WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 22, 2023
Genetic Algorithm-Based Optimization Approach for Solving a Class of Inverse Problems with Tikhonov Regularization
Authors: ,
Abstract: In this paper, we are interested in solving the data completion problem for the Laplace equation. It consists to determine the missing data on the inaccessible part of the boundary from overspecified conditions in the accessible part. Knowing that this problem is severely ill-posed, we consider its formulation as an optimization problem using Tikhonov regularization. Then, we consider an optimization approach based on adapted Real Coded Genetic Algorithm (RCGA) to minimize the cost function and recover the missing data. The performed numerical simulations, with different domains, illustrate the accuracy and efficiency of the proposed method with an adequate regularization parameter, in addition to the good agreement between the numerical solutions and different noise level of the given data.
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Keywords: Inverse Problem, Tikhonov regularization , Genetic Algorithm, Data completion problem,
Optimization
Pages: 842-853
DOI: 10.37394/23206.2023.22.92