基于盲人探路寻优思想的二阶近似式定点法研究

分析一维和多维二阶近似式定点法的迭代点计算公式,提出基于盲人探路寻优思想的改进算法,给出算法步骤、程序流程图及计算机子程序。对于目标函数为二次函数正弦的算例,极值点基本上在由当前点指向极值点的方向上。对于目标函数为二次函数八分之一次方的算例,极值点在该方向上,且须反向寻找最优点。对于目标函数为二次函数四次方的算例,第一个点的迭代点指向极值点,且步长为当前点离极值点距离的整数分之一。结果表明,提出的基于盲人探路寻优思想的优化算法具有实用性强、计算量小的优点。

Investigation on the second-order approximation point method based on blind walking idea

The one-dimensional and multi-dimensional the second-order approximation fixed iterative point formulas methods were analyzed in this paper. Firstly, the improved optimization algorithm based on the blind walking idea was proposed, where the step algorithm, program flowchart and computer subroutines were given. For the example where the objective function is the quadratic sine function, it is judged that the position of the extreme point is almost in the direction from the current point to the extreme. For the example where the objective function is a quadratic function with the 1/8 power, the extreme point is just in this direction, and the optimal point should be sought in the reversal direction. For the example where the objective function is the aquatic function of one quarter, the iterative point of the first current point points to the extreme point, and the distance from the current point to the extreme point is divided by an integer step. The result shows that the proposed method has the advantages of strong practicability and small amount of calculation, etc.