Abstract: How to effectively solve complex nonlinear system of equations is a novel research problem in evolution field. Nonlinear system of equations is transformed into a multi-objective optimization problem and a new multi-objective optimization evolutionary algorithm is proposed. In order to enhance the search ability of the proposed algorithm and avoid the algorithm falls into the local optimum, the self-adaptive evolution operator and the uniform crossover operator are used. The computer simulations demonstrate the effectiveness of the proposed algorithm to solve nonlinear system of equations.

Key words: nonlinear system of equations, evolutionary computation, multi-objective optimization, optimal solutions

摘要： 如何有效地求解复杂非线性方程组是进化计算领域一个新的研究问题。将非线性方程组等价地转化成多目标优化问题，同时设计了求解的多目标优化进化算法。为了提高算法的搜索能力及避免算法陷入局部最优，采用了自适应Levy变异进化算子和均匀杂交算子。计算机仿真表明该算法对非线性方程组的求解是有效的。

关键词: 非线性方程组, 进化计算, 多目标优化, 最优解