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
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.