Julia集具有分形结构,一旦确定吸引域边界上任一点,就可通向任一个吸引周期点的吸引域.Newton-Raphson法利用此性质可计算方程所有根,并可精确计算BFGS法和共轭梯度法中下降方向步长,将两种算法分别与混沌优化算法结合,因而从新的视角建立一种融合分形理论的混合混沌优化算法.研究表明,所提出算法的计算效率高于利用Wolf一维不精确搜索求得步长的混合算法,而且混合混沌BFGS算法的优化能力优于混合混沌共轭梯度算法,也说明BFGS的局部搜索能力比共轭梯度法强.
The Julia set has the fractal structure,and once an arbitrary point on the boundary of attraction domain is determined,it can get into the attraction domain of any attracted periodic point.The Newton-Raphson method can compute all roots of equations using the above-mentioned property.This paper utilizes accurately the step length of descent direction in BFGS method and conjugate gradient method using it,respectively,which combines with chaos optimization algorithm with global search ability.Therefore,a kind of hybrid chaos optimization algorithm incorporating fractal theory is established from a new perspective.It is indicated that the computational efficiency of hybrid chaos optimization algorithm is higher than that of the combined algorithm using Wolf method for one dimensional inexact search to calculate the step length of descent direction,and the optimization ability of hybrid algorithm of chaos search and BFGS is superior to that of hybrid algorithm of chaos search and conjugate gradient method.It is also illustrated that the local search ability of BFGS in hybrid chaos optimization algorithm is better than that of conjugate gradient algorithm.