用演化算法求解抛物型方程扩散系数的识别问题

基于演化算法给出了一类求解参数识别反问题的一般方法，该方法表明只要找到好的、求解相应的正问题的数值方法，演化算法就可以用于求解此类反问题。设计有效的求解反问题的演化算法的关键是寻找一种适合反问题的解空间的编码表示形式、适当的适应值函数形式以及有效的计算正问题的数值方法。该文结合算法、传统的求解反问题的工方法和正则化技术，设计了一类求解参数识别反问题的方法。为验证此类方法，将其用于求解一维扩散方程的

Identification of Spatially-Varying Parameters of Parabolic Partial Differential Equation by Evolutionary Algorithms

This paper describes a general approach to solve inverse problems by using evolutionary algorithms (EAs). As a viable and general optimization techniques, EAs seems to be extremely appropriate for solving inverse problems. Attention has been focused on representation and on specific operators for EAs. Whenever a appropriate numerical model of the direct problem exists, the inverse problem can be formulated as function optimization problem. Thus, EAs can be used to address the parameter identification inverse problem. A new class of hybrid solution schemes integrating evolutionary computation,standard iterative inverse methods and regularization techniques is proposed. Using the hybrid schemes avoids some of the weakness of traditional gradient based analytical search methods including the difficulty in constructing well defined mathematical methods directly from practical inverse problems and easily getting trapped or oscillating between local minima and thus failing to produce optimal solutions. Numerical experiments for the spatially varying parameters identification problem of one dimensional parabolic partial differential equations demonstrate that the proposed schemes are viable and effective.