基于差分进化的混合蛙跳算法  

Hybrid frog leaping algorithm based on differential evolution

作　　者：黄柳玉 高淑萍 王军宁[2] 薛小娜 

机构地区：[1]西安电子科技大学数学与统计学院,陕西西安710071 [2]西安电子科技大学通信工程学院,陕西西安710071

出　　处：《系统工程与电子技术》2017年第10期2382-2392,共11页Systems Engineering and Electronics

基　　金：高等学校学科创新引智基地"111"计划(B08038)资助课题

摘　　要：为高效处理3D视线跟踪技术中的非线性优化问题,使系统满足实时准确及稳定性需求,以差分进化(differential evolution,DE)为核心,结合混合蛙跳算法(shuffled frog-leaping algorithm,SFLA)及Nelder-Mead单纯形法算法思想,提出了一种新型混合算法,即DE-SFL-NM混合算法。利用无穷乘积的性质对DE-SFL-NM进行了收敛性分析,并得出依概率收敛结论。使用包含单、多模态的10个基准测试函数的数值实验结果进行比较,验证了该算法在收敛速度、求解精度及鲁棒性能方面的有效性和进步性。同时,应用DE-SFL-NM快速且精准地求解了3D视线跟踪系统中的角膜曲率中心。In order to deal with the nonlinear optimization problems of three-dimentional （3D） gaze tracking technology efficiently and make the system satisfy the requirements of real-time, accuracy and stability, this pa- per presents a hybrid algorithm, known as differential evolution-shuffled frog leaping-Nelder-Mead （DE-SFL- NM）, which is based on the differential evolution algorithm and takes full advantages of the shuffled frog lea- ping algorithm and the Nelder-Mead simple method. The convergence of DE-SFL-NM is discussed by exploring infinite products property, which arrives at the conclusion of probabilistic convergence. Numerical experiments are designed for verifying the effectiveness and advancement of the proposed algorithm in terms of convergence rate, precision and robustness on 10 benchmark functions including single mode and multi-modal. Meanwhile, the center of corneal curvature of 3D gaze tracking system can be accurately estimated by using DE-SFL-NM.

关 键 词：差分进化 混合蛙跳算法 Nelder-Mead单纯形法 依概率收敛 角膜曲率中心 

分 类 号：O224[理学—运筹学与控制论]