混合蛙跳算法及其改进算法的运动轨迹及收敛性分析  

Study on Trajectory and Convergence Analysis of Shuffled Frog Leaping Algorithm and Its Improved Algorithm

作　　者：骆剑平[1] 陈泯融[1] 

机构地区：[1]深圳大学信息工程学院,广东深圳518060

出　　处：《信号处理》2010年第9期1428-1433,共6页Journal of Signal Processing

基　　金：国家自然科学基金(60772148)项目;高等学校博士点基金(200805900001)资助

摘　　要：本文通过求解差分方程分析混合蛙跳算法(Shuffled Frog Leaping Algorithm,SFLA)青蛙运动轨迹;进一步利用Solis和Wets提出的随机搜索算法收敛性判据讨论SFLA全局收敛性,得出SFLA全局收敛的结论;为提高SFLA收敛效率,提出一种在SFLA深度搜索方向上融合极值动力学优化(Extremal Optimization,EO)的改进算法EO-SFLA,并证明其依概率1收敛于全局最优。EO-SFLA中,改进的EO变异概率选取方式拓展了算法搜索空间,赋予了算法跳出局部极值点的能力,保证了算法全局收敛性。通过四个广泛使用的基准函数对两种算法进行实验仿真,仿真结果表明改进算法在保持全局收敛性的同时显著提高收敛速度。In order to understand the convergence characteristics of Shuffled Frog Leaping Algorithm （ SFLA）, the trajectories of frog of SFLA was analyzed by solving the differential equation. Further, the global convergence analysis was made using random search algorithm convergence criterion which was present by Solis and Wets, and the conclusion that SFLA is global convergent was drawn in this paper. A new optimization method, called hybrid extremal optimization and shuffled frog leaping algorithm（ EO-SFLA）, which introduces EO local search method to SFLA, was presented based on the convergence analysis of SFLA, and it was proved to be guaranteed to get the global optimization solution with probability one. EO-SFLA combines the merits of both SFLA and EO, improves local search ability while keeping the global convergence of SFLA. Tile mutation selection method of EO-SFLA referring to the Power-law expands the search space, gives the algorithm ability to jump out of local extreme points, and ensures the global convergence of the algorithm. The results of experiments carried out with four well-known benchmark functions had shown the proposed algorithm possesses outstanding performance in convergence speed and solution results. The simulation results matched the convergence analysis.

关 键 词：智能优化 混合蛙跳算法 极值动力学优化(EO) 收敛性 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程] TP183[自动化与计算机技术—控制科学与工程]