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| Hybrid Genetic Algorithm for solving systems of nonlinear equations |
| Revised:April 14, 2003 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20051023 |
| KeyWord:systems of nonlinear equations,Hybrid Genetic Algorithm (HGA),optimization and iteration,nesting hybrid,quasi-newton iterations |
| LUO Ya-zhong YUAN Duan-cai TANG Guo-jin~* |
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| Abstract: |
| Solving systems of nonlinear equations is perhaps the most difficult problem in all of numerical computation. For most numerical methods such as Newton's method for solving systems of nonlinear equations, their convergence and performance characteristics can be highly sensitive to the initial guess of the solution supplied to the methods. However, it is very difficult to select a good initial guess for most systems of nonlinear equations. Aiming at these problems, a Hybrid Genetic Algorithm (HGA) was put forward , which combined the advantages of Genetic Algorithm (GA) and classical algorithms. The HGA sufficiently exerted the advantages of GA such as group search and global convergence, can efficiently overcome the problem of high sensitivity to initial guess; and it also had a high convergence rate and solution precision just because it used those high local-convergence classical algorithms (Powell, Quasi-Newton Method) for local search. Convergence reliability, computational cost and applicability of different algorithms were compared by testing several classical equations of nonlinear equations. The numerical computations show that hybrid approach for solving systems of nonlinear equations has reliable convergence probability, high convergence rate and solution precision ,and is a successful approach in solving systems of nonlinear equations. |
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