SOLUTIONS TO SYSTEMS OF NONLINEAR EQUATIONS VIA A GENETIC ALGORITHM

Citation
Cl. Karr et al., SOLUTIONS TO SYSTEMS OF NONLINEAR EQUATIONS VIA A GENETIC ALGORITHM, Engineering applications of artificial intelligence, 11(3), 1998, pp. 369-375
Citations number
9
Categorie Soggetti
Computer Science Artificial Intelligence","Robotics & Automatic Control","Computer Science Artificial Intelligence",Engineering,"Robotics & Automatic Control","Engineering, Eletrical & Electronic
ISSN journal
09521976
Volume
11
Issue
3
Year of publication
1998
Pages
369 - 375
Database
ISI
SICI code
0952-1976(1998)11:3<369:STSONE>2.0.ZU;2-H
Abstract
Solving systems of nonlinear equations is perhaps the most difficult p roblem in all of numerical computation. It is also a problem that occu rs frequently in a spectrum of engineering applications such as electr ic power generation and distribution, multi-objective optimization, an d trajectory/path-planning applications. Although numerous methods hav e been developed to attack this class of numerical problems, one of th e simplest and oldest methods, Newton's method, is arguably the most c ommonly used. Like most numerical methods for solving systems of nonli near equations, the convergence and performance characteristics of New ton's method can be highly sensitive to the initial guess of the solut ion supplied to the method. In this paper, a hybrid scheme is presente d, in which a genetic algorithm is used to locate efficient initial gu esses, which are then supplied to a Newton method for solving a system of nonlinear equations. The hybrid scheme is tested on a specific exa mple that is representative of this class of problems-one of determini ng the coefficients used in Gauss-Legendre numerical integration. Resu lts show that the hybrid of a genetic algorithm and Newton's method is effective, and represents an efficient approach to solving systems of nonlinear equations. (C) 1998 Elsevier Science Ltd. All rights reserv ed.