Research Article
Chaotic Enhanced Genetic Algorithm for Solving the Nonlinear System of Equations
Table 2
Results for benchmark 2, Arithmetic application.
| Method | | | | No. of iterations |
| EAA | | 0.2077500302 | | 0.0464943 | 0.2344 | 300 | | 0.0299198492 | | 0.3489889 | | −0.0339491324 | | 0.3058418 | | −0.2027950317 | | 0.4012915 | | 0.2131771707 | | 0.2284027 | | 0.0568458067 | | 0.0886970 | | 0.2267650517 | | 0.2024745 | | −0.0977041236 | | 0.1687259 | | −0.0339921200 | | 0.3787652 | | 0.2532921324 | | 0.1741025 |
| GAs | | 2.5783339E − 01 | | −7.3844E − 10 | 1.2674E − 09 | 10 | | 3.8109715E − 01 | | −1.1684E − 12 | | 2.7874502E − 01 | | 1.7931E − 09 | | 2.0066896E − 01 | | −8.8837E − 10 | | 4.4525142E − 01 | | −4.5866E − 10 | | 1.4918391E − 01 | | −5.270E − 09 | | 4.3200969E − 01 | | −6.3852E − 09 | | 7.3402777E − 02 | | −9.7362E − 10 | | 3.4596683E − 01 | | −6.0389E − 11 | | 4.2732628E − 01 | | 3.0841E − 10 |
| Hybrid-GOA-GA | | 0.2578333 | | 1.2656E − 12 | 1.7220E − 12 | 1200 | | 0.3810971 | | 7.9096E − 14 | | 0.2787450 | | 1.7517E − 12 | | 0.2006689 | | 4.5315E − 12 | | 0.4452514 | | 1.1361E − 12 | | 0.1491839 | | 2.2230E − 12 | | 0.4320096 | | 1.4795E − 12 | | 0.0734027 | | 6.5123E − 13 | | 0.3459668 | | 3.5476E − 12 | | 0.4273262 | | 5.5468E − 13 |
| Original GA | | 0.257833393700735 | | 2.6685E − 13 | 1.7873E − 12 | 1200 | | 0.381097154600942 | | 1.8415E − 12 | | 0.278745017345425 | | 1.0000E − 12 | | 0.200668964224041 | | 1.3058E − 12 | | 0.445251424840196 | | 8.3411E − 13 | | 0.149183919967650 | | 1.8859E − 12 | | 0.432009698988807 | | 4.9226E − 12 | | 0.0734027777813010 | | 5.0493E − 12 | | 0.345966826875570 | | 3.8700E − 14 | | 0.427326275994071 | | 7.2846E − 13 |
| CEGA | | 0.257833393700561 | | 5.7399E − 14 | 3.0855E − 14 | 272 | | 0.381097154602820 | | 1.2136E − 14 | | 0.278745017346455 | | 1.3031E − 14 | | 0.200668964225329 | | 1.5905E − 14 | | 0.445251424841115 | | 7.1657E − 14 | | 0.149183919969369 | | 1.4279E − 14 | | 0.432009698983808 | | 8.7737E − 14 | | 0.0734027777762290 | | 2.1295E − 14 | | 0.345966826875559 | | 4.9712E − 15 | | 0.427326275993280 | | 1.0141E − 14 |
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