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以锗基红外宽带增透膜(AR)为例,基于Matlab最优化工具箱,研究了多种局部优化算法在多层膜设计中的性能和反向工程算法开发中的可行性,并就数值实验中出现多解性问题的成因、分析及解决方案进行了探讨。结果表明,Matlab最优化工具箱中的导数算法在多层膜局部优化设计上具有更好的局部极值搜索性能和收敛速度;非导数算法性能较差且收敛时间较长,但具有更多的搜索路径,较适用于设计初期开拓搜索方向。在多层膜反演中,导数算法中的非线性最小二乘估计指令lsqnonlin和非线性方程求解指令fsolve的性能出色,建议作为多层膜反向工程问题的主要算法。无约束优化指令fminunc性能次之,约束优化指令fmincon再次之,可作为备用反演算法。而多目标优化指令fminimax和其余非导数算法由于算法的性能不足和自身内在多解性的原因,不利于多层膜的反演,容易得到错误的结果,不建议作为反演算法使用,仅可作为可选算法以供对比参考。
Taking the germanium-based infrared wideband anti-reflection coating (AR) as an example, the feasibility and feasibility of various local optimization algorithms in multi-layer film design and reverse engineering algorithm development are studied based on Matlab optimization toolbox. The causes, analysis and solutions of the multi-solution problems in the experiment were discussed. The results show that the derivative algorithm in Matlab optimization toolbox has better performance of local extremum search and convergence speed in multilayer local optimization design. The non-derivative algorithm has poor performance and long convergence time, but has more Search path, more suitable for the design of the early exploration of search direction. In multi-layer inversion, the nonlinear least-squares estimator lsqnonlin in the derivative algorithm and fsolve in the nonlinear equation are excellent, which is suggested as the main algorithm of multilayer engineering reverse engineering. Unconstrained optimization instruction fminunc second performance, constraint optimization instructions fmincon again, can be used as a backup inversion algorithm. The multi-objective optimization instruction fminimax and the other non-derivative algorithms are not conducive to the inversion of multi-layer film due to the performance of the algorithm and the inherent multi-solution of the algorithm, it is easy to get wrong results. It is not recommended as an inversion algorithm, As an alternative algorithm for comparison purposes.