摘要
对模拟退火算法寻找极值的非线性动力学行为进行了研究.通过图像对比直观说明算法涉及的主要参数对寻优结果的影响,如初始温度、步长、退火速率等.适当控制模拟退火算法参量,画出步长、初值及最终所得到极值点的关系图像,在极大值吸引域附近对图像进一步放大,发现了和原图相似的图形和分形结构,分形维数为2维,将这一现象归原因于吸引子之间的相互作用.进一步对图形进行分析,发现随着初值的增加,最小值的寻优概率变化呈现很好的相变曲线和类渗流现象.
Nonlinear dynamical behavior of simulated annealing algorithm has been investigated.The probability of finding quality solutions is positively related to initial temperature,step length and annealing rate etc.Simulation results show that there are fractal structures in the domain of attraction and the fractal dimension has been obtained by fractal box dimension,and the fractal dimension is two.This phenomenon is attributed to the interaction between two attractors.A sigmoid curve which indicates the phase transition（especially percolation-like phenomenon） has been presented when discuss the probability of minimal value with the increase of initial state.
出处
《南开大学学报（自然科学版）》
CAS
CSCD
北大核心
2013年第1期1-5,共5页
Acta Scientiarum Naturalium Universitatis Nankaiensis
基金
国家自然科学基金(10675060
11247217)
江苏省高校自然科学基金(10KJB14002)
南京林业大学高学历人才(B2010-14)
关键词
模拟退火
分形
类渗流
相变现象
simulated annealing
fractal
percolation-like
phase transition
