欧拉型光线寻优算法  

Eulerian Light ray optimization algorithm

作　　者：沈继红[1] 李加莲[2] 李焱[2] 

机构地区：[1]哈尔滨工程大学理学院,黑龙江哈尔滨150001 [2]哈尔滨工程大学自动化学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2012年第7期929-934,共6页Journal of Harbin Engineering University

基　　金：黑龙江省自然科学基金资助项目(F200931)

摘　　要：针对光线寻优算法的收敛性及其推广到高维收敛速度慢的问题,利用变分法和微分方程理论,对二维连续可导介质中的光线方程欧拉数值解法与光线寻优算法迭代公式的关系进行了研究.在光线寻优算法迭代公式中加入一项来改进算法,不仅使得精度提高一阶,而且加快了收敛速度,同时也为光线寻优算法的收敛性证明提供了新思路.6个标准测试函数的仿真结果表明:与光线寻优算法、保留精英遗传算法、标准粒子群算法相比,改进算法收敛速度较快,收敛成功率较高,其求解Rosenbrock的成功率高达98%,远高于保留精英遗传算法和标准粒子群算法.In order to solve the problems of convergence in a light ray optimization algorithm as well as its slow convergence speed when extending to higher dimensional space, the relationship between the Euler method of ray equations of two-dimensional continuous derivable media and the iterative formula of light ray optimization were studied using the variational method and differential equation theory. The accuracy was improved one order and a higher convergence speed was obtained hy adding a term to improve the iterative formula of a light ray optimization algorithm, and an idea for convergence proof of light ray optimization algorithm was also obtained. The simulation resuits of six benchmark functions show that the improved algorithm has a higher convergence speed and success rate than light ray optimization algorithm, elitist genetic algorithm, and standard particle swarm algorithm. The success rate of the improved algorithm for solving Rosenbrock function is 98%, which is much higher than that of elite genetic algorithm and standard particle swarm algorithm.

关 键 词：光线方程 欧拉法 光线寻优算法 函数优化 收敛速度 

分 类 号：O224[理学—运筹学与控制论]