Genetic programming for the two-dimensional boundary reconstruction problem

Ігор Борачок

Анотація


We consider the application of the genetic programming for solving a non-linear ill-posed problem, namely for the reconstruction of the inner boundary of the annular planar domain from the known measurement data of the harmonic function. A candidate solution of the genetic algorithm is presented in a tree form, for which the fitness function is computed by solving the mixed boundary value problem by the method of boundary integral equations. Algorithm configurations and results of numerical experiments for exact and noisy input data are given.

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Baravdish G. An iterative method for the Cauchy problem for second-order elliptic equations / G. Baravdish, I. Borachok, R. Chapko, B.T. Johansson, M. Slodička // International Journal of Mechanical Sciences. — 2018.— Vol. 142. — P. 216—223.

Cakoni F. Integral equations for inverse problems in corrosion detection from partial Cauchy data / F. Cakoni, R. Kress // Inverse Probl. Imaging. — 2007.— Vol. 1. — P. 229—245.

Chapko R. On the non-linear integral equation approaches for the boundary reconstruction in double-connected planar domains / R. Chapko, O. Ivanyshyn Yaman, T. Kanafotskyi // Journal of Numerical and Applied Mathematics. — 2016.— Vol. 2 (122). — P. 7—20.

Chapko R. On a nonlinear integral equation approach for the surface reconstruction in semi-infinite-layered domains / R. Chapko, O. Ivanyshyn, O. Protsyuk // Inverse Problems in Science and Engineering. — 2013.— Vol. 21. — P. 547—561.

Chapko R. On the use of an integral equation approach for the numerical solution of a Cauchy problem for Laplace equation in a doubly connected planar domain / R. Chapko, B.T. Johansson, Y. Savka // Inverse Problems in Science and Engineering. — 2013.— Vol. 22. — P. 130—149.

Chapko R. On the Non-Linear Integral Equation Approach for an Inverse Boundary Value Problem for the Heat Equation / R. Chapko, L. Mindrinos // Journal of Engineering Mathematics. — 2019.— Vol. 119. — P. 255—268.

Eckel H. Numerical study of an evolutionary algorithm for electrical impedance tomography, Dissertation / H. Eckel. — Göttingen, 2008.

Eckel H. Non-linear integral equations for the complete electrode model in inverse impedance tomography / H. Eckel, R. Kress // Applicable Analysis. — 2008.— Vol. 87. — P. 1267—1288.

Ivanyshyn O. Nonlinear integral equation methods for the reconstruction of an acoustically sound-soft obstacle / O. Ivanyshyn, B.T. Johansson // J. Integral Equations Appl. — 2007.— Vol. 19. — P. 289—308.

Ivanyshyn O. Nonlinear integral equations for solving inverse boundary value problems for inclusions and cracks / O. Ivanyshyn, R. Kress // J. Integral Equations Appl. — 2006.— Vol. 18. — P. 13—38.

Goldberg D.E. Genetic Algorithm in Search, Optimisation and Machine Learning / D.E. Goldberg. — Addison-Wesley, Reading, MA, 1989.

Holland J.H. Adaptation in Natural and Artificial System / J.H. Holland. — University of Michigan Press, Ann Arbor, 1975.

Kress R. Linear Integral Equations, 2nd. ed. / R. Kress. — Springer-Verlag, Berlin Heidelberg New York, 1999.

Kress R. Nonlinear integral equations and the iterative solution for an inverse boundary value problem / R. Kress, W. Rundell // Inv. Probl. — 2005.— Vol. 21. — P. 1207—1223.

Luke S. Issues in Scaling Genetic Programming: Breeding Strategies, Tree Generation, and Code Bloat / S. Luke. — [Dissertation] University of Maryland, 2000.

McLean W. Strongly Elliptic Systems and Boundary Integral Operators, Cambridge University Press / W. McLean. — Cambridge, 2000.

Mera N.S. On the use of Genetic Algorithms for Solving Ill-Posed Problems / N.S. Mera, L. Elliott, D.B. Ingham // Inverse Problems in Engineering. — 2010.— Vol. 11. — P. 105—121.

Michalewicz Z. Genetic Algorithms + Data Structures = Evolution Programs, 3rd ed. / Z. Michalewicz. — Springer-Verlag, Berlin, 1996.

Pourgholi R. Solving an inverse heat conduction problem using genetic algorithm: Sequential and multi-core parallelization approach / R. Pourgholi, H.L. Dana, S.H. Tabasi // Applied Mathematical Modelling. — 2014.— Vol. 38. — P. 1948—1958.

Shahnazari M.R. Solving inverse heat conduction problems by using Tikhonov regularization in combination with the genetic algorithm / M.R. Shahnazari, A. RoohiShali, A. Saberi // Inv. Probl. — 2021.— Vol. 3. — P. 60—66.




DOI: http://dx.doi.org/10.30970/vam.2023.31.11848

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