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

Table 7

Comparison of results for neurophysiology application benchmark.

Algorithm	EA			DEIWO
	Solutions	Functions values	Error	Solutions	Functions values	Error
Solution 1	−0.8282192996; 0.5446434961; −0.0094437659; 0.7633676230; 0.0199325983; 0.1466452805	0.3139636069; 0.1206333341; 0.0652332757; 0.0123681793; 0.0465408323; 0.0330776356	0.1207940789	−0.513317629102986; 0.494147884422256; 0.857821264907119; −0.869276357234471; 0.035896065698353; 0.035302984144262	6.476891252397143𝐸−004; 1.764830741770584𝐸−004; 5.303409416579433𝐸−004; 5.954489839492686𝐸−004; 3.768837806613808𝐸−004; 6.201719809721604𝐸−004	0.0000016131
Solution 2	−0.6512719807; −0.6858609598; −0.4637572369; −0.6450853748; 0.1535909562; −0.0036883801	0.3607740323; 0.1134596029; 0.0143291397; 0.0412380343; 0.0204607154; 0.0290928705	0.1462019196	0.474689101876457; −0.473073184862286; −0.879846849365024; 0.880629205401128; 0.021597922714450; 0.021393481167399	5.397782221636671𝐸−004; 6.939643588305122𝐸−004; 1.003432819985314𝐸−004; 4.515693669908784𝐸−005; 8.794875317431894𝐸−005; 6.561341485605571𝐸−005	0.0000007971
Solution 3	0.0425943625; −0.1626952821; −0.9215324786; 0.9841530788; −0.6789794019; −0.9070329917	0.1489636110; 0.0049729625; 0.3332320690; 0.0038536711; 0.1183698936; 0.0224932754	0.1477907295	0.509450781724102; 0.513500001903592; 0.860888906816676; 0.858125508396048; −0.150516100248646; 0.151302300254598	6.698088793095636𝐸−004; 6.164011496423427𝐸−005; 4.250176942812017𝐸−004; 5.847818530452624𝐸−004; 3.818324226455561𝐸−004; 6.049508942429435𝐸−004	0.0000014868
Solution 4	0.3269911198; 0.0266425162; 0.7886843835; 0.9866658030; −0.2403284017; 0.2613854687	0.2710537507; 0.0257807695; 0.1331679003; 0.0083976429; 0.0421023524; 0.2008350695	0.1340463271	−0.866626598784898; 0.864802076273302; −0.499291890387587; 0.502959292343981; 0.028130597707313; 0.027625633057264	3.340535282903012𝐸−004; 8.506808817729805𝐸−004; 1.347578366112058𝐸−005; 4.419943585350222𝐸−004; 3.384546104441034𝐸−005; 1.571583020721235𝐸−004	0.0000010566
Solution 5	0.8625703877; −0.7176375053; −0.2271912801; 0.5169409578; −0.1305290129; 0.1532817352	0.2043564483; 0.2177684569; 0.0227051752; 0.1404211857; 0.0352067233; 0.0628718325	0.1151261990	−0.999219226854328; −0.999969649944819; 0.030375755917241; 0.022170611106836; 0.036181758812701; −0.036046852107358	6.382501370955085𝐸−004; 4.308368076140212𝐸−004; 6.212509562937959𝐸−007; 5.350559335882965𝐸−005; 1.564056883091377𝐸−005; 2.982004995065353𝐸−004	0.0000006850
Solution 6	0.7618711576; 0.6775336796; 0.5086028850; −0.6713892035; 0.2563543063; 0.0555642759	0.1608754444; 0.0901846503; 0.0169111046; 0.1306483985; 0.0674916558; 0.0585551925	0.0596389890	0.855393409271579; 0.865828873424174; 0.518752115726210; 0.500755833107956; −0.003420786702082; 0.002831763536266	8.016421956744679𝐸−004; 4.160424466184143𝐸−004; 1.219573478839314𝐸−004; 3.030021758793175𝐸−004; 1.726192288883470𝐸−004; 2.353934715277509𝐸−004	0.0000010225
Solution 7	0.6609930931; −0.4821043312; 0.8042915766; −0.8729660781; −0.8987020407; −0.1909288931	0.0837968094; 0.0055056402; 0.3405628319; 0.2381471738; 0.3141261109; 0.2770687343	0.4711746758	0.757633159666954; 0.737153307517733; −0.652140850599093; −0.675824989376039; 0.015414698314102; −0.015418973671849	7.043063529591498𝐸−004; 1.344150494564378𝐸−004; 4.842380876615825𝐸−004; 5.273519108908182𝐸−004; 2.245659170263979𝐸−004; 1.077840862562709𝐸−004	0.0000013232
Solution 8	0.2739187054; 0.1077541336; 0.9656734396; 0.9240784300; −0.3143660356; −0.0314940456	0.0075566488; 0.1344681018; 0.3079429049; 0.0065004171; 0.0831983095; 0.0231155825	0.2152949830	0.643020583613510; −0.662772222883848; −0.766232339637761; 0.748885036051881; −0.015577794653013; −0.016554865087646	5.874692574154850𝐸−004; 9.581664882496455𝐸−005; 5.491014584886340𝐸−005; 6.779650279244136𝐸−004; 2.724638197823467𝐸−004; 5.105665891994952𝐸−004	0.0000011549
Solution 9	−0.0838634907; −0.1437222650; 0.8847221485; 0.8477645497; 0.1777227339; −0.0455327341	0.2102336348; 0.2606391818; 0.0953305060; 0.0000303505; 0.0069629557; 0.0003085023	0.1303553523	−0.943535194739874; −0.856135906960048; 0.330665259088240; 0.516998990062110; 0.003385954254385; −0.003000958247795	4.018227192950086𝐸−004; 2.566469115463654𝐸−004; 2.922768011053473𝐸−004; 9.610052402960732𝐸−004; 3.374094591558359𝐸−004; 1.404462148891126𝐸−004	0.0000014553
Solution 10	0.4612359064; 0.2783584687; 0.9360523694; −0.9009125260; −0.1421082154; −0.2759388163	0.0889325997; 0.1108731832; 0.0852199228; 0.0198955321; 0.1197727508; 0.0090365095	0.0495497431	−0.594047159308489; −0.642823012010247; −0.804411318752719; −0.765987085952347; 0.004090936206997; −0.004733324210377	3.040278002663932𝐸−005; 4.235938430474651𝐸−005; 2.090792562180113𝐸−006; 3.997031908528915𝐸−004; 2.127225008508227𝐸−004; 3.369070905144755𝐸−004	0.0000003212
Solution 11	−0.6907741758; 0.8565963646; −0.5428400528; 0.5465986672; −0.2327716625; −0.0607828078	0.2281557150; 0.0325274349; 0.0273082414; 0.0385212104; 0.0318257635; 0.0359158033	0.0583912523	0.818188591099612; −0.819888086423616; −0.574896979975124; 0.572533090358964; 0.007674059020755; 0.007253138354942	6.089180991386556𝐸−005; 1.061381536349160𝐸−005; 9.690837191759410𝐸−005; 2.057404583100777𝐸−004; 1.258799064935345𝐸−004; 1.619105484420356𝐸−004	0.0000001070
Solution 12	−0.8078668904; −0.9560562726; 0.5850998782; −0.2219439027; 0.0620152964; −0.0057942792	0.0050092197; 0.0366973076; 0.0124852708; 0.0276342907; 0.0168784849; 0.0248569233	0.0033499526	0.728516375898463; 0.710260686224578; 0.684731209007270; 0.704073008291695; 0.022870698246558; −0.022612099542858	4.070614592122102𝐸−004; 1.890434011242448𝐸−004; 5.496957312890105𝐸−004; 7.409173419877374𝐸−004; 1.495429352398985𝐸−004; 2.800232682831274𝐸−004	0.0000014555