Memetic niching-based evolutionary algorithms for solving nonlinear equation system

Abstract

In numerical computation, finding multiple roots of nonlinear equation systems (NESs) in a single run is a fundamental and difficult problem. Recently, evolutionary algorithms (EAs) have been applied to solve NESs. However, due to the diversity preservation mechanism that EAs use, the accuracy of the roots may be reduced. To remedy this drawback, we propose a generic framework of memetic niching-based EA, referred to as MENI-EA. The main features of the framework are: i) the numerical method for a NES is integrated into an EA to obtain highly accurate roots; ii) the niching technique is employed to improve the diversity of the population; iii) different roots of the NESs are located simultaneously in a singe run; and iv) different numerical methods and different niching techniques can be used in the framework. To evaluate the performance of our approach, thirty NESs were chosen from the literature as the test suite. Experimental results show that the proposed approach is capable of yielding promising performance for different NESs in both the root ratio and success rate.