一种求非线性全局最优解的分形算法  

Fractal algorithm for finding nonlinear global optimal solution

作　　者：宋巨龙[1] 钱富才[2] 

机构地区：[1]西安石油大学理学院,陕西西安710065 [2]西安理工大学自动化与信息工程学院,陕西西安710049

出　　处：《系统工程与电子技术》2005年第12期2051-2053,2102,共4页Systems Engineering and Electronics

摘　　要：运用分形原理给出了求解全局优化问题的一种新算法——分形算法。该算法充分利用了分形的局部精细构造和黄金分割法的快速收敛性,只需搜索很少一部分区间就可以找到最优全局解,因而是一种高效快速的寻优算法。其优点为:适应性强,可适用于较为复杂的函数,计算精度是令人满意的。此外,克服了传统的直接解法所共有的要求大量计算机内存的缺点。给出了算法收敛性的证明。仿真结果表明算法是有效的。A new algorithm based on fractal and golden section for solving nonlinear global optimal solution is presented, which is called fractal algorithm. The algorithm has taken the full advantage of the local fine structure of fractal and the quick convergence of golden section, and only few part of research interval is searched, so it is a high efficient and high speedy optimal algorithm. The following is the character of the algorithm： strong adaptability, adapting to complex function. The precision of calculation is satisfying. On the other hand, this method needs so little memory that it almost can be implemented on any personal computer and its efficiency is not influenced. The proof of convergence of the algorithm is given. The illustrations show the algorithm is effective.

关 键 词：分形 黄金分割 全局优化 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] O221.2[自动化与计算机技术—计算机科学与技术]