Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Applied Geodesy

Editor-in-Chief: Kahmen, Heribert / Rizos, Chris

CiteScore 2018: 1.61

SCImago Journal Rank (SJR) 2018: 0.532
Source Normalized Impact per Paper (SNIP) 2018: 1.064

See all formats and pricing
More options …
Ahead of print


Solution method for ill-conditioned problems based on a new improved fruit fly optimization algorithm

Qian Fan / Xiaolin MengORCID iD: https://orcid.org/0000-0003-2440-8054 / Chengquan Xu / Jiayong Yu
Published Online: 2019-11-08 | DOI: https://doi.org/10.1515/jag-2019-0025


Based on deeply analysis for optimization process of basic fruit fly optimization algorithm (FOA), a new improved FOA (IFOA) method is proposed, which modifies random search direction, increases the adjustment coefficient of search radius, and establishes a multi-sub-population solution mechanism. The proposed method can process the nonlinear objective function that has non-zero and non-negative extreme points. In the paper, IFOA method is applied to ill-conditioned problem solution in the field of surveying data processing. Application of the proposed method on two practical examples show that solution accuracy of IFOA is superior to that of three well-known intelligent optimization algorithms and two existing improved FOA methods, and it is also better than truncated singular value decomposition method and ridge estimation method. In addition, compared with intelligent search method represented by particle swarm optimization algorithm, The IFOA method has the advantages of less parameter settings, simple optimization process and easy program implementation. So, IFOA method is feasible, effective and practical in solving ill-conditioned problems.

Keywords: ill-conditioned problem solution; improved fruit fly optimization algorithm; random search direction; multi-sub-population; particle swarm optimization


  • [1]

    Hemmerle, W.J., & Brantle, T.F. 1978. Explicit and Constrained Generalized Ridge Estimation. Technometrics, 20, 109–120.CrossrefGoogle Scholar

  • [2]

    Hu, H.C. 2005. Ridge estimation of a semiparametric regression model. J Comput Appl Math, 176, 215–222.CrossrefGoogle Scholar

  • [3]

    Hansen, P.C. 1990. Truncated Singular Value Decomposition Solutions to Discrete Ill-Posed Problems with Ill-Determined Numerical Rank. Siam J Sci Stat Comp, 11, 503–518.CrossrefGoogle Scholar

  • [4]

    Hansen, P.C., Sekii, T., & Shibahashi, H. 1992. The Modified Truncated Svd Method for Regularization in General-Form. Siam J Sci Stat Comp, 13, 1142–1150.CrossrefGoogle Scholar

  • [5]

    Xu, P.L. 1998. Truncated SVD methods for discrete linear ill-posed problems. Geophys J Int, 135, 505–514.CrossrefGoogle Scholar

  • [6]

    Hanke, M., & Groetsch, C.W. 1998. Nonstationary iterated Tikhonov regularization. J Optimiz Theory App, 98, 37–53.CrossrefGoogle Scholar

  • [7]

    Hansen, P.C. 2007. Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems. Numerical algorithms, 46, 189–194.Google Scholar

  • [8]

    Tang, K.S., Man, K.F., Kwong, S., & He, Q. 1996. Genetic algorithms and their applications. Ieee Signal Proc Mag, 13, 22–37.CrossrefGoogle Scholar

  • [9]

    Zeng, Q.Y., & Ou, J.K. 2003. Study on Application of Genetic Algorithms In Solving Ill-conditioned Equations. Journal of Geodesy and Geodynamics, 23, 93–97.Google Scholar

  • [10]

    Chen, S., Wu, Y., & Luk, B.L. 1999. Combined genetic algorithm optimization and regularized orthogonal least squares learning for radial basis function networks. IEEE Trans Neural Netw, 10, 1239–1243.CrossrefGoogle Scholar

  • [11]

    Lee, S. 2017. Multi-parameter optimization of cold energy recovery in cascade Rankine cycle for LNG regasification using genetic algorithm. Energy, 118, 776–782.Web of ScienceCrossrefGoogle Scholar

  • [12]

    Trelea, I.C. 2003. The particle swarm optimization algorithm: convergence analysis and parameter selection. Inform Process Lett, 85, 317–325.Web of ScienceCrossrefGoogle Scholar

  • [13]

    Karaboga, D., & Basturk, B. 2007. A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. Journal of Global Optimization, 39, 459–471.CrossrefWeb of ScienceGoogle Scholar

  • [14]

    Mirjalili, S., Mirjalili, S.M., & Lewis, A. 2014. Grey Wolf Optimizer. Advances in Engineering Software, 69, 46–61.CrossrefWeb of ScienceGoogle Scholar

  • [15]

    Mirjalili, S., & Lewis, A. 2016. The Whale Optimization Algorithm. Advances in Engineering Software, 95, 51–67.Web of ScienceCrossrefGoogle Scholar

  • [16]

    Aryanezhad, M.B., & Hemati, M. 2008. A new genetic algorithm for solving nonconvex nonlinear programming problems. Appl Math Comput, 199, 186–194.Web of ScienceGoogle Scholar

  • [17]

    Jain, A., & Chaudhari, N.S. 2017. An Improved Genetic Algorithm for Developing Deterministic OTP Key Generator. Complexity, 2017.Web of ScienceGoogle Scholar

  • [18]

    Ali, K.B., Telmoudi, A.J., & Gattoufi, S., 2018. An Improved Genetic Algorithm with Local Search for Solving the DJSSP with New Dynamic Events, 2018 IEEE 23rd International Conference on Emerging Technologies and Factory Automation (ETFA). IEEE, pp. 1137–1144.Google Scholar

  • [19]

    Wang, J., Zhang, X.Z., & Zhang, Y. 2012. Research on Ambiguity Resolution of GPS Short Baseline by Using Improved Particle Swarm Optimization. Journal of Geodesy and Geodynamics, 32, 148–151.Google Scholar

  • [20]

    Wang, G.G., Gandomi, A.H., Yang, X.S., & Alavi, A.H. 2014. A novel improved accelerated particle swarm optimization algorithm for global numerical optimization. Eng Computation, 31, 1198–1220.Web of ScienceCrossrefGoogle Scholar

  • [21]

    Lu, Y.H., Liang, M.H., Ye, Z.Y., & Cao, L.C. 2015. Improved particle swarm optimization algorithm and its application in text feature selection. Appl Soft Comput, 35, 629–636.CrossrefWeb of ScienceGoogle Scholar

  • [22]

    Pan, W.T. 2012. A new Fruit Fly Optimization Algorithm: Taking the financial distress model as an example. Knowl-Based Syst, 26, 69–74.CrossrefWeb of ScienceGoogle Scholar

  • [23]

    Pan, W.T. 2014. Mixed modified fruit fly optimization algorithm with general regression neural network to build oil and gold prices forecasting model. Kybernetes, 43, 1053–1063.CrossrefWeb of ScienceGoogle Scholar

  • [24]

    Pan, Y.Y., & Shi, Y.D. 2017. A Grey Neural Network Model Optimized by Fruit Fly Optimization Algorithm for Short-term Traffic Forecasting. Eng Let, 25, 198–204.Google Scholar

  • [25]

    Lin, S.M. 2013. Analysis of service satisfaction in web auction logistics service using a combination of Fruit fly optimization algorithm and general regression neural network. Neural Comput Appl, 22, 783–791.CrossrefWeb of ScienceGoogle Scholar

  • [26]

    Hu, R., Wen, S.P., Zeng, Z.G., & Huang, T.W. 2017. A short-term power load forecasting model based on the generalized regression neural network with decreasing step fruit fly optimization algorithm. Neurocomputing, 221, 24–31.CrossrefWeb of ScienceGoogle Scholar

  • [27]

    Han, S.Z., Pan, W.T., Zhou, Y.Y., & Liu, Z.L. 2018. Construct the prediction model for China agricultural output value based on the optimization neural network of fruit fly optimization algorithm. Future Gener Comp Sy, 86, 663–669.CrossrefWeb of ScienceGoogle Scholar

  • [28]

    Mhudtongon, N., Phongcharoenpanich, C., & Kawdungta, S. 2015. Modified Fruit Fly Optimization Algorithm for Analysis of Large Antenna Array. Int J Antenn Propag, 2015.Web of ScienceGoogle Scholar

  • [29]

    He, Z.Z., Qi, H., Yao, Y.C., & Ruan, L.M. 2015. Inverse estimation of the particle size distribution using the Fruit Fly Optimization Algorithm. Appl Therm Eng, 88, 306–314.Web of ScienceCrossrefGoogle Scholar

  • [30]

    Sheng, W., & Bao, Y. 2013. Fruit fly optimization algorithm based fractional order fuzzy-PID controller for electronic throttle. Nonlinear Dynam, 73, 611–619.Web of ScienceCrossrefGoogle Scholar

  • [31]

    Zheng, X.L., Wang, L., & Wang, S.Y. 2014. A novel fruit fly optimization algorithm for the semiconductor final testing scheduling problem. Knowl-Based Syst, 57, 95–103.Web of ScienceCrossrefGoogle Scholar

  • [32]

    Shan, D., Cao, G.H., & Dong, H.J. 2013. LGMS-FOA: An Improved Fruit Fly Optimization Algorithm for Solving Optimization Problems. Math Probl Eng, 2013.Web of ScienceGoogle Scholar

  • [33]

    Pan, Q.K., Sang, H.Y., Duan, J.H., & Gao, L. 2014. An improved fruit fly optimization algorithm for continuous function optimization problems. Knowl-Based Syst, 62, 69–83.CrossrefWeb of ScienceGoogle Scholar

  • [34]

    Liu, X., Shi, Y., & Xu, J. 2017. Parameters Tuning Approach for Proportion Integration Differentiation Controller of Magnetorheological Fluids Brake Based on Improved Fruit Fly Optimization Algorithm. Symmetry, 9.Web of ScienceGoogle Scholar

  • [35]

    Wolpert, D.H., & Macready, W.G. 1997. No free lunch theorems for optimization. IEEE Trans on Evolutionary Computation, 1, 67–82.CrossrefGoogle Scholar

  • [36]

    Yuan, X.F., Dai, X.S., Zhao, J.Y., & He, Q. 2014. On a novel multi-swarm fruit fly optimization algorithm and its application. Appl Math Comput, 233, 260–271.Web of ScienceGoogle Scholar

About the article

Received: 2019-06-03

Accepted: 2019-10-23

Published Online: 2019-11-08

This paper is supported by National Natural Science Foundation of China (No. 41404008), The Science and Technology Program of Fuzhou (No. 2017-G-73), Open Foundation of Key Laboratory for Digital Land and Resources of Jiangxi Province (No. DLLJ201911), Guiding Project of Fujian Science and Technology Program (No. 2018Y0021).

Citation Information: Journal of Applied Geodesy, ISSN (Online) 1862-9024, ISSN (Print) 1862-9016, DOI: https://doi.org/10.1515/jag-2019-0025.

Export Citation

© 2019 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in