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将基因方法应用于网格结点位置的优化中。文中首先简单介绍了基因优化方法中基于达尔文进化论和 Mendel基因理论的基本原理 ,其中包括插索空间表达、三个基因作用器 (选择、交配和变异 )等要点 ;然后着重阐述了相关偏微分方程的离散误差和三角形网格几何形状的适应度函数的定义、结点位置的二进制基因表达及基因方法的优化进程。离散误差是在二次非连续鼓包(bump)函数的空间中近似定义的 ,并且在点移动过程中相关解的二次导数保持为常值以适应度函数 ,仅与坐标值相关。文中采取的是一点移动时其他点不动、逐点移动的当地优化方法。最后 ,给出了有关广义 Stokes问题的优化算例
The genetic method is applied to the optimization of the position of the grid nodes. In this paper, the basic principle of genetic optimization based on Darwin’s theory of evolution and Mendel’s gene theory is briefly introduced. The main points of this paper include the spatial expression of the spline, the three gene effectors (selection, mating and mutation), and then the related partial differential equations The definition of fitness function of triangular mesh geometry, the binary gene expression at node location and the optimization of genetic methods. The discrete error is approximately defined in the space of the quadratic discontinuity bump function, and the second derivative of the correlation solution remains as a constant fitness function and only correlates with the coordinate value during the point move. The article takes a little while moving the other points do not move, point by point movement of the local optimization methods. Finally, an optimal example of the generalized Stokes problem is given