求解非线性方程组系统的改进差分进化算法

Solving nonlinear equations system with an improved differential evolution

针对基于邻域拥挤的差分进化算法求解非线性方程组系统时存在丢根、陷入局部最优等不足,提出一种改进的差分进化算法.首先,提出一种个体预判机制,判断当前群体的个体属于哪一类,并分别采取不同的操作;其次,设计一种新的混合差分变异算子,以增强算法跳出局部最优的能力;然后,改进外部存档策略,延长了父代优秀个体在种群的保存时间,有利于搜索该优秀个体附近的根.在所选测试函数集上的实验结果表明,所提出的算法能有效搜索到非线性方程组系统的多个根,并与当前5种算法进行对比,所提出算法在找根率和成功率上更具优越性.

In order to remedy the drawbacks of neighborhood-based crowding differential evolution for losing the roots and trapping into the local optima when solving nonlinear equations systems(NESs), this paper presents an improved differential evolution, which can be featured as follows: 1) An individual pre-judgement mechanish is proposed, which is used to divide the individuals into different groups, and different operations are used for different groups. 2) An improved hybrid differential mutation is developed to make the algorithm escape the local optima. 3) An improved archive strategy is presented to enhance the algorithm to find more roots. The experimental results on the selected test functions show that the proposed method can locate mutiple roots of the NES efficiently. Compared with other state-of-the-art methods, the propsoed method obtains better results in terms of both the root rate and the success rate.