A Novel Differential Evolution Invasive Weed Optimization Algorithm for Solving Nonlinear Equations Systems

Table 9

Comparison of results for kinematic application benchmark.

Algorithm	EA			DEIWO
	Solutions	Functions values	Error	Solutions	Functions values	Error
Solution 1	−0.0625820337; 0.7777446281; −0.0503725828; 0.3805368959; −0.5592587603; −0.6988338865; 0.3963927675; 0.0861763643	0.3911967824; 0.3925758963; 0.8526542737; 0.5424213097; 0.7742116224; 0.1537105718; 0.9116019977; 0.1519175234	2.8055186567	0.045507371706493; 0.998085408972999; 0.024366076545306; −0.998881362713880; −0.008164213640613; −0.773486615357711; 0.001737164451486; −1.189751083986727	0.001754595515567; 0.003231810708989; 0.001642317536650; 0.002169368838492; 0.004282027104326; 0.001214133281959; 0.003982242223259; 0.006623094167720	0.0001004601
Solution 2	−0.1564353525; 0.4507122320; 0.4622139796; −0.8818348503; −0.6522824284; 0.4082826235; 0.4718261386; −0.5070478474	0.7723864643; 0.5832167209; 0.0087255337; 0.2031050697; 0.6056929403; 0.3663682493; 0.3532359802; 0.4646334692	1.8197999485	−0.209908402344501; 0.978141679315801; 0.203396084482184; 0.981576540651021; −0.195397812001838; 0.225356569439925; −0.346358155642600; −1.054154642146118	0.000822682189556; 0.001868888002580; 0.004862472339110; 0.001672810091532; 0.006669856089477; 0.004274595104825; 0.003392827053353; 0.006142247670554	0.0001426091
Solution 3	−0.5618177814; 0.8473813517; 0.2226897354; −0.0846064846; −0.7914861841; −0.4111014166; 0.3056098314; 0.4290046184	0.0336943748; 0.2323541264; 0.9432510244; 0.3663913629; 0.0081327333; 0.2206688453; 0.624967041; 0.4690397335	1.7384318314	−0.202282750875349; 0.980451072049731; 0.204486405102704; 0.980955265324429; −0.200955394943197; 0.226603999519539; −0.346215357036744; −1.055887922168507	0.002202615985165; 0.003098994555294; 0.004087922439548; 0.002656303324497; 0.007030249990859; 0.000351392074988; 0.002940170368879; 0.004663375717434	0.0001181619
Solution 4	0.0608363294; 0.5053398770; 0.3301025811; −0.3441350935; −0.2611454909; −0.1335439441; 0.7518856650; −0.3711959678	0.7409305497; 0.6356638946; 0.7726033233; 0.8133740699; 0.0176109130; 0.0929407653; 0.2565663633; 0.260158013	2.3539965598	0.089422621197712; 0.997785665917926; 0.068431332656990; −0.997200694366805; 0.035163660058698; −0.842053211908446; −0.019839283580881; −1.151839767619862	0.003572640293149; 0.000259082400491; 0.000907927865151; 0.004354292165639; 0.003188494681972; 0.001119794486023; 0.003566152462141; 0.004730361789871	0.0000791293
Solution 5	−0.7461742647; 0.5365985698; 0.4907094198; 0.1144124666; −0.5433290610; 0.3443841680; 0.6758924483; −0.3341809018	0.1552859413; 0.4712662401; 0.7461140527; 0.6917033188; 0.9909917470; 0.0271473496; 0.0900355495; 0.20247922410	2.3132511111	0.005618623394285; 0.993946653150363; 0.118580049821602; −0.993497493618748; −0.114812848523787; −0.699491795013951; 0.036947466879746; −1.208913136968972	0.012038481762346; 0.001991177524501; 0.001098498042427; 0.000219260012879; 0.001036835150341; 0.001125049094542; 0.000179375216701; 0.002011941060148	0.0001565654
Solution 6	−0.3064809352; −0.0056167467; −0.5007294639; −0.0944531990; −0.7161265376; 0.6371096100; 0.4792262814; −0.4680908930	0.9060378884; 0.7492384561; 0.7403485971; 0.4782413752; 0.8882665877; 0.2081000785; 0.7690562864; 0.4979341279	3.8308029184	0.077779987853934; 0.997317971174144; 0.056964437816277; −0.998437109323217; 0.037128587012228; −0.830589842164460; −0.026418733632420; −1.159254624161276	0.000692862137470; 0.002111917197364; 0.000121608449425; 0.001744806752775; 0.001103067513220; 0.003814260073128; 0.005523418787933; 0.006023917232275	0.0000905605
Solution 7	−0.5739275815; 0.3767142036; 0.1299295442; −0.8025240903; −0.3026761756; 0.1226779594; 0.7855891471; −0.1240877403	0.5286935399; 0.8412047222; 0.3390733979; 0.2643422170; 0.5162506493; 0.2659449070; 0.4029986127; 0.5347985046	1.9576485695	0.062451694147746; 0.999289247478883; −0.065940504171922; −0.998657897816642; 0.031995659386056; −0.777915484740598; 0.011189710814883; −1.188813754784150	0.002479214228837; 0.002927150217360; 0.001665746962001; 0.001658680908898; 0.000472802926307; 0.000768554472374; 0.004544515610755; 0.003312159443232	0.0000526779
Solution 8	0.7822939914; −0.4935865657; 0.8029653752; 0.0804385674; 0.9223437373; 0.0296919251; 0.7980078255; −0.8324923146	0.1443884130; 0.1116189082; 0.3487762429; 0.1428116670; 0.3802921343; 0.5311414488; 0.0338066582; 0.0083023855	0.6032920001	0.129736374626430; 0.991078327417070; 0.114651095272193; −0.993508195985984; 0.094700498150336; −0.914637593030690; −0.052275570550158; −1.115505051433812	0.000932222022973; 0.004618875277069; 0.000203409138437; 0.003973280158754; 0.001204313453836; 0.001429540419579; 0.003053228353648; 0.004263676032891	0.0000690265
Solution 9	−0.7461742647; 0.6057926381; 0.9271482376; 0.2664085959; −0.4794066217; −0.3302191010; 0.7692157072; −0.1642217317	0.0762392460; 0.2265885749; 0.0694226055; 0.6991957509; 0.0290725466; 0.1921690687; 0.4459273853; 0.7592540224	1.3773369662	0.028424442196598; 0.997354294976930; 0.049494813895825; −0.999159498545526; −0.049400903337364; −0.740573888955816; 0.016727719945304; −1.200998766591111	0.004476461376883; 0.002834673688489; 0.000769440136329; 0.000760152784294; 0.000030652634633; 0.001888111028099; 0.003940336679685; 0.002887323459874	0.0000566727
Solution 10	−0.6205399028; 0.6846519932; −0.9933817672; −0.0541621937; −0.0748152730; 0.37913950333; −0.4826393335; −0.7830381952	0.1461818771; 0.4555568728; 0.0102591212; 0.9914691316; 0.2920414356; 0.5909270772; 0.8366810215; 0.7918662138	2.5250914998	0.270276389119342; 0.966742987729601; 0.251572811188323; −0.968707517259438; 0.233925117931725; −1.122930726803439; −0.122906457137246; −1.014959836413780	0.007641330839746; 0.002119116346448; 0.001683133324140; 0.006884785205684; 0.002237943072133; 0.002719402992536; 0.004568280905804; 0.000607655156908	0.0001467558