基于盲人探路寻优思想的二阶近似式定点法研究
发布时间：2019-01-08 20:46
【摘要】：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。
[Abstract]:This paper analyzes the iterative point calculation formula of one-dimensional and multi-dimensional second-order approximate fixed-point method, puts forward an improved algorithm based on the idea of blind search, and gives the steps of the algorithm, the program flow chart and the computer subroutine. For an example where the objective function is a sinusoidal quadratic function, the extreme point is basically in the direction from the current point to the extreme point. For an example where the objective function is a quadratic function to the power of 1/8, the extremum is in this direction and the best point must be found in reverse. For an example where the objective function is a quadratic function to the fourth power, the iteration point of the first point points to the extremum point, and the step size is one integral part of the distance between the current point and the extremum point. The results show that the proposed optimization algorithm based on the idea of blind road finding has the advantages of strong practicability and low computational cost.
【作者单位】： 中国石油大学胜利学院;东营市胜利第二中学;东营市胜利第一中学;
【基金】：山东省自然科学基金项目(Q2006A08) 中国石油大学胜利学院科技计划项目(KY2015025)
【分类号】：O224
本文编号：2405099
[Abstract]:This paper analyzes the iterative point calculation formula of one-dimensional and multi-dimensional second-order approximate fixed-point method, puts forward an improved algorithm based on the idea of blind search, and gives the steps of the algorithm, the program flow chart and the computer subroutine. For an example where the objective function is a sinusoidal quadratic function, the extreme point is basically in the direction from the current point to the extreme point. For an example where the objective function is a quadratic function to the power of 1/8, the extremum is in this direction and the best point must be found in reverse. For an example where the objective function is a quadratic function to the fourth power, the iteration point of the first point points to the extremum point, and the step size is one integral part of the distance between the current point and the extremum point. The results show that the proposed optimization algorithm based on the idea of blind road finding has the advantages of strong practicability and low computational cost.
【作者单位】： 中国石油大学胜利学院;东营市胜利第二中学;东营市胜利第一中学;
【基金】：山东省自然科学基金项目(Q2006A08) 中国石油大学胜利学院科技计划项目(KY2015025)
【分类号】：O224
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