Solving nonlinear equation systems using multiobjective differential evolution

Abstract

Nonlinear equation systems (NESs) usually have more than one optimal solution. However, locating all the optimal solutions in a single run, is one of the most challenging issues for evolutionary optimization. In this paper, we address this issue by transforming all the optimal solutions of an NES to the nondominated solutions of a constructed multiobjective optimization problem (MOP). In the general case, we prove that the proposed transformation fully matches the requirement of multiobjective optimization. That is, the multiple objectives always conflict with each other. In this way, multiobjective optimization techniques can be used to locate these multiple optimal solutions simultaneously as they locate the nondominated solutions of the MOPs. Our proposed approach is evaluated on 22 NESs with different features, such as linear and nonlinear equations, different numbers of optimal solutions, and infinite optimal solutions. Experimental results reveal that the proposed approach is highly competitive with some other state-of-the-art algorithms for NES. © Springer Nature Switzerland AG 2019.