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

Table 10

Comparison of results for combustion application benchmark.

Algorithm	EA			DEIWO
	Solutions	Functions values	Error	Solutions	Functions values	Error
Solution 1	−0.0552429896; −0.0023377533; 0.0455880930; −0.1287029472; 0.0539771728; −0.0151036079; 0.1063159019; 0.0386267592; −0.1144905135; 0.0872294353	0.0274133878; 0.0841848522; 0.1482418893; 0.0839188567; 0.0030517851; 0.0000109317; 0.0165644486; 0.0025184283; 0.0001291515; 0.0000003019	0.0371466690	0.003672929585885; 0.025839710713681; 0.521599141528195; 0.004984881426735; 0.628058027576599; 1.337360448010958; −0.001636439489080; −0.525728707174303; 1.237228898173834; −1.967867906657906	0.002043691593620; 0.004159565646108; 0.000758296565400; 0.001702002448575; 0.000013458126816; 0.001335246636430; 0.000024849042839; 0.001915875580313; 0.000094830798928; 0.000002452380746	0.0000304137
Solution 2	−0.0338378558; 0.0185669333; 0.0534924988; −0.0392784517; 0.0183882247; 0.0005245892; −0.1024269629; 0.0500461848; −0.1013361102; 0.0404252678	0.0008794626; 0.1035086837; 0.0955626197; 0.2441423777; 0.0011449995; 0.0006894619; 0.0015427967; 0.0018100789; 0.0006282589; 0.0000116649	0.0794603736	0.000170916648864; −0.007197346940591; −0.063594314222215; −0.012650838988592; 1.737695584563462; −0.347952826255259; 0.006032977400039; 0.064865246780411; −7.783877291359830; 4.243918883408473	0.000847476006004; 0.001240932558196; 0.001348023865310; 0.000594884188514; 0.000000060112646; 0.000103638642450; 0.000160043727115; 0.000010859621702; 0.000001712311771; 0.000000008853799	0.0000044657
Solution 3	−0.0103209333; 0.0021201108; 0.1207182825; −0.0263026679; 0.0044219824; −0.0850838579; 0.0053645992; −0.0480333324; 0.0732269061; 0.1059498141	0.1170689295; 0.0726549501; 0.2023013696; 0.0155834694; 0.0001065214; 0.0000089983; 0.0006918303; 0.0012459181; 0.0000218860; 0.0000000463	0.0601546074	0.012819319246173; −0.019071587101257; 0.081305679904288; 0.029533158589909; 0.443752747560672; −1.815950119305152; −0.016526743634385; −0.082102054652280; −5.292468955772288; 4.472259351235464	0.001067920987079; 0.000826374747992; 0.002833219569578; 0.003530328678861; 0.000164312135105; 0.000727633722950; 0.000872207456297; 0.001042295751625; 0.000244156926303; 0.000004662712454	0.0000247769
Solution 4	0.0177198747; 0.0030100424; 0.0676669725; −0.0408039903; 0.0852565598; 0.0536056660; 0.1635419218; −0.0031889394; −0.1390794276; 0.0275601661	0.0262522791; 0.0644480331; 0.1379528266; 0.286269853; 0.0003139895; 0.0000181153; 0.0016649656; 0.0011990507; 0.0000533461; 0.0000001605	0.1058284540	0.015469554753745; −0.027948524788676; −0.031112943145748; 0.000991240275462; −3.984894922917517; −4.439885695760647; −0.000857889955385; 0.030633924509136; 6.948027176097301; 0.978107982563108	0.003486775086451; 0.000509018636612; 0.001919773451644; 0.000734539635309; 0.000239511965292; 0.001562687142025; 0.000000982557284; 0.000481307961101; 0.000432781623864; 0.000012083579193	0.0000195602
Solution 5	0.0348357700; 0.1092386108; 0.1250085306; −0.0107958218; −0.1399310251; −0.0177642059; −0.0787941605; 0.0917803902; −0.0422169082; −0.0302349392	0.0289865877; 0.2167589209; 0.0089588165; 0.1683941428; 0.0012135380; 0.0238661499; 0.0001165497; 0.0043547546; 0.0038054137; 0.0004156978	0.0768661970	−0.001269492482752; 0.013623874571987; −1.175677942247783; −0.030597939250755; −2.528288495278615; −4.876718138697484; 0.016294345284874; 1.173144422478730; −1.968788171623771; 5.854744353118305	0.000878131789857; 0.002563519769053; 0.001329398835772; 0.001980751318993; 0.000001741576241; 0.000371710969061; 0.000936233886393; 0.001492338779729; 0.000017173451524; 0.000000235630459	0.0000162755
Solution 6	0.0172348545; −0.0049839785; −0.0036835674; −0.0401647761; 0.0334303826; −0.0049589041; 0.0505724112; −0.0076509738; −0.1141678724; 0.0544069796	0.0202656999; 0.0113645412; 0.0052992119; 0.0609700462; 0.0002970384; 0.0000496805; 0.0016132092; 0.0000634846; 0.0000858910; 0.0000004281	0.0042879841	−0.001858395184513; 0.023721236556167; 0.653216998921955; −0.018603147142958; 3.776633185434082; 4.088647518759656; 0.008694690681967; −0.657906149925889; −5.577580694917199; −1.310802573641980	0.001820431874319; 0.004719151003933; 0.000379406194652; 0.001223765779024; 0.000003259497212; 0.001124982428505; 0.000346077083623; 0.001213836886952; 0.000043737933515; 0.000001045713511	0.0000300866
Solution 7	−0.1443475355; 0.0137124749; 0.0532523778; −0.0407593315; 0.0053340672; 0.0390841261; 0.0196593075; 0.0396094025; 0.0463257617; −0.0921334590	0.0460704291; 0.0928317803; 0.0470659155; 0.0014507164; 0.0208362107; 0.0003760600; 0.0016613231; 0.0076868554; 0.0019793648; 0.0000271419	0.0134575843	−0.002441213851907; −0.007212781373596; −0.632390997817911; 0.021860340733110; −1.135708922430422; 3.176958936133236; −0.009642875855651; 0.636176225306324; 9.619896251014470; −7.984037980824944	0.001484619742542; 0.003755227488414; 0.001910664271513; 0.002564589021807; 0.000006017905472; 0.000103728532125; 0.000477874496968; 0.001543706476717; 0.000017012045888; 0.000000127002218	0.0000291561
Solution 8	0.1612054472; 0.1001108591; −0.0303525758; 0.0015541591; 0.0464169709; 0.0906816701; −0.0263359667; −0.0540477839; 0.0577884947; −0.121281367	0.0966899590; 0.0844303598; 0.0520483724; 0.0511277742; 0.0259871938; 0.0200443591; 0.0000024154; 0.0048929924; 0.0161384122; 0.0016156306	0.0231646270	−0.013880682509557; 0.015121949074709; −0.275566456809759; −0.040530104159630; −1.600723894610612; −2.981776673353555; 0.021263311619477; 0.275465137078247; −0.071979725029653; 3.011085635104662	0.001750147547270; 0.000131319731513; 0.000908744309037; 0.001986519079324; 0.000192755631134; 0.000457646932271; 0.001642689343190; 0.003825009281174; 0.000209898515312; 0.000003174142090	0.0000254721