Solving Nonlinear Equation Systems by a Two-Phase Evolutionary Algorithm

A two-phase evolutionary algorithm is developed to find multiple solutions of a nonlinear equations system. It transforms a nonlinear equations system into a multimodal optimization problem. In phase one of the proposed algorithm, a strategy combines a multiobjective optimization technique and a niching technique to maintain the population diversity. Phase two consists of a detection method and a local search method for encouraging the convergence. The detection method finds several promising subregions and the local search method locates the corresponding optimal solutions in each promising subregion. The experiments on a set of 30 nonlinear equation systems demonstrate that the proposed algorithm is better than other state-of-the-art algorithms.

Automated summary

A two-phase evolutionary algorithm is proposed to find multiple solutions of a nonlinear equations system. The algorithm transforms the nonlinear equations system into a multimodal optimization problem by combining multiobjective optimization technique and niching technique in phase one, and using a detection method and a local search method in phase two to encourage convergence. Experimental results show that the proposed algorithm outperforms other state-of-the-art algorithms.