092880	45
		(−2, 2)	(1.000000321772440, 0.999999706335175)	5.427186156663280	39
	2	(−2, −2)	(0.025802684495041, 0.484606092900819)	2.236704842114040	55
		(−2, 2)	(0.025802684495041, 0.484606092900819)	1.206260598539464	33
	2	(−2, −2)	(−2.000000119209290, 0.000000000000016)	2.236704842114040	9
		(−2, 2)	(−2.000000119209290, −0.000000000000016)	2.236704842114040	9
	2	(5, 5)	(5.482864160335367, 4.858056875878652)	−186.7309088310190	52
		(8, 8)	(18.049234762369981, 4.858057086084300)	−186.7309088309161	93
	2	(8, 8)	(−1.425128433538681, −0.800321104507429)	−186.7309088310213	123
	2	(8, 8)	(−1.425128424119843, −0.800321101249553)	−186.7309088310201	91
	4	(3, 3, 3, 3)	(4.000037114918254, 4.000133242814511, 4.000037114918254, 4.000133242814511)	−10.153199679057712	80
	4	(3, 3, 3, 3)	(4.000572886907811, 4.000689336992803, 3.999489678498883, 3.999606128564901)	−10.402940566818305	110
	4	(3, 3, 3, 3)	(4.000746502821329, 4.000592906692932, 3.999663365362384, 3.999509769213728)	−10.536409816691679	110
	6	(5, …, 5)	(1.000000001648912, 1.000002074290066, 1.000002058608007, 1.000002058496111, 1.000002058496307, 1.000002058512318)	1.112809898134190	49
		(8, …, 8)	(1.000000053505098, 0.999999912139717, 0.999999918053981, 0.999999918047487, 0.999999918031023, 0.999999905452657)	1.687131064818418	63
	6	(5, …, 5)	(1.000000102099649, 0.999999675649315, 0.999998985096000, 1.000005834707141, 0.999992602921426, 1.000002804125038)	3.233163366392778	357
		(8, …, 8)	(0.999999977831993, 1.000001966743495, 0.999999885358024, 1.000000409193240, 1.000000132358755, 0.999999852114368)	1.353844335746799	413
	6	(4, …, 4)	(1.000000178908328, 1.000007873947206, 1.000002877836001, 0.999999355316356, 0.999984951143500, 1.000000910594055)	2.983417815754360	835
		(8, …, 8)	(1.000000346074765, 0.999995860881688, 1.000000027091785, 1.000006231036376, 1.000001238636247, 0.999998410125881)	6.132259614323958	266
	30	(500, …, 500)	(420.96874, …, 420.96874)	−12569.48661817271	217
		(321, …, 321)	(420.96873, …, 420.96873)	−12569.48661817220	310
	30	(−3, …, −3)	(0.15432, …, 0.15432)	0	217
		(−5, …, −5)	(−0.78662277565, …, −0.78662277565)	3.730349362740526	217
		(5, …, 5)	(−0.78662277565, …, −0.78662277565)	3.730349362740526	217
	30	(50, …, 50)	(−2.9035340, …, −2.9035340)	−1174.984971113140	652