本論文比較自我適應之動態差異型演化法和非同步粒子群聚法應用於半空間二維非完全導體之逆散射問題。針對物體照射TM(Transverse Magnetic)極化波之情況，在半空間非完全導體的逆散射進行探討。利用在導體表面的邊界條件及在物體外部量測的散射電場，可推導出一組非線性積分方程，將散射場積分方程式透過動差法求得散射電場相關資訊。在此使用傅立葉極數展開及描述物體的形狀，並在演算法中使用自我適應之動態差異型演化法和非同步粒子群聚法重建半空間非完全導體之形狀和導電率進行比較。 不論初始的猜測值如何，自我適應之動態差異性演化法總會收歛到整體的極值(global extreme)，因此在數值模擬顯示中，即使最初的猜測值遠大於實際值，我們仍可求得準確的數值解，成功的重建出物體的形狀函數、導電率。而且在數值模擬顯示中，量測的散射場即使加入均勻分佈的雜訊存在，依然可以得到良好的重建結果，研究證實其有良好的抗雜訊能力。我們也發現，在非完全導體中，形狀函數的收斂速度總是優於導電率。因此可知形狀函數對散射場之貢獻大於導電率，導電率對散射場的貢獻次之。利用上述新型最佳化演算法提供更準確形狀函數的重建，使導電率的重建能更準確。 This paper presents an inverse scattering problem for recovering the shape of an imperfectly conducting cylinder buried in a half space by self-adaptive dynamic differential evolution (SADDE). The imperfectly conducting cylinder of unknown conductivity and shapes are buried in one half-space and illuminated by the transverse magnetic (TM) plane wave from the other half space. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equation is derived and the imaging problem is reformulated into optimization problem. The particle swarm optimization algorithm is employed to find out the global extreme solution of the object function. Numerical results show that the conductivity and the shape of the conductor are well reconstructed.
