Abstract
Gene expression programming (GEP) is a mathematical model that can be used to optimize complex systems. It has not only limited to specific problems, but also has good robustness in solving various problems, which has been applied in many disciplines such as biochemistry, physics, and mathematics. In this paper, the IGEP algorithm was proposed based on the optimization of GEP algorithm, and the algorithm for solving the inverse problem of parameter identification of partial differential equations based on this algorithm was studied. The structure and steps of GEP algorithm were analyzed firstly, and the GEP (IGEP) based on improved mutation operator was proposed. The algorithm advantage of IGEP for solving the inverse problem of partial differential equations was discussed. In addition, the simulation experiments were carried out to prove the feasibility and superiority of the proposed algorithm.
Similar content being viewed by others
Change history
01 December 2022
This article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1007/s10586-022-03882-y
References
Chen, Y., Li, K., Chen, Z., et al.: Restricted gene expression programming: a new approach for parameter identification inverse problems of partial differential equation. Soft. Comput. 21(10), 1–13 (2017)
Guo, P., Wu, X., Wang, L.B.: Multiple soliton solutions for the variant Boussinesq equations. Adv. Differ. Equ. 2015(1), 37 (2015)
Denisov, A.M.: Inverse problem for a quasilinear system of partial differential equations with a nonlocal boundary condition containing a retarded argument. Differ. Equ. 51(9), 1126–1136 (2015)
Pintarelli, M.B.: Linear partial differential equations of first order as bi-dimensional inverse moments problem. Appl. Math. 6(6), 979–989 (2015)
Denisov, A.M.: Integral equations related to the study of an inverse coefficient problem for a system of partial differential equations. Differ. Equ. 52(9), 1142–1149 (2016)
Zhang, W., Sun, Z., Wang, Z., et al.: A coupled model of partial differential equations for uranium ores heap leaching and its parameters identification. J. Inverse Ill-posed Probl. 24(1), 41–50 (2015)
Pintarelli, M.B.: Parabolic partial differential equations as inverse moments problem. Appl. Math. 07(1), 77–99 (2017)
Liu, T.: A wavelet multiscale-homotopy method for the parameter identification problem of partial differential equations. Comput. Math. Appl. 71(7), 1519–1523 (2016)
Groh, A., Kohr, H., Louis, A.K.: Numerical rate function determination in partial differential equations modeling cell population dynamics. J. Math. Biol. 74(3), 1–33 (2016)
Gepreel, K.A., Nofal, T.A.: Extended trial equation method for nonlinear partial differential equations. Zeitschrift Für Naturforschung A 70(4), 269–279 (2015)
Acknowledgements
The study was supported by “Science and Technology Project of China Railway Corporation, China (Grant No. 1341324011)” and “National key innovation prediction project of Mudanjiang Normal University (Grant No. GY201205)”.
Author information
Authors and Affiliations
Corresponding author
Additional information
This article has been retracted. Please see the retraction notice for more detail: https://doi.org/10.1007/s10586-022-03882-y
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Baolin, F. RETRACTED ARTICLE: Solving algorithm for inverse problem of partial differential equation parameter identification based on IGEP. Cluster Comput 22 (Suppl 2), 3935–3941 (2019). https://doi.org/10.1007/s10586-018-2543-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10586-018-2543-y