斐波那契树优化算法求解多峰函数全局最优解的可达性分析  

On Accessibility of Fibonacci Tree Optimization Algorithm for Global Optima of Multi-modal Functions

作　　者：董易[1] 施心陵[1] 王霞 王耀民 吕丹桔[1] 张松海[1] 李孙寸 DONG Yi;SHI Xin-Ling;WANG Xia;WANG Yao-Min;LV Dan-Ju;ZHANG Song-Hai;LI Sun-Cun(School of Information Science and Engineering,Yunnan University,Kunming 650504)

机构地区：[1]云南大学信息学院,昆明650504

出　　处：《自动化学报》2018年第9期1679-1689,共11页Acta Automatica Sinica

基　　金：国家自然科学基金(61661050);云南省教育厅科学研究基金项目(2017ZZX229)资助~~

摘　　要：为分析和验证斐波那契树优化算法(Fibonacci tree optimization algorithm,FTO)求解多峰函数全局最优解的算法性能,对算法的可达性问题进行研究.本文基于斐波那契法构造一个斐波那契树结构,在搜索空间中进行全局、局部交替搜索,不易陷入局部最优解.对斐波那契树优化算法基于该结构的可达性进行分析和证明.通过跟踪算法求解过程中坐标点的累积分布仿真实验和到达率的对比实验,分析和验证了算法求解多峰函数全局最优解的可达性.This paper investigates the accessibility of Fibonacci tree optimization algorithm（FTO） in order to analyze and prove its ability in solving the problem of global optima of multi-modal functions. A structure called Fibonacci tree based on Fibonacci search method is created, which conducts alternating global and local retrievals in the search space of the target function with lower probability of trapping into local optima. The accessibility of FTO is analyzed and proved on the basis of Fibonacci tree. A simulation experiment of tracing accumulation distribution of solution coordinates validates the global optima accessibility of FTO, and a contrast experiment of accessible rate further points to the better accessibility of FTO.

关 键 词：斐波那契树优化算法 可达性 多峰函数优化 全局最优解 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]