结构优化设计的改进交叉熵支持向量机方法
Improved Cross Entropy Support Vector Machine Method for Structural Design Optimization

针对工程优化设计中隐式函数和高计算量困难，提出了支持向量机与改进交叉熵算法的组合优化算法。采用在设计变量空间内分布更为均匀的拉丁重心Voronoi结构抽样方法（Latinized centroidal Voronoi tessellation，LCVT）获得试验点，进而利用支持向量机得到高精度的代理模型。同时采用改进交叉熵方法，引入"全局精英样本"与"局部精英样本"概念，构建新的参数更新策略，以充分提取迭代过程中的隐含的有用信息。同时增加变异操作避免陷入局部最优。通过2个数值算例验证改进交叉熵支持向量机方法优于传统交叉熵支持向量机方法，利用1个工程算例验证改进交叉熵支持向量机方法在工程领域的可行性。
Aiming at the difficulties of implicit functions and high computation cost in engineering design optimization, a combined method is proposed in this paper, which takes advantage of support vector machine(SVM) and cross entropy method(CE). Used the ‘Latinized’ centroidal Voronoi tessellation(LCVT) which can generate much uniform supporting points in the design variable space, a high accurate surrogate model is obtained by SVM. At the same time, the traditional cross entropy method is improved by the concepts of "global elite samples" and the "local elites samples" and a new parameter updating strategy for extracting the useful information in iteration history. To avoid trapping in the local optimum, a mutation operation is also included in the proposed method. Two numerical examples are used to illustrate the performance of the improved method superior to that of the traditional one. Finally, an engineering example is employed to demonstrate the feasibility of the proposed method in the field of engineering