电磁领域中复超越方程的遗传算法求解方法

将遗传算法与参数跟踪策略有效结合,跟踪过程中进行搜索域压缩与位移操作,形成了一种功能强大的新算法,可成功应用于电磁领域中各种各样复超越方程的高精度求解问题.在算法实现过程中,使用参数跟踪策略有效地缩小了搜索区域,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;应用三阶差商公式预估新的搜索中心,使运算速度得以进一步提高.应用本文发展的算法详细求解了终端短路法测量材料的复介电常数时得到的复超越方程和部分填充矩形波导的特征方程,计算结果表明该算法能够轻松地解决复超越方程中的多值问题,解集完备性好,算法鲁棒性强.

Solving method based on genetic algorithm to complex transcendental equations in electromagnetic field

A new effective algorithm combining genetic algorithm(GA) and parameter tracking scheme(PTS) is developed.By using this algorithm,the rooting problem of all kinds of complex and transcendental equations in electromagnetic field can be solved successfully.In the realization process of the method,the searching area is decreased,the solution is simplified and the calculating speed is accelerated due to the parameter tracking.The precision of solutions is enhanced due to the dynamic searching area.The prediction of the new searching center by the application of a 3-order difference formula speeds up the calculation further.Based on the developed algorithm,the complex transcendental equation of medium permittivity that is measured by the method of terminal short circuit and the eigenvalue equation of rectangular waveguide that is filled partially are solved in detail.The computing results show that the algorithm can easily solve the multi-root problem of complex transcendental equations.The solution set is complete,and the algorithm is robust.