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

doi:10.11947/j.AGCS.2016.20150606

Acta Geodaetica et Cartographica Sinica ›› 2016, Vol. 45 ›› Issue (6): 670-676.doi: 10.11947/j.AGCS.2016.20150606

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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)

Abstract

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

CLC Number:

P207

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.

References

[1] HANSEN P C. Truncated Singular Value Decomposition Solutions to Discrete Ill-posed Problems with Ill-determined Numerical Rank[J]. SIAM Journal on Scientific and Statistical Computing, 1990, 11(3):503-518.
[2] HANKE M, GROETSCH C W. Nonstationary Iterated Tikhonov Regularization[J]. Journal of Optimization Theory and Applications, 1998, 98(1):37-53.
[3] 曾群意, 欧吉坤. 用遗传算法解算病态方程[J]. 大地测量学与地球动力学, 2003, 23(3):93-97. ZENG Qunyi, OU Jikun. Study on Application of Genetic Algorithms in Solving Ill-conditioned Equations[J]. Journal of Geodesy and Geodynamics, 2003, 23(3):93-97.
[4] 王建, 张献州, 张勇. 改进粒子群算法求解GPS短基线整周模糊度的研究[J]. 大地测量学与地球动力学, 2012, 32(4):148-151. WANG Jian, ZHANG Xianzhou, ZHANG Yong. Research on Ambiguity Resolution of GPS Short Baseline by Using Improved Particle Swarm Optimization[J]. Journal of Geodesy and Geodynamics, 2012, 32(4):148-151.
[5] 梁兴建, 詹志辉. 基于双模式变异策略的改进遗传算法[J]. 山东大学学报(工学版), 2014, 44(6):1-7. LIANG Xingjian, ZHAN Zhihui. Improved Genetic Algorithm Based on the Dual-mode Mutation Strategy[J]. Journal of Shandong University (Engineering Science), 2014, 44(6):1-7.
[6] 赵新超, 刘子阳. 差分和扰动混合的多策略粒子群优化算法[J]. 计算机科学与探索, 2014, 8(2):218-225. ZHAO Xinchao, LIU Ziyang. Hybrid Particle Swarm Optimization with Differential and Perturbation[J]. Journal of Frontiers of Computer Science and Technology, 2014, 8(2):218-225.
[7] 隋立芬. 抗差岭估计原理及其应用[J]. 测绘通报, 1994(1):9-12. SUI Lifen. The Principle of Robust Rridge Estimation and Its Applications in Geodetic Adjustments[J]. Bulletin of Surveying and Mapping, 1994(1):9-12.
[8] 归庆明, 黄维彬, 张建军. 抗差泛岭估计[J]. 测绘学报, 1998, 27(3):211-216. GUI Qingming, HUANG Weibin, ZHANG Jianjun. Robust Universal Ridge Estimation[J]. Acta Geodaetica et Cartographica Sinica, 1998, 27(3):211-216.
[9] 刘雁雨, 隋立芬, 刘青利. 抗差岭型组合主成分估计及误差影响[J]. 测绘科学, 2004, 29(2):50-52. LIU Yanyu, SUI Lifen, LIU Qingli. Robust Ridge Combined Principal Components Estimation and Influence of Errors[J]. Science of Surveying and Mapping, 2004, 29(2):50-52.
[10] 何然, 黄思训, 周晨腾, 等. 遗传算法结合正则化方法反演海洋大气波导[J] 物理学报, 2012, 61(4):504-511. HE Ran, HUANG Sixun, ZHOU Chenteng, et al. Genetic Algorithm with Regularization Method to Retrieve Ocean Atmosphere Duct[J]. Acta Physica Sinica, 2012, 61(4):504-511.
[11] 崔希璋, 於宗俦, 陶本藻, 等. 广义测量平差[M]. 第2版. 武汉:武汉大学出版社, 2009. CUI Xizhang, YU Zongchou, TAO Benzao, et al. Generalized Surveying Adjustment[M]. 2nd ed. Wuhan:Wuhan University Press, 2009.
[12] HANSEN P C, O'LEARY D P. The Use of L-curve in the Regularization of Discrete III-posed Problems[J]. SIAM Journal on Scientific Computing, 1993, 14(6):1487-1503.
[13] HANSEN P C, JENSEN T K, RODRIGUEZ G. An Adaptive Pruning Algorithm for the Discrete L-curve Criterion[J]. Journal of Computational and Applied Mathematics, 2007, 198(2):483-492.
[14] GOLUB G H, HEATH M, WAHBA G. Generalized Cross-validation as a Method for Choosing a Good Ridge Parameter[J]. Technometrics, 1979, 21(2):215-223.
[15] 王振杰. 大地测量中不适定问题的正则化解法研究[D]. 武汉:中国科学院测量与地球物理研究所, 2003. WANG Zhenjie. Research on the Regularization Solutions of Ill-posed Problems in Geodesy[D]. Wuhan:Institute of Geodesy and Geophysics, CAS, 2003.
[16] PAN W T. A New Fruit Fly Optimization Algorithm:Taking the Financial Distress Model as an Example[J]. Knowledge-based Systems, 2012, 26:69-74.
[17] SHAN Dan, CAO Guohua, DONG Hongjiang. LGMS-FOA:An Improved Fruit Fly Optimization Algorithm for Solving Optimization Problems[J]. Mathematical Problems in Engineering, 2013, 2013:108768.
[18] PAN Quanke, SANG Hongyan, DUAN Junhua, et al. An Improved Fruit Fly Optimization Algorithm for Continuous Function Optimization Problems[J]. Knowledge-based Systems, 2014, 62:69-83.
[19] YUAN Xiaofang, DAI Xiangshan, ZHAO Jingyi, et al. On a Novel Multi-swarm Fruit Fly Optimization Algorithm and Its Application[J]. Applied Mathematics and Computation, 2014, 233:260-271.
[20] 雷英杰. MATLAB遗传算法工具箱及应用[M]. 西安:西安电子科技大学出版社, 2005. LEI Yingjie. MATLAB Genetic Algorithm Toolbox and Its Application[M]. Xi'an:Xidian University Press, 2005.
[21] 龚循强, 李志林. 稳健加权总体最小二乘法[J]. 测绘学报, 2014, 43(9):888-894, 901. DOI:10.13485/j.cnki.11-2089.2014.0140. GONG Xunqiang, LI Zhilin. A Robust Weighted Total Least Squares Method[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(9):888-894, 901. DOI:10.13485/j.cnki.11-2089.2014.0140.
[22] GUI Q, LI X, GONG Y, et al. A Bayesian Unmasking Method for Locating Multiple Gross Errors Based on Posterior Probabilities of Classification Variables[J]. Journal of Geodesy, 2011, 85(4):191-203.

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

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