改进的果蝇优化与Tikhonov正则化相结合的病态问题稳健解法

doi:10.11947/j.AGCS.2016.20150606

测绘学报 ›› 2016, Vol. 45 ›› Issue (6): 670-676.doi: 10.11947/j.AGCS.2016.20150606

改进的果蝇优化与Tikhonov正则化相结合的病态问题稳健解法

范千^1,2,3, 张宁⁴

1. 福州大学土木工程学院, 福建福州 350108;
2. 桂林理工大学广西空间信息与测绘重点实验室, 广西桂林 541004;
3. 精密工程与工业测量国家测绘地理信息局重点实验室, 湖北武汉 430079;
4. 闽江学院物理学与电子信息工程系, 福建福州 350108

收稿日期:2015-12-04 修回日期:2016-02-03 出版日期:2016-06-20 发布日期:2016-06-29
作者简介:范千(1981-),男,博士,副教授,研究方向为变形监测数据处理及GNSS定位技术。E-mail:fanqian1981@163.com
基金资助:
国家自然科学基金(41404008);广西空间信息与测绘重点实验室开放基金(桂科能1103108-21);精密工程与工业测量国家测绘地理信息局重点实验室开放基金(PF2015-12);江西数字国土重点实验室开放基金(DLLJ201408);福州大学科技发展基金(2014-XQ-33)

Ill-conditioned Problems Robust Solution of Improved Fruit Fly Optimization Algorithm Combining with Tikhonov Regularization Method

FAN Qian^1,2,3, ZHANG Ning⁴

1. College of Civil Engineering, Fuzhou University, Fuzhou 350108, China;
2. Guangxi Key Laboratory of Spatial Information and Geomatic, Guilin Uninversity of Technology, Guilin 541004, China;
3. Key Laboratory of Precise Engineering and Industry Surveying of National Administration of Surveying, Mapping and Geoinformation, Wuhan 430079, China;
4. Department of Physics & Electronic Information, Minjiang University, Fuzhou 350108, China

Received:2015-12-04 Revised:2016-02-03 Online:2016-06-20 Published:2016-06-29
Supported by:
National Natural Science Foundation of China(No.41404008);Open Foundation of Guangxi Key Laboratory of Spatial Information and Geomatics (No.1103108-21);Open Foundation of Key Laboratory of Precise Engineering and Industry Surveying of National Administration of Surveying, Mapping and Geoinformation (No.PF2015-12);Open Foundation of Jiangxi Province Key Lab for Digital Land(DLLJ201408);Science and Technology Development Foundation of Fuzhou University(No.2014-XQ-33)

摘要/Abstract

摘要： 在对基本果蝇优化算法的优化流程进行深入分析的基础上,通过改变其随机搜索方向与增加搜索半径调整系数,给出了一种改进的果蝇优化算法(IFOA)。并在IFOA算法的目标函数中引入正则化项,提出了将IFOA算法与Tikhonov正则化方法进行结合以进行病态问题解算的方法。通过实例分析表明:该方法的解算精度要优于遗传算法和单一的Tikhonov正则化方法;在观测值含有粗差时,使用最小二乘法进行求解,其结果与真值的偏差会迅速增大,而此时本文方法的解算结果具有一定的稳健性。与以遗传算法为代表的智能搜索方法相比,本文方法具有参数设置少、计算速度快、寻优过程简单等特点,在病态问题解算中更具有实用性。

关键词: 果蝇优化算法, 随机搜索方向, Tikhonov正则化方法, 病态问题解算, 粗差

Abstract: Based on deeply analysis for optimization process of basic fruit fly optimization algorithm, an improved fruit fly optimization (IFOA) algorithm is proposed via changing random search direction and adding to a tuning coefficient of search radius. Moreover, through introducing the regularization term of objective function in IFOA algorithm, a new method that IFOA algorithm is combined with Tikhonov regularization method is put forward in order to resolving ill-conditioned problems. Analysis results of practical example show that solution accuracy of new method is superior to genetic algorithm and single Tikhonov regularization method. When observation contains gross errors, the deviation between the results and the true value will increase rapidly using least square method to solve ill-conditioned problems. At this time, the new method has strong robustness. Compared with intelligent search method represented by genetic algorithm, new method has the characteristics of less parameter, fast calculation speed, simple optimization process. It is more practical in ill-conditioned problems solution.

Key words: fruit fly optimization, random search direction, Tikhonov regularization method, ill-conditioned problems solution, gross error

中图分类号:

P207

范千, 张宁. 改进的果蝇优化与Tikhonov正则化相结合的病态问题稳健解法[J]. 测绘学报, 2016, 45(6): 670-676.

FAN Qian, ZHANG Ning. Ill-conditioned Problems Robust Solution of Improved Fruit Fly Optimization Algorithm Combining with Tikhonov Regularization Method[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(6): 670-676.

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改进的果蝇优化与Tikhonov正则化相结合的病态问题稳健解法

Ill-conditioned Problems Robust Solution of Improved Fruit Fly Optimization Algorithm Combining with Tikhonov Regularization Method

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