基于三个典型函数的交叉熵优化方法评价研究

Research on the Cross Entropy Optimization Method Evaluation Based on the Three Typical Functions

摘要: 本文介绍了从估计失效概率的交叉熵法转化而来的交叉熵优化方法。它通过构建人工可靠性问题，将问题聚集在最值搜索上，从而求出函数的最小值。本文根据三个典型函数的测试结果，并将其与遗传算法的运算结果进行对比，结果表明交叉熵优化方法在单峰和多峰函数的全局收敛速度和精确度均优于遗传算法，对于难以全局极小化的病态函数，交叉熵优化方法也克服了局部最优的问题，其优化结果更接近于理论最优值。

Abstract: The cross entropy optimization method is transformed from the cross entropy method to estimate the probability of failure. By constructing the artificial reliability problem, it concentrates the problem on the search of the maximum value, and then the minimum value of the function can be solved. According to three typical functions, the test results of the cross entropy optimization method are compared with those of the genetic algorithm. The results show that the global convergence rate and accuracy of the cross entropy optimization method are better than the genetic algorithm for single-peak and multi-peak functions. For this Pathological function, which is difficult to minimize globally, the cross entropy optimization method also overcomes the problem of local optimization, and the optimization result is closer to the theoretical optimal value.