多导体柱微波成像的连续编码遗传算法

MICROWAVE IMAGING OF MULTIPLE PERFECTLY CONDUCTING CYLINDERS USING REAL-CODED GENETIC ALGORITHM

提出一种能同时重建多个二维良导体目标外形轮廓的新方法——连续编码遗传算法．将目标的横截面轮廓近似表达为三角级数形式，由边界条件得到一积分方程组，在此基础上将成像问题转化为约束优化问题，级数的各项系数为待优化量．积分方程组为约束条件，目标函数定义为实际测量的散射场与反演过程中得到的散射场之间的相对误差函数．采用连续编码遗传算法求解，优化过程通过选择、交叉、变异等遗传操作的选代而实现，待优化目标函数进行线性变换并采用模拟退火原理确定目标后表达为适应度函数，采用联赛选择与比例选择相结合的选择机制和单点交叉方式，变异操作通过对基因施加微小随机扰动实现．上一代中适应度最高的个体直接保留．数值模拟反演实验验证了方法的有效性．与其他反演方法相比，本法具有简单、通用、鲁棒性强等特点．

A novel approach for microwave imaging of two-dimensional perfectly conductingobjects in free space using real-coded genetic algorithm is put forward in this paper.The shape function of each contour is approximated by triangular series. A set ofintegral equations with respect to the coefficients of these series are derived accordingto the boundary conditions. The imaging problem is then reformulated into arestrained optimization one where the variables to be optimized are the coefficients ofthe series and the cost function is defined as the relative error between the measuredscattered electric field and the simulated one. Using real-coded genetic algorithm, theimaging is done by genetic operating iteratively. The fitness function is obtained bytransforming and scaling the cost function using simulated annealing method.Tournament selection, proportional model, one-point crossover and elitist model areused while the mutation is done by adding a random purtabation item to the gene tobe mutated. Numerical examples show the validity of this method.Compared withother inversion algorithms, our method is more simple, versatile and robust.