基于新拟牛顿方程的优化算法设计及应用  

Design and Application of Optimization Algorithm Based on New Quasi-Newton Equation

作　　者：易君君[1] 汪保[1] 颜倩倩[1] 

机构地区：[1]宁波工程学院,浙江宁波315211

出　　处：《宁波工程学院学报》2015年第1期12-18,共7页Journal of Ningbo University of Technology

摘　　要：通过四阶泰勒展开对拟牛顿方程进行修正,提出新拟牛顿方程。根据标准DFP及BFGS算法中Hessian矩阵(逆)的构造方法,给出对应的新拟牛顿方法,并结合0.618线性搜索编写出新拟牛顿算法的程序。三个标准测试函数数值试验结果显示,新拟牛顿算法的收敛效率比标准拟牛顿算法快。将新拟牛顿方法应用到实际问题,解决消防站选址问题,并进一步阐释新拟牛顿算法的优越性。A new quasi-Newton equation is derived by modifying usual quasi-Newton equation from a fourth order Taylor expansion. According to the method of structuring Hessian Matrix（inverse） of DFP algorithm and BFGS algorithm, a quasi-Newton method is presented with Goldstein line search. Some standard test functions are tested, and the numerical results show the advantages of the modified quasi-Newton algorithm（including modified DFP and modified BFGS algorithm）. Besides, the application of the new quasi-Newton method is discussed and the problem of choosing the best location of the fire station successfully solved.

关 键 词：新拟牛顿方程 DFP算法 BFGS算法 0.618线性搜索 

分 类 号：O224[理学—运筹学与控制论]