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

Table 8

Comparison of results for chemical equilibrium application benchmark.

Algorithm	EA			DEIWO
	Solutions	Functions values	Error	Solutions	Functions	Error
Solution 1	−0.0163087455; 0.2613604709; 0.5981559224; 0.8606983883; 0.0440020125	0.1525772447; 0.3712483549; 0.0265535280; 0.2784694066; 0.1168649339	0.2537179573	0.047039050817101; 1.869415636872731; −0.265064210870296; −0.849394548238717; 0.036068394869839	0.026769403348726; 0.006747169898629; 8.805250733959802𝐸−004; 1.522979575456773𝐸−004; 9.201328624012376𝐸−004	0.0007637704
Solution 2	0.3357311285; 0.1015972384; 0.1959807715; 0.5298149584; 0.0069016628	0.3491354953; 0.3388481591; 0.0324919199; 0.2853430985; 0.3380473798	0.4345218367	0.026474719105915; 3.527094917732416; 0.199080066736952; −0.855305091111645; 0.036701709037720	0.009748439199621; 0.013690244877239; 0.001726981982017; 0.005077554838563; 7.862731788029286𝐸−004	0.0003118371
Solution 3	0.3273318676; 0.0396552907; 0.5208586308; −0.4442729860; 0.0065409250	0.3206895328; 0.2986524101; 0.0741335715; 0.1331193703; 0.3989667326	0.3799218328	0.043701369103126; 2.049069927756282; 0.252703525295020; −0.852671096585522; 0.036246028365058	0.024510445238943; 0.008581129313918; 0.003229156423991; 0.004195330599570; 0.003804521422204	0.0007169003
Solution 4	0.1626252165; −0.3017126041; −0.1783889066; 0.7137275251; 0.0278993324	0.0298611415; 0.2240794988; 0.2301576033; 0.0971666758; 0.3805446921	0.3113039788	0.041608285134930; 2.045381329230565; 0.256879114658442; −0.848553325138083; 0.036215168144720	0.018067590257058; 0.015129175003949; 0.006078177707939; 0.008580373137608; 0.005202632121528	0.0006.929642
Solution 5	0.3221051215; 0.2525051386; −0.4189363818; −0.6331604264; 0.0174557111	0.3510711865; 0.3544681189; 0.0165037731; 0.1035503586; 0.1177149436	0.2740228596	0.041994672912187; 2.105373855163727; −0.254482330009030; 0.850700424653915; 0.036482968084062	0.020960255065471; 0.009880976362258; 0.005430820903461; 0.011875271190618; 0.002615595117843	0.0007143232
Solution 6	0.0429158354; 0.0811055468; −0.2662203512; −0.7711670069; 0.0303442027	0.0446360606; 0.2478304056; 0.2040211938; 0.0243731377; 0.3396013173	0.2625846864	0.039142614022070; 2.315919558093960; −0.242200440749196; 0.851329829612683; 0.036288481660450	0.020928314409356; 0.006812894119697; 0.003638624072727; 0.001947129057743; 0.001400229470722	0.0005034014
Solution 7	0.7276812579; −0.4551167619; −0.2113909448; −0.4895999565; 0.0075452271	0.3738656386; 0.0304080605; 0.0838221369; 0.1776147414; 0.3755303113	0.3273224789	0.029777144983889; 3.130317377778047; −0.210038553008973; −0.855206644040595; 0.036744343061275	0.012756030203747; 0.013574181713828; 0.001175210980581; 0.007108131624504; 4.544958713665148𝐸−004	0.0003990879
Solution 8	0.1296088399; 0.2275206857; −0.1061140447; −0.8124975178; 0.0310264084	0.0660183067; 0.1191351931; 0.2387977164; 0.0792417966; 0.1760779901	0.1698830307	0.034568611394593; 2.701986140890615; 0.225725393195049; −0.853903291996822; 0.036519499172778	0.018414022774285; 0.005877945460186; 0.003279597720941; 0.002556918408524; 0.004983364513138	0.0004157540
Solution 9	0.3367208030; 0.1420207287; −0.1427721429; −0.8435618534; 0.0349599086	0.2796624109; 0.0856442848; 0.2660909007; 0.0247927741; 0.1028940828	0.2383566164	0.029700290568578; 3.233972423385453; 0.207655335416109; −0.849852570852197; 0.036240046204135	0.017030072621489; 8.550186286035441𝐸−004; 0.006078174688298; 0.005196711511919; 0.003857570695716	0.0003695853
Solution 10	0.4224008806; −0.1889079092; 0.3561384679; −0.7390069308; 0.0237712845	0.2712921597; 0.0011063024; 0.1890226787; 0.1414158627; 0.1106294577	0.1772971294	0.039076419522626; 2.195407554156290; −0.246825556242421; 0.857523650896189; 0.036753497883680	0.014604592480938; 0.023351748126232; 0.003407541582840; 6.178556688816173𝐸−004; 0.005393500809564	0.0007996812
Solution 11	0.2395706253; 0.4637567881; 0.0154833612; −0.5861394961; 0.0177082676	0.2975483261; 0.2847994096; 0.1413409742; 0.02122094995; 0.3056084889	0.3034471293	0.029989577399948; 3.042439401620619; 0.212865462882654; −0.854930903089161; 0.036718962042137	0.011074163193089; 0.016575368131918; 1.046629449772713𝐸−004; 0.007033411425349; 8.967043275154037𝐸−004	0.0004476638
Solution 12	0.1671662105; 0.2358035522; −0.1121274369; −0.7953186041; 0.0273318802	0.1245889560; 0.0243717563; 0.2079331799; 0.1717817639; 0.1555592488	0.1562964598	0.026264550497174; 3.679702397787328; 0.193832890273980; 0.850241727008394; 0.036012370926070	0.014873167160221; 0.001793762023353; 0.003373540589790; 0.005433755376894; 0.008086975223007	0.0003307343
Solution 13	0.4586478321; −0.1011456067; −0.0115635220; −0.75891034603; 0.02454099949	0.3386346204; 0.1204471133; 0.1963075419; 0.1702524624; 0.0117867162	0.2353790429	0.039763793276441; 2.261109646335777; 0.245179433647380; 0.851709222649360; 0.036466833083980	0.020273590576762; 0.008783261436782; 0.003715808978656; 0.007790504369955; 0.003080933278725	0.0005721555
Solution 14	0.4064810686; 0.0073246701; 0.0846953560; 0.6726843741; 0.0234023812	0.3392512646; 0.1784649874; 0.1843099545; 0.0310865463; 0.1365650475	0.2344978766	0.042494575252538; 2.060377057920538; −0.253929806014199; 0.846954259610168; 0.035785075844889	0.022694195654279; 0.007609342603815; 0.003926958981918; 0.003319461816077; 0.007645558185311	0.0006578230