A Co-Evolutionary Dual Niching Differential Evolution Algorithm for Nonlinear Equation Systems Optimization

Abstract

A nonlinear equation system often has multiple roots, while finding all roots simultaneously in one run remains a challenging work in numerical optimization. Although many methods have been proposed to solve the problem, few have utilised two algorithms with different characteristics to improve the root rate. To locate as many roots as possible of nonlinear equation systems, in this paper, a co-evolutionary dual niching differential evolution with information sharing and migration is developed. To be specific, firstly it utilizes a dual niching algorithm namely neighborhood-based crowding/speciation differential evolution co-evolutionary to search concurrently; secondly, a parameter adaptation strategy is employed to ameliorate the capability of the dual algorithm; finally, the dual niching differential evolution adaptively performs information sharing and migration according to the evolutionary experience, thereby balancing the population diversity and convergence. To investigate the performance of the proposed approach, thirty nonlinear equation systems with diverse characteristics and a more complex test set are used as the test suite. A comprehensive comparison shows that the proposed method performs well in terms of root rate and success rate when compared with other advanced algorithms.