A multi-root solver for discontinuous and non-differentiable equations by integrating genetic algorithm and derivative-free iterative methods

Abstract

Genetic Algorithm (GA) has a strong global searching ability but limited convergence efficiency at later stage, while derivative-free iterative methods have high local convergence efficiency but strict requirements on the initial approximation. Combining GA and derivative-free iterative methods, a multi-root solver is proposed for a class of complex nonlinear functions with discontinuity, non-differentiability and multi-root in this work. Firstly, an improved GA (IGA) is presented by integrating an adaptive crossover operator and three kinds of manual intervention measures into the standard GA to further improve the global searching ability. Then, a global search in the domain is implemented by using the proposed IGA, and the qualified individuals are selected as initial approximations. Finally, based on this, local accurate convergence is achieved by combining the derivative-free iterative method. To demonstrate the effectiveness of the proposed method, a series of numerical experiments are conducted, and the results show that the proposed multi-root solver has better performance in efficiency, stability as well as applicability.