A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations

In order to solve the system of compatible nonlinear equations, the author proposes a hybrid computational intelligence method of Newton's method and genetic algorithm. First, the Quasi-Newton Methods (QN) method is given. Aiming at the local convergence of the algorithm, it is easy to cause the solution to fail. By embedding the QN operator in the Genetic Algorithm (GA) and defining the appropriate fitness, thus, a hybrid computational intelligence algorithm of CNLE is obtained that combines the advantages of GA and QN method, which has both faster convergence and higher probability of solving. Experimental results show that: The value of the selection probability p_n of the QN operator also directly affects the solution efficiency. Generally speaking, for strong nonlinear CNLE composed of multimodal functions, p_n can be larger; For weakly nonlinear CNLE composed of functions with fewer extreme points and stronger monotonicity, p_n can be smaller. It is demonstrated that the computational results show that this method significantly outperforms the GA and QN methods.