求解电磁领域中复超越方程的PSO-PTS混合算法

Rooting Complex Transcendental Equations in Electromagnetic Fields in Terms of the Mixed PSO-PTS Algorithms

将改进的粒子群算法(PSO)与参数跟踪策略(PTS)及动态搜索域相结合形成一种新的混合算法,用于求解电磁领域中复超越方程的高精度求根问题。在算法实现过程中,采用在粒子群算法中加入基于群体适应度方差的自适应变异操作来增加群体多样性,有效地避免算法陷入早熟收敛;使用参量跟踪策略有效地缩小了粒子群算法搜索区域,保证了解的单一性,提高了运算速度;使用动态搜索域提高了解的精度,并使运算速度得以进一步提高。通过实例说明该混合算法能够精确地解决复超越方程中的多值问题,解集完备性好,且与现有结果相吻合。

A new hybrid algorithm combining improved Particle Swarm Optimization （PSO） with the Parameter Tracking Scheme （PTS） is developed. The algorithm can root complex transcendental equations in electromagnetic field with high precision. In the process of implementing this method, adaptive mutation PSO algorithm is used to increase population diversity and effectively avoid the pre-mature convergence, which is based on the variance of the population＇s fitness. Due to the technologies of parameter tracking and the dynamic searching area, the searching area is decreased, solution is simplified, the calculating speed is accelerated, and the precision of the results is improved. The simulating example shows that the mixing algorithm can accurately solve complex multi-valued transcendental equation, keep the completeness of the solution set, and be in accordance with the presented results.