基因方法在网格结点位置优化中的应用

Application of Genetic Algorithms in Movement of Mesh Nodes

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

The application of genetic algorithms (GAs) in the optimization of mesh node location is discussed. At first, the basic principles of GAs based on Darwin′s evolution theory and Mandel′s gene theory are described. Then, this paper concentrates on the definition of fitness function associated with the error estimate and the mesh geometrical quality, the binary genetic representation of node location and the process of GAs evolution. The discrete errors are approximated in the space of discontinue quadratic bump functions. The second derivatives of solutions are kept constant while the nodes are being moved, so that the fitness function is only dependent of the node coordinates. Considering the scale and complexity of the problem, the optimization is localized in order to reduce computing time. At last, some numerical results for the generalized Stokes equations are given.