一种求解一维全局优化问题的重点取样统计模拟算法

An Importance Sampling Simulation Method for Global Optimization Problem with Single Variable

针对无约束一维全局优化问题,提出一种基于重点取样的统计模拟算法,在原始积分水平集方法中引入交叉熵方法进行样本点选择,并在迭代过程中保留精英样本集.在最后的迭代中选取当前样本集对应的最小值点作为最优点.在一定条件下证明了算法收敛到问题的全局最优解.实验结果表明,所提算法采样效率更高,函数计算次数和运行时间比修正的纯自适应搜索方法更有优势.

An importance sampling simulation method is proposed for global optimization problem with single variable.Based on the integral level set method,the cross-entropy method is used to select the sample set,and retain the elite set in the iterative process.At the last iteration,the point with minimal value in the current sample set is chosen as the optimal solution.The convergence of the proposed method is proved under certain assumptions.Experimental results show that compared with the existing level value estimation methods,the proposed method is more efficient in sampling and has more advantages in function evaluation and CPU-time than the modified pure adaptive search method.